Theories of Consciousness: A Meta-Comparative Analysis

Bridge from the previous section

In the States sections we examined how the $\Gamma$-profile determines normal and pathological states. Now — context: how does the UHM formalism relate to 42 alternative theories of consciousness? Each of them is a projection of $\Gamma$ onto a specific aspect: integration (IIT), access (GWT), reflection (HOT), prediction error (FEP), projective spatial geometry (PWT).

On notation

In this document:

• $\Gamma$ — coherence matrix
• $\varphi$ — self-modelling operator
• $\Phi$ — integration measure
• $R$ — reflection measure
• $\mathcal{R}[\Gamma, E]$ — regenerative term
• $\rho_E$ — reduced density matrix of the Interiority dimension
• $\mathbf{Hol}$ — Holon category
• [T] — theorem, [C] — conditional theorem, [I] — interpretation. Details: status registry

Introduction: 42 theories and one problem

Consciousness science is a young field. Although philosophers have discussed the nature of consciousness since Descartes (1641), systematic scientific theories appeared only in the 1980–2000s. By the mid-2020s there are more than thirty — from neurobiological (NCC, RPT, DIT) to mathematical (IIT, FEP), philosophical (panpsychism, Russellian monism), wave-based (Pribram holonomic, CEMI, PWT), category-theoretic (Tsuchiya–Saigo, Kleiner–Tull) and quantum-informational (Tegmark, D'Ariano–Faggin, Fields–Glazebrook–Levin).

All these theories try to answer one question: what is consciousness and why does it exist? But each approaches the question from its own side, focusing on one aspect: information integration (IIT), recurrent processing (RPT), predictive coding (PP), self-modelling (AST), metarepresentation (HOT), or the undistorted geometry of phenomenal space (PWT).

CC claims that each of these theories is a projection of a unified formalism onto a specific aspect. IIT projects $\Gamma$ onto integration ($\Phi$), GWT onto the access threshold ($P > 2/7$), HOT onto reflection ($R \geq 1/3$), PP onto prediction error ($\sigma_k$), PWT onto the projective spatial sector $\{A,S,D\} \to \Sigma^3$. None covers everything; CC claims to unify them.

This is a serious claim, and it demands careful analysis. In this document we:

1. Examine each of the 42 theories: its history, central idea, and formal core
2. Show the precise mapping into the CC formalism (functor)
3. Honestly indicate what each theory does better than CC
4. Close with a master table and assessment of completeness

Document navigation

Theories are grouped by type:

Group	Theories	Sections
Cybernetic	Autopoiesis, FEP, PP, PCT	§1-3, 6, 14, 18
Informational	IIT, GWT, CEMI	§2, 4, 17
Reflexive	HOT, AST, RPT	§5-6, 10
Neurobiological	TNGS, ART, DIT, OA, NCC	§11-12, 16, 19-20
Somatic/enactive	Enactivism, SMCT, Damasio, Seth	§13-14, 27-28
Quantum	Quantum Cognition, Orch-OR, Quantum Mind	§7-8, 22
Russian school	Anokhin (P.K.), Shvyrkov, Ivanitsky, Allakhverdov	§32-35
Philosophical	Russellian monism, Dennett	§24-25
Affective	Panksepp, Solms, Merker	§26, 29-30
Wave / field	Holonomic Brain (Pribram), CEMI, PWT (Worden)	§31, 17, 36
Mathematical / categorical	Category theory of qualia (Tsuchiya, Saigo); formal IIT and process theories (Kleiner, Tull, Signorelli, Coecke, Prentner)	§37–38
Quantum-informational	Minimal physicalism and quantum FEP (Fields, Glazebrook, Levin); perceptronium (Tegmark); quantum-information panpsychism (D'Ariano, Faggin)	§39–41
Physics of observers	Observer theory (Wolfram)	§42

The formal critiques that bind every theory of this kind — UHM's own consciousness predicate included — are collected right after §9, in Formal critiques that bind UHM's consciousness predicate.

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1. Autopoiesis (Maturana, Varela)

Focus: Self-production, operational closure.

Source: Maturana H., Varela F. «Autopoiesis and Cognition» (1980).

Creators and history

Humberto Maturana (1928–2021) — Chilean biologist and neurobiologist. In 1968, while working on the problem of colour vision in pigeons, Maturana arrived at a radical conclusion: the nervous system does not "represent" the world — it creates its own reality through its own operations. Together with his student Francisco Varela (1946–2001) he introduced the concept of autopoiesis — self-production — in 1972.

The context was political: Chile in the era of Allende, then Pinochet. Maturana and Varela developed the theory under conditions of intellectual isolation from Anglo-American science. Their book Autopoiesis and Cognition (1980) became a classic, but received wide recognition only in the 1990s — through its influence on sociologist Niklas Luhmann and philosopher Evan Thompson.

Key concepts:

• Autopoietic organisation — a network of processes producing components that reproduce this network
• Operational closure — the system is defined through its internal operations
• Structural coupling — interaction with the environment while preserving identity

Mapping in CC:

Autopoiesis (Maturana, Varela)	CC
Autopoietic organisation	(AP): $\varphi(\Gamma^*) = \Gamma^*$
Network components	Dimensions $A$, $S$, $D$, $L$
Structural coupling	Holon's interaction with environment $E$
Operational closure	Structural invariance under viability
—	L-unification: $L_k = \sqrt{\chi_{S_k}}$

Added:

• Operational closure (fixed point of $\varphi$)
• Distinction between organisation/structure

What is lost:

• Phenomenology (E-dimension as fundamental)
• Quantum foundation (QG)
• Formal dynamics (no analogue of the evolution equation)
• Logical origin of dynamics (L-unification in UHM derives dissipation from the structure of Ω)

2. Integrated Information Theory (IIT)

Focus: Information integration as a measure of consciousness.

Source: Tononi G. «Integrated Information Theory» (IIT 3.0: 2014, IIT 4.0: 2023).

Creators and history

Giulio Tononi (b. 1960) — Italian-American neurobiologist, professor at the University of Wisconsin-Madison. He began as a student of Gerald Edelman (creator of TNGS, see §11) and co-author of the concept of "neural complexity". In 2004 Tononi proposed IIT as an independent theory that split from TNGS. The key idea: consciousness is identical to a specific mathematical structure — the cause-effect structure of a system with maximal integrated information.

IIT has gone through four versions: IIT 1.0 (2004), 2.0 (2008), 3.0 (2014), and 4.0 (2023). Each added formal rigour and introduced new postulates. IIT 4.0 is the most complete version, defining $\Phi$ through the "unfolded" cause-effect structure.

IIT became one of the most discussed theories of consciousness and was subjected to experimental testing in the COGITATE project (Templeton Foundation) — the first "adversarial collaboration" in history between competing theories of consciousness (IIT vs GWT).

Key concepts:

• $\Phi^{\mathrm{IIT}}$ — integrated information of the system
• IIT postulates — existence, composition, information, integration, exclusion
• Q-shape (qualia-space) — geometry of experience

Conceptual correspondences (not formal isomorphisms):

Important distinction

$\Phi^{\mathrm{IIT}}$ and $\Phi(\Gamma)$ are different mathematical objects:

• $\Phi^{\mathrm{IIT}}$ is computed through the minimum information partition (NP-hard task)
• $\Phi(\Gamma)$ in CC is a simple ratio of Frobenius norms

CC defines its own integration measure, inspired by IIT ideas but not identical to $\Phi^{\mathrm{IIT}}$.

IIT (Tononi)	Conceptual analogue in CC
$\Phi^{\mathrm{IIT}}$ (MIP-based)	$\Phi(\Gamma)$ (norm-based)
Mechanisms and states	Holon $\mathbb{H}$
Q-shape (cause-effect structure)	Phenomenal geometry (projective space)
Integration postulate	U-dimension
Exclusion postulate	Uniqueness of the fixed point $\Gamma^*$

Added:

• Formal integration measure
• Connection to consciousness
• Axioms linking structure and experience

What is lost:

• Dynamics (unitary, dissipative, regenerative terms)
• Viability
• Self-modelling ($\varphi$)
• Quantum foundation (QG) — absent from Tononi's IIT 3.0 and 4.0, but not from the IIT programme at large: quantum versions of IIT exist (Zanardi, Tomka & Campos Venuti 2018; Kleiner & Tull 2021 — see §38)

3. Free Energy Principle (FEP)

Focus: Minimisation of variational free energy.

Source: Friston K. «The free-energy principle: a unified brain theory?» (2010); «Active inference and learning» (2016).

Creators and history

Karl Friston (b. 1959) — British neurobiologist, professor at University College London (UCL), creator of Statistical Parametric Mapping (SPM) — the standard tool for fMRI analysis. Friston is the most-cited neurobiologist in the world (h-index > 250). In 2006–2010 he proposed FEP — a principle unifying perception, action, learning, and evolution under a single mathematical roof: minimisation of variational free energy $F$.

FEP grew from the Bayesian approach to the brain (Helmholtz, Dayan, Hinton) and the thermodynamics of non-equilibrium systems. Friston claims that FEP is not merely a theory of the brain but a principle of existence: any system that exists (does not disintegrate) necessarily minimises free energy. This is the most ambitious claim in modern neuroscience — and the most controversial.

Key concepts:

• Variational free energy $F$ — upper bound on surprise
• Markov blanket — statistical boundary separating internal from external states
• Active inference — actions as minimisation of expected free energy

Retracted (2026-09-25): "FEP is the classical limit of UHM"

"Theorem 4.2: Friston's FEP is the classical limit of the variational characterisation of φ in UHM … This is a strictly proven correspondence, not a conceptual analogy." Retracted with the FEP derivation (Theorems 3.1, 4.2 (iii)–(iv) and 4.3; registry row 39e [✗]). The UHM functional is a cross-entropy, $S_{vN}(\rho) + D_{KL}(\rho \,\|\, \Gamma) = -\mathrm{Tr}(\rho\log\Gamma)$, linear in $\rho$ and minimised by the projection onto the top eigenvector of $\Gamma$, not by $\varphi$; on diagonal states it becomes $H(q) + D_{KL}(q \,\|\, p) = -\sum_i q_i \ln p_i$ — for $p = (0.7, 0.2, 0.1)$ it is $0.802$ at $q = p$ and $0.357$ at the point mass — and this is not Friston's variational free energy. What stands: that identity on diagonal states (Theorem 4.1) and Theorem 5.1 ($S_{\mathrm{spec}} = S_{vN}$ on density matrices). Whether Friston's free energy arises as a limit of UHM is an open research programme [Pr].

Formal correspondences:

FEP (Friston)	Formal analogue in CC	Status
Free energy $F = \langle E \rangle_q - H(q)$	$\mathcal{F} = S_{vN}(\psi(\Gamma)) + D_{KL}(\psi(\Gamma) \| \Gamma)$ — a cross-entropy, not $F$	Theorem 4.2 retracted [✗] (FEP derivation)
Markov blanket	Boundary of Holon — dimension A	Conceptual
Internal states	Coherence matrix $\Gamma$	Formal
Active inference	Regenerative term $\mathcal{R}[\Gamma, E]$	Conceptual
Generative model	Self-modelling operator $\varphi$	Theorem 3.1 retracted [✗] (row 39e: $\varphi$ is not the minimiser) — FEP derivation
Sensory states	Interaction with environment through O-dimension	Conceptual

Key result: In UHM φ is defined categorically (adjunction $\varphi \dashv i$). "The variational form $\varphi = \arg\min[S_{vN} + D_{KL}]$ is a proven theorem (Theorem 3.1)." Retracted (2026-09-25, registry row 39e [✗]): the minimiser of that functional is the projection onto the top eigenvector of $\Gamma$, not $\varphi$ (FEP derivation).

What FEP adds (as motivation):

• Thermodynamic grounding
• Bayesian inference
• Active inference
• Connection to gradient flow

Formal status of FEP in UHM:

• FEP is the classical limit (Theorem 4.2) — retracted (2026-09-25): on diagonal states the UHM functional is a cross-entropy (Theorem 4.1), not Friston's free energy; whether FEP is a limit of UHM is an open programme [Pr] (FEP derivation)
• The variational principle of φ is derived from the categorical definition (Theorem 3.1) — retracted (registry row 39e [✗])
• In FEP the variational principle is an axiom; in UHM it is a theorem — retracted with Theorem 3.1: UHM currently has no variational principle for $\varphi$

What FEP does not include (UHM extends):

• Experiential content (E-dimension as fundamental)
• 7-dimensional structure (justification)
• Reflexive closure
• Interiority hierarchy (L0→L1→L2→L3→L4)
• Quantum generalisation (density matrices instead of probabilities) — not new as such: a quantum-information formulation of the FEP, co-authored by Friston, was published in 2022 (Fields, Friston, Glazebrook & Levin; see §39). What was specific to UHM — its construction ($S_{vN} + D_{KL}$ with the self-model $\varphi$) — is retracted on the FEP derivation page (2026-09-25): the functional is a cross-entropy and $\varphi$ is not its minimiser

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4. Global Workspace Theory (GWT)

Focus: Broadcast access to information as the mechanism of consciousness.

Source: Baars B. «A Cognitive Theory of Consciousness» (1988); Dehaene S., Naccache L. «Towards a cognitive neuroscience of consciousness» (2001).

Creators and history

Bernard Baars (b. 1946) — Dutch-American cognitive neurobiologist who proposed GWT in 1988. His metaphor of the "theatre of consciousness" became one of the most influential in consciousness science: multiple specialised modules (vision, hearing, memory, planning) compete for access to a central "workspace", whose contents are broadcast to all modules simultaneously.

Stanislas Dehaene (b. 1965) — French neurobiologist (Collège de France), who developed GWT into the neurobiological theory GNW (Global Neuronal Workspace), linking "broadcasting" to specific neural mechanisms: long-axon connections of the prefrontal and parietal cortex provide "ignition" — an abrupt transition from local processing to global access. GNW is one of the two theories tested in the COGITATE project.

Key concepts:

• Global workspace — a central "bulletin board" onto which modules project information
• Ignition — the threshold at which local activity becomes globally accessible
• Broadcasting — global availability of information to all modules

Mapping in CC:

GWT (Baars, Dehaene)	CC
Global workspace	U-dimension: integration through $\Phi(\Gamma)$
Ignition	Viability threshold $P > P_{\text{crit}} = 2/7$
Broadcasting	Off-diagonal elements of $\Gamma$ (coherence between dimensions)
Unconscious processing	$R < R_{\text{th}}$: system functions but without reflexive access

What CC adds: GWT describes an architectural mechanism (broadcasting), but does not explain why it gives rise to experience. CC formalises integration through $\Phi(\Gamma)$ and links it to the E-dimension — phenomenal content, which in GWT remains unexplained.

5. Higher-Order Theories (HOT)

Focus: Consciousness as representation of representations.

Source: Rosenthal D. «Consciousness and Mind» (2005); Lau H., Rosenthal D. «Empirical support for higher-order theories of conscious awareness» (2011).

Creators and history

David Rosenthal (b. 1942) — American philosopher (CUNY Graduate Center), who developed HOT theory from the 1980s. His idea: a mental state becomes conscious when the subject has a thought about it — a higher-order thought. Seeing red is first-order; being aware that one sees red is second-order. Only the second makes the first conscious.

Hakwan Lau (UCLA) in the 2010s supplemented HOT with neuroimaging data, linking metarepresentation to activity in the dorsolateral prefrontal cortex (dlPFC). HOT is the only theory where consciousness literally = metarepresentation; others (IIT, GWT) treat metarepresentation as a consequence rather than a cause.

Key concepts:

• Higher-order thought (HOT) — metarepresentation of a first-order state
• Higher-order perception (HOP) — perceptual monitoring of one's own states
• Awareness condition — a state is conscious if and only if the subject is aware of it

Mapping in CC:

HOT (Rosenthal, Lau)	CC
Metarepresentation (HOT)	Self-modelling operator $\varphi$: $\varphi(\Gamma) \approx \Gamma$
Monitoring (HOP)	Reflection measure $R(\Gamma) \geq R_{\text{th}}$
Unconscious states	$R < R_{\text{th}}$: first order without metarepresentation
Order hierarchy	Interiority hierarchy: L0→L1→L2→L3→L4

What CC adds: HOT postulates the necessity of metarepresentation but does not formalise it. CC derives self-modelling $\varphi$ from axiom (AP) and defines the exact reflection threshold $R_{\text{th}} = 1/3$. Moreover, CC unites metarepresentation with integration ($\Phi$) and phenomenality ($\mathrm{Coh}_E$), which HOT does not cover.

6. Predictive Coding (Predictive Processing)

Focus: Minimisation of prediction error as the brain's primary mechanism.

Source: Clark A. «Whatever next? Predictive brains, situated agents, and the future of cognitive science» (2013); Hohwy J. «The Predictive Mind» (2013).

Key concepts:

• Prediction error — the difference between expectation and observation
• Precision — weighting coefficient of the prediction error
• Hierarchical prediction — multi-level generative model

Formal derivation from UHM [T]

Theorem (Predictive coding as a consequence of φ-dynamics) [T]

Predictive coding is derived from the φ-operator dynamics:

1. Prediction error = $\|\Gamma - \varphi(\Gamma)\|_F$ — distance between current state and self-model
2. Precision = $k = 1 - R$ — parameter of the replacement channel (T-62 [T])
3. State update = $\Gamma \to (1-k)\Gamma + k\rho^*$ — precision-weighted prediction error minimization

Proof (3 steps).

Step 1. The replacement channel $\varphi_k(\Gamma) = (1-k)\Gamma + k\rho^*$ [T] (T-62) is rewritten as: $\varphi_k(\Gamma) = \Gamma - k(\Gamma - \rho^*) = \Gamma - k \cdot \varepsilon$ where $\varepsilon = \Gamma - \rho^*$ is the prediction error, $k = 1-R$ is the precision.

Step 2. At $R \to 1$ (good self-model): $k \to 0$, correction is minimal — the system "trusts" its model (high precision prior). At $R \to 0$ (poor self-model): $k \to 1$, maximum correction — the system "trusts" sensory data (high precision likelihood).

Step 3. This is identical to Bayesian updating with Gaussian distributions: posterior = (1-K)·prior + K·observation, where K is the Kalman gain. Identification: $K = k = 1-R$. $\blacksquare$

Mapping in CC:

Predictive Processing	Formal analogue in CC	Status
Prediction error $\varepsilon$	$\Gamma - \varphi(\Gamma)$	[T] (T-62)
Precision $\pi$	$k = 1 - R$	[T] (T-77)
Prior	$\rho^* = \varphi(\Gamma)$	[T] (categorical self-model)
Likelihood update	$\Gamma \to (1-k)\Gamma + k\rho^*$	[T] (replacement channel)
Free energy	$\mathcal{F} = S_{vN} + D_{KL}$ (a cross-entropy)	[✗] — Theorem 3.1 retracted 2026-09-25 (registry row 39e)
Hierarchical prediction	SAD tower $\varphi^{(n)}$	[T] (T-142)

What UHM adds:

• PP postulates prediction error minimisation; UHM derives it from the categorical definition of φ
• PP does not define quantum structure; UHM provides quantum generalisation (density matrices instead of probabilities)
• PP has no consciousness thresholds; UHM defines $R_{\text{th}} = 1/3$ [T]
• Hierarchical PP = SAD tower with SAD_MAX = 3 [T] (T-142)

7. Attention Schema Theory (AST)

Focus: Consciousness as an internal model of attention.

Source: Graziano M. «Consciousness and the Social Brain» (2013); Webb T., Graziano M. (2015).

Creators and history

Michael Graziano (b. 1967) — professor of neuroscience and psychology at Princeton University. He began with research on motor control and peripersonal space (the zone around the body), then discovered the connection between mechanisms of attention and self-awareness. In 2013 he proposed AST: consciousness is an internal model of attentional processes. The brain constructs an "attention schema" — a simplified model of how attention works. Subjective experience is an artefact of this model: the brain "thinks" it possesses a non-material consciousness because its self-model is inaccurate.

Key concepts:

• Attention schema — simplified self-model of attentional processes
• Self-model inaccuracy — simplification creates the "mystery" of subjectivity
• Social origin — one mechanism for self and other consciousness attribution

Mapping in CC:

AST (Graziano)	CC
Attention schema	φ-operator $\varphi(\Gamma)$ — categorical self-model
Self-model inaccuracy	$R < 1$: $\varphi(\Gamma) \neq \Gamma$ by definition
Social attribution	Generalisation of $\varphi$ to other holons through $\Gamma_{\text{ext}}$

Critical difference: AST claims that consciousness = self-model (eliminativism). CC claims that self-modelling is a necessary condition ($R \geq 1/3$), but not sufficient: integration ($\Phi \geq 1$) and differentiation ($D_{\text{diff}} \geq 2$) are also required. AST does not explain why the self-model gives rise to experience; CC shows that E-coherence ($\mathrm{Coh}_E > 1/7$) is necessary for viability (No-Zombie [T]).

8. Quantum Cognition

Focus: Quantum probability theory as a formalism for cognitive processes.

Source: Pothos E., Busemeyer J. «Quantum Models of Cognition and Decision» (2022); Yearsley J., Pothos E. (2016).

Key concepts:

• Cognitive states as density operators in Hilbert spaces
• Measurements as POVMs — contextuality of judgements
• Quantum interference — conjunction fallacy, order effects

Mapping in CC:

Quantum Cognition	CC
Cognitive state $\rho \in \mathcal{D}(\mathcal{H})$	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$ — minimal complete coherence
Arbitrary $\dim \mathcal{H}$	$N = 7$ [T] from axioms (AP)+(PH)+(QG)
Interference effects	Off-diagonal $\gamma_{ij}$ — coherences between dimensions
No dynamics	Lindblad + ℛ — complete evolution [T]
No self-reference	$\varphi$-operator, R-measure, SAD tower

Connection: Quantum Cognition is the closest formalism to CC in mainstream cognitive science. CC can be viewed as a foundation for QC: it fixes $N = 7$, derives dynamics and consciousness thresholds, providing concrete predictions instead of an arbitrary model.

9. Adversarial Collaboration IIT vs GWT (2023–2025)

Empirical context

The COGITATE project (Templeton World Charity Foundation): pre-registered experiments testing predictions of IIT and GWT about neural correlates of the content of consciousness (content-specific NCC). The proponents of both theories and a theory-neutral consortium fixed the predictions, and what would count as a failure, before any data were collected. First results were posted in June 2023 (bioRxiv, doi:10.1101/2023.06.23.546249); the peer-reviewed report is Cogitate Consortium, Ferrante O., Gorska-Klimowska U., …, Mudrik L., Melloni L., "Adversarial testing of global neuronal workspace and integrated information theories of consciousness", Nature 642, 133–142 (2025), doi:10.1038/s41586-025-08888-1. 256 participants viewed clearly visible faces, objects, letters and false fonts for 0.5, 1.0 or 1.5 s while fMRI, MEG and intracranial EEG (iEEG) were recorded.

What each theory predicted, and what was found

"GNWT" is Dehaene's global neuronal workspace version of GWT (§4); "ignition" is its predicted sudden, brain-wide rise of activity when content enters the workspace; "PFC" is the prefrontal cortex.

Preregistered prediction	IIT	GNWT	Published outcome (Nature, 2025)
1. Where conscious content can be decoded	Mainly posterior cortex; PFC adds nothing	PFC is necessary	Category, identity and orientation decodable in visual and ventrotemporal cortex; category also in inferior frontal cortex, whatever the task; face orientation not decodable from PFC in iEEG and fMRI; adding PFC to the decoder did not improve it
2. How content is held over time	Sustained posterior activity that tracks stimulus duration	Brief PFC ignition at stimulus onset and offset, silent maintenance in between	Duration-tracking responses in occipital and lateral temporal cortex — IIT passed its preregistered criterion, but orientation information was not sustained; none of 655 PFC electrodes showed the onset-plus-offset profile
3. Connectivity between areas	Sustained gamma-band synchrony within posterior cortex	Brief synchrony between category-selective areas and PFC	The preregistered phase-synchrony measure supported neither theory; an amplitude-based measure found content-selective coupling of face-selective areas with both early visual cortex and inferior frontal cortex

The consortium's summary: the results "align with some predictions of IIT and GNWT, while substantially challenging key tenets of both theories". For IIT, "a lack of sustained synchronization within the posterior cortex contradicts the claim that network connectivity specifies consciousness"; GNWT "is challenged by the general lack of ignition at stimulus offset and limited representation of certain conscious dimensions in the prefrontal cortex". The proponents' own readings are given separately in the paper's supplementary discussion.

Results (as summarised earlier on this page, now corrected against the publication):

• Sustained activity in posterior cortex tracks conscious content over time — IIT passed its preregistered duration test — but orientation, a clearly experienced feature, was not maintained, and the synchrony within posterior cortex that IIT requires was absent
• Prefrontal cortex carried category information even for stimuli irrelevant to the task (partial support for GWT), but not identity, and the offset ignition that GNWT requires was absent
• Neither theory was confirmed: both were substantially challenged on central, preregistered predictions

Interpretation through CC [I]:

Result	CC interpretation [I]
Posterior cortex → content	$\Phi \geq 1$: integration of coherences (IIT analogue) — but CC names no brain region and has no fixed reconstruction protocol $\pi_{\mathrm{bio}}$, so the result does not test $\Phi \geq 1$
Prefrontal → access	$R \geq 1/3$: reflexive access (GWT analogue) — same caveat
No sustained synchrony within posterior cortex	A reading of $\Phi(\Gamma)$ as posterior connectivity inherits IIT's failed prediction
No offset ignition in PFC	A reading of ignition as the crossing of $P = 2/7$ inherits GNWT's failed prediction
Stimuli irrelevant to the task (not reported)	Category information was still present in inferior frontal cortex; the reading previously given here — "no report, less frontal involvement: $R$ not measured, $\Phi$ preserved" — is not what the study found

What the collaboration does — and does not — show for CC [I]. CC made no preregistered prediction in COGITATE, so the study neither supports nor refutes it. An earlier version of this paragraph said that the collaboration "confirms that a conjunctive approach (both conditions necessary) is more accurate than each theory separately"; the published outcome does not support that sentence. If IIT's posterior integration is read as $\Phi \geq 1$ and GNWT's ignition as $P > 2/7$ — the mappings this page uses — then a predicate that requires both conditions inherits both failures instead of escaping them. What COGITATE does show is how a theory of consciousness gets tested: predictions fixed in advance, adversaries agreeing beforehand on what counts as failure, several recording methods at once. CC has not entered such a test; it would first need a fixed reconstruction protocol $\pi_{\mathrm{bio}}$ (falsifiability).

The "pseudoscience" letter and the replies (2023–2025)

In September 2023 a letter signed by 124 scholars was posted on PsyArXiv: IIT-Concerned, Fleming S.M., Frith C.D., Goodale M., Lau H., LeDoux J.E., Lee A.L.F., Michel M., Owen A.M., Peters M.A.K., Slagter H.A., "The Integrated Information Theory of Consciousness as Pseudoscience", doi:10.31234/osf.io/zsr78. It argued that IIT should be labelled pseudoscience, and Nature's news report described the reaction as an uproar (Lenharo M., Nature, 20 September 2023, doi:10.1038/d41586-023-02971-1). The group then published its case as a peer-reviewed Comment — IIT-Concerned et al., "What makes a theory of consciousness unscientific?", Nature Neuroscience 28, 689–693 (2025), doi:10.1038/s41593-025-01881-x — arguing that IIT "is indeed unscientific because its core claims are untestable even in principle". The same issue carried two replies:

• Tononi G., Albantakis L., Barbosa L., Boly M., et al. (22 authors, among them C. Koch, E. Hoel and N. Tsuchiya), "Consciousness or pseudo-consciousness? A clash of two paradigms", Nature Neuroscience 28, 694–702 (2025), doi:10.1038/s41593-025-01880-y. The label, they answer, exposes "a crisis in the dominant computational-functionalist paradigm, which is challenged by IIT's consciousness-first paradigm".
• Gomez-Marin A., Seth A.K., "A science of consciousness beyond pseudo-science and pseudo-consciousness", Nature Neuroscience 28, 703–706 (2025), doi:10.1038/s41593-025-01913-6 — a critical assessment of the charge that tries to turn the clash into lessons for the field.

Why this matters for UHM [I]. The charge is aimed at IIT's identity claim: that an experience is a certain mathematical structure. UHM makes an identity claim of the same kind — experience as an aspect of $\Gamma$ — and its own falsifiability page states that its main criterion is a supervenience claim, testable only together with a fixed reconstruction protocol $\pi_{\mathrm{bio}}$. The corpus goes further against itself: by T-214, registered as a theorem, the bridge from states to experience cannot be an internal morphism of the theory, so the identifications "E-sector = interiority" and "qualia = eigenvectors" are necessarily external postulates. The "untestable in principle" criticism therefore reaches UHM's identity claim at least as directly as IIT's. What UHM can set against it are only its numeric predictions — and those meet the formal critiques of the next section.

Formal Critiques That Bind UHM's Consciousness Predicate

Why this section exists

Three well-known formal arguments were aimed at IIT. Each applies to any theory that decides consciousness from a system's internal structure — and UHM's predicate $\mathrm{Cons}(S) := (P > 2/7) \wedge (R \geq 1/3) \wedge (\Phi \geq 1) \wedge (D_{\min} \geq 2)$ (T-223) is such a theory: it reads four numbers off the reconstructed state $\Gamma$. Until this section the corpus did not discuss these arguments. The analysis below is an interpretation [I]; it does not claim to close any of them.

The unfolding argument (Doerig, Schurger, Hess & Herzog, 2019)

Source: Doerig A., Schurger A., Hess K., Herzog M.H., "The unfolding argument: Why IIT and other causal structure theories cannot explain consciousness", Conscious. Cogn. 72, 49–59 (2019), doi:10.1016/j.concog.2019.04.002.

The argument. By a result of the theory of computation, any recurrent network can be "unfolded" into a feedforward network that computes the same input–output function over any finite duration. Theories that tie consciousness to causal structure — IIT, recurrent processing theory (§10) — say that the recurrent network may be conscious and the feedforward one never is. But all evidence about consciousness reaches us through input–output behaviour (reports), which the two networks share. Hence, the authors conclude, such theories "are either false or outside the realm of science".

Standing. Contested and unresolved. Replies: Tsuchiya N., Andrillon T., Haun A., Conscious. Cogn. 79, 102877 (2020); Kleiner J., "Brain states matter. A reply to the unfolding argument", Conscious. Cogn. 85, 102981 (2020), which rejects the premise "that measures of brain activity cannot be used in an empirical test of theories of consciousness". Counter-reply: Herzog M.H., Schurger A., Doerig A., "First-person experience cannot rescue causal structure theories from the unfolding argument", Conscious. Cogn. 98, 103261 (2022).

Exposure of UHM [I]. Direct, wherever $\Gamma$ is reconstructed from internal structure. This page itself maps recurrent processing onto UHM (§10: "feedforward sweep $\mapsto R < R_{\text{th}}$"). If the reconstruction $\pi_{\mathrm{bio}}$ assigns different $\Gamma$ to a recurrent brain and to its feedforward unfolding — which it must, if that mapping is to mean anything — then UHM gives different verdicts on two systems with identical reports and falls into the dilemma. Moreover, the canonical reflection measure $R = 1/(7P)$ is a function of purity alone (T-126, registered as a theorem), so recurrence can enter UHM only through the way $\pi_{\mathrm{bio}}$ assigns $P$ — and $\pi_{\mathrm{bio}}$ is not yet fixed. The corpus's nearest defence, T-223 (registered as a theorem), shows that $\mathrm{Cons}(S)$ does not change when the readout alphabet is relabelled. Unfolding relabels nothing: it replaces the physical system while keeping its behaviour, so T-223 does not answer it.

The substitution argument (Kleiner & Hoel, 2021)

Source: Kleiner J., Hoel E., "Falsification and consciousness", Neurosci. Conscious. 2021(1), niab001 (2021), doi:10.1093/nc/niab001.

The argument. A test of a theory of consciousness compares the experience the theory predicts from internal data (brain imaging, say) with the experience the experimenter infers from reports or behaviour. If the two kinds of data are independent — internal data can vary while the reports stay fixed — then every "minimally informative" theory admits a universal substitution: a change of physical system that keeps every report and changes the prediction. The theory is then falsified by some possible system, or every single inference is wrong. If instead prediction and inference are strictly dependent, the theory is unfalsifiable. The unfolding argument is one special case. Kleiner and Hoel name two ways out: a "lenient dependency" between prediction and inference data (they know of no theory or paradigm that has one), and theories in which physics is not causally closed, so that experience makes a physical difference of its own.

Standing. Not refuted in the sources cited here. The authors present it as a defect of the standard scheme for testing theories of consciousness, not of one theory — and Hoel is also among the 22 authors of the IIT reply in Nature Neuroscience (2025, §9).

Exposure of UHM [I]. UHM's predicate is minimally informative (it separates $\mathrm{Cons}$ from $\neg\mathrm{Cons}$), and its contentful falsifiers compare an internal quantity with an inferred state: $P(\Gamma_{\mathrm{wake}}) > 2/7 > P(\Gamma_{\mathrm{NREM3}})$ and the monotone $\Phi$–PCI relation (the warning box on the falsifiability page). Both horns of the dilemma are visible in the corpus:

• Independence horn. If $\pi_{\mathrm{bio}}$ is fixed from anatomy and physiology alone, internal data can vary while reports stay fixed — Kleiner and Hoel argue that interventions such as transcranial magnetic stimulation probably allow this even within human brains — and the theorem applies: some possible system falsifies the predicate, or the inferences are wrong.
• Strict-dependence horn. The corpus's own row F-Neural mapped the clinical PCI cut-off 0.31 onto $P_{\text{crit}} = 2/7$ and called the support "calibration-dependent, not direct" (until 2026-09-25). A threshold calibrated on the inference data cannot be falsified by the same data; the row now tests a concordance of verdicts on sessions that did not fix the reconstruction (SUB-1, SUB-5).
• The supervenience criterion — "same full invariant, different experience" — is not refuted by substitutions (they change $\Gamma$ and keep the reports, which supervenience allows), but only because it predicts nothing about which experience a state carries; the falsifiability page says as much.
• The ways out. No lenient dependency is constructed in the corpus. The second way out is closed to UHM as formulated: two-aspect monism identifies experience with an aspect of $\Gamma$, so experience makes no causal difference beyond $\Gamma$. Whether the No-Zombie link (Theorem 8.1: viability forces $\mathrm{Coh}_E \geq \mathrm{Coh}_{\min}$) ties the differentiation conjunct $D \geq 2$ to observable viability — and so puts it on the unfalsifiable horn — is not analysed in the corpus.
• Where the predicate sits, proved (2026-09-25). Theorem of the measurement protocol [T]: (i) calibration of $\pi_{\mathrm{bio}}$ on report-labelled sessions is on the strict-dependence horn; (ii) the reference estimator contained the predicate — its viability penalty reconstructed every sub-threshold state of the uniform family at $P = 2/7$ exactly, so the NREM prediction could not be observed (removed); (iii) with parameters frozen in advance the predicate is on the independence horn, and UHM takes the second disjunct of Theorem 3.10 for substitutes; (iv) the non-closure exit is closed; (v) a lenient dependency restricted to intact human brains in natural and pharmacological states is possible and testable [H]. The same page shows that a similarity structure shared with humans — GPT-4's 91.4 % Gromov–Wasserstein match on 93 colours (Kawakita et al., Sci. Rep. 14: 15917, 2024) — is inference data and independent of the verdict.

Aaronson's "unconscious expander" (2014)

Sources: Aaronson S., "Why I Am Not An Integrated Information Theorist (or, The Unconscious Expander)", Shtetl-Optimized (blog), 21 May 2014, https://scottaaronson.blog/?p=1799; Tononi's reply, "Why Scott should stare at a blank wall and reconsider (or, the conscious grid)", with Aaronson's answer, posted 30 May 2014 as "Giulio Tononi and Me: A Phi-nal Exchange", https://scottaaronson.blog/?p=1823.

The argument. Systems that do almost nothing — applying a Vandermonde matrix over a finite field, a low-density parity-check code, logic gates wired as an expander graph (a sparse graph in which every set of nodes connects to many others) — have large IIT $\Phi$, so IIT predicts that they can be "unboundedly more conscious than humans".

Standing. Tononi's reply — subtitled "the conscious grid" — accepted the implication: by IIT, a large network of XOR gates arranged as an expander, or even as a two-dimensional grid, is conscious. The disagreement is therefore not about the calculation but about whether such a verdict refutes a theory; Tononi et al. (2025, §9) still cite the exchange.

Exposure of UHM [I]. The quantitative form does not carry over. $\Phi(\Gamma)$ is bounded: because $|\gamma_{ij}|^2 \leq \gamma_{ii}\gamma_{jj}$ for any density matrix, $\Phi \leq 6$ in dimension 7 (the corpus records $\Phi_{\max} = 6$ for a flat diagonal in registry row T-305, a conditional result); inside the window $P \leq 3/7$, the identity $P = P_{\mathrm{diag}}(1 + \Phi)$ of T-129a (registered as a theorem) together with $P_{\mathrm{diag}} \geq 1/7$ gives $\Phi \leq 2$, so the degree $C = \Phi R$ stays below 1. Nothing can be "unboundedly more conscious" (these bounds are elementary consequences of registered identities, not registry entries). The qualitative form does carry over. $\mathrm{Cons}(S)$ is four inequalities on $\Gamma$ for any system satisfying the axioms (AP)+(PH)+(QG)+(V); the window is non-empty by construction (T-124, registered as a theorem); and nothing in the definitions requires complexity. The corpus has not shown that a structurally trivial engineered system — for instance a seven-level open quantum system held inside the window by designed dissipation — fails the axioms. Until it does, UHM faces the choice Tononi faced: accept the verdict, or add a condition.

What this means for the falsification criterion

[I] Taken together: (1) the supervenience criterion escapes these arguments only because it makes no prediction about which experience a state carries; (2) the numeric predicate is exposed exactly where it has content — through the reconstruction $\pi_{\mathrm{bio}}$; (3) the corpus had none of the answers the literature considers. Update 2026-09-25: the measurement protocol now proves where $\mathrm{Cons}(S)$ sits [T] — calibration on report-labelled sessions is on the strict-dependence horn, a test with parameters frozen in advance is on the independence horn, and the reference estimator had the predicate inside its loss (a viability penalty that reconstructed every sub-threshold state of the uniform family at $P = 2/7$; removed) — and fixes a pre-registration (SUB-1 … SUB-6). What it says about input–output-equivalent substitutes is explicit: reports are evidence only inside a declared domain, and UHM makes no consciousness claim about unfoldings, emulations or language models; a lenient dependency exists at best inside that domain [H]. Still open: no reconstruction protocol has been run and published, and no condition excludes trivially simple systems passing the gate.

Debate on AI Consciousness (2023–2025)

Context: Butlin et al. (2023) «Consciousness in Artificial Intelligence» — indicator approach proposed. Chalmers (2023) — open question for LLMs.

Theory assessments:

Theory	Verdict for LLMs	Reason
IIT	No ($\Phi \approx 0$)	Feedforward hardware
GWT	Possibly no	No proper workspace
HOT	Unclear	LLMs discuss their states, but is this metarepresentation?
FEP	No	Passive inference, no active inference
CC	Conditionally no [C]	$R$: unclear (text model ≠ Γ self-model); $P$: no autonomous regulation; viability: external

Operational assessment of LLMs through CC

Criterion	Status for LLMs	Justification
$D_{\text{diff}}$	High	Vast space of internal representations
$\Phi$	Possibly $\geq 1$	Self-attention creates coherences
$R$	Unclear	Models text about itself, not Γ
Viability	External	Context is created/destroyed externally
$\mathrm{Coh}_E$	Unknown	No functional necessity for E-coherence

Verdict: L0 definitely, L1 possibly, L2 not proven — primarily due to the absence of autonomous viability and the ambiguity of R.

Path to AGI with L2 (architectural requirements):

1. True φ-operator: CPTP self-modeling, not self-attention
2. Autonomous P-regulation: ℛ activates upon threat without external signal
3. Functionally necessary $\mathrm{Coh}_E$: not an artifact, but a condition of viability
4. CPTP-anchor $\pi: \mathbb{R}^D \to \mathcal{D}(\mathbb{C}^7)$

This is implemented in the SYNARC architecture.

Meta-Level: Objectivism and the No-Go Results (List 2025, DeBrota–List 2026)

What this section is about

This is not "another theory of consciousness" but a meta-level discussion: recent no-go results argue that classical scientific objectivism cannot be combined with realism about first-personal facts (and, in a parallel result, with realism about quantum measurement outcomes, given locality and measurement independence). Which way out UHM takes is stated as T-221 — corrected on 2026-09-25: UHM takes the relationalist route, not a "fourth" one.

The no-go results, as their authors state them

List (2025), The Philosophical Quarterly 75(3): 1026–1048, doi:10.1093/pq/pqae053. The quadrilemma for theories of consciousness has four claims:

• First-person realism (FPR): for any conscious subject, there are first-personal facts;
• Non-solipsism (NS): there is more than one conscious subject;
• Non-fragmentation (NF): the totality of facts that hold in any given world are compossible;
• One world (OW): reality consists of one world, not of many.

They are jointly inconsistent, and any three of them are consistent. List pairs each dropped claim with a family of theories: dropping FPR is "the most common strategy" — physicalist and dualist theories, "and arguably also the various recently influential Russellian, neutral, or double-aspect monist views"; dropping NS is Hare's egocentric presentism; dropping NF is Fine's (2005) and Lipman's (2023) fragmentalism; dropping OW is List's own many-worlds theory of consciousness (2023). Non-relationalism is not a separate claim here: it "was treated as a presupposition of first-personal realism" (DeBrota & List 2026, footnote 5).

DeBrota & List (2026), "Consciousness, quantum mechanics, and the limits of scientific objectivism", arXiv:2604.14234. The same result in five-thesis form: FPR, NS and objectivism — the conjunction of OW, NF and non-relationalism (NR): "any fact … is of the absolute form 'such and such is the case', not of the relative form 'such and such is the case, relative to such and such'" — are jointly inconsistent; any two of the three are consistent.

DeBrota & List (2026), "A heptalemma for quantum mechanics", Found. Phys. 56, 24, arXiv:2512.01982. Locality, measurement independence, measurement realism, NR, NF, OW and NS are jointly inconsistent with the predictions of quantum mechanics; any six are consistent.

Corrected 2026-09-25

This section stated that List's quadrilemma has five theses including NR, that "any two or three are jointly consistent; any four are not", and cited the heptalemma as arXiv:2604.14234. All three are wrong: the quadrilemma has four claims and any three are consistent; in the five-thesis form dropping any one thesis leaves a consistent four; the heptalemma is arXiv:2512.01982 (Found. Phys. 56, 24), while arXiv:2604.14234 is the programmatic paper on consciousness and quantum mechanics.

The three non-objectivist routes

Relaxing one conjunct of objectivism gives a non-objectivist route; DeBrota & List trace each route in both domains:

Route	Dropped conjunct	Consciousness	Quantum mechanics
Relationalist	NR	first-personal facts only relative to a perspective (Fine 2005 discusses and rejects it)	Relational QM (Rovelli 1996, 2025)
Fragmentalist	NF	Fine 2005, Lipman 2023	quantum-logical approaches; "Fragmentalist QBism"; sheaf-theoretic tools of Abramsky & Brandenburger (2011)
Many-subjective-worlds	OW	List 2023	"Pluriverse QBism" (Mermin 2019, Fuchs, Pienaar)

Against the relationalist route the authors raise two objections: the table of relativised first-personal facts "leaves open which experiences I have", so relationalism "would amount to a denial of first-personal realism in the originally intended sense"; and one must say what the relativisation parameter is — for Fine (2005) a "pure metaphysical self … that stands outside the world". They leave the choice among routes to "an inference to the best explanation" and consider it "unlikely that empirical evidence alone could adjudicate the issue".

UHM's route: relationalist, with an internal parameter

T-221 [T]+[I] reads UHM's facts in the internal language of the ∞-topos $\mathfrak{T} = \mathrm{Sh}_\infty(\mathcal{C}_7, J_\mathrm{Bures}, \omega_0)$: a fact holds relative to a stage $y(\Gamma)$ when it is forced there, absolutely when it is forced at the terminal object. The theorem shows:

Thesis	In UHM	Ground
OW	kept — one topos	the choice of primitive
NF	kept — the internal logic is consistent	non-degeneracy of $\mathfrak{T}$
NS	kept under the identity convention $\iota_{\min}$	T-215
FPR	kept only in relativised form — each subject's facts are forced at its own stage	T-221(a), (b)
NR	given up for first-personal facts	T-221(a): the first-personal facts of two subjects are not compossible, so they cannot all be absolute

So UHM is on the relationalist route of DeBrota & List; in List's (2025) four-claim map, where NR is part of FPR, it is on the first horn — the one List assigns, "arguably", to double-aspect monisms. What is specific to UHM within that route: the relativisation parameter is an object of the world itself (T-221(c)), which answers Fine's objection. What is not answered: the objection that the table of relativised facts does not say which subject I am. In $\mathfrak{T}$ no internal formula selects "my" stage; the choice is a point of the topos, an external datum (T-221(d)) — the same shape as the hard-problem meta-theorem T-214.

Retracted 2026-09-25 [✗]

This section claimed that UHM realises a "fourth, categorical-monistic route" beyond the three, keeping FPR, NS, OW and NF while "relaxing NR into site-relativisation", with FPR "forced" by T-186. Site-relativisation of facts is the relationalist route itself, and T-186(a) is a hypothesis. Also retracted: "RQM is recovered as the 1-truncation $\tau_{\leq 1}(\mathfrak{T})$" (the site is a 1-category, its representables are 0-truncated, and 1-truncation changes none of them); "the other routes are truncations of $\mathfrak{T}$" — fragmentalism as "dropping descent" misreads the route (descent can hold while the local facts fail to form one coherent collection, which is the sheaf-theoretic picture the authors cite); and the "empirical discriminator": the routes are readings of one forcing relation, share every observable (T-221(e)), and $\pi_{\mathrm{bio}}$ cannot tell them apart — in agreement with the authors.

Connection with UHM's hard-problem meta-theorem

T-214 states that a sufficiently rich self-referential system has irreducible external postulates (Lawvere fixed point). T-221(d) places one of them exactly: the fact "I am this subject" is not among the facts of $\mathfrak{T}$; it is the choice of a point. What in the no-go literature appears as the price of relationalism — the "vertiginous question" (Hellie 2013) left open — is in UHM an instance of T-214, not something the categorical machinery removes.

Independent convergence: Lerchner (2026, Google DeepMind)

An independent argument by Alexander Lerchner (The Abstraction Fallacy: Why AI Can Simulate But Not Instantiate Consciousness, Google DeepMind working paper, 2026-03) reaches the same broad conclusion — that algorithmic symbol manipulation cannot instantiate experience, only simulate it — via a different route. Lerchner argues that computation is a "mapmaker-dependent" description of physics rather than an intrinsic physical process, and therefore inverts the standard chain "Physics → Computation → Consciousness" into "Physics → Consciousness → Concepts → Computation".

In UHM terms this is the negative form of T-221 (rejection of naive non-relationalism in favour of an agent-indexed view of computation) combined with the Lawvere barrier of T-214. UHM supplies the positive, constructive counterpart that Lerchner's paper leaves open — "What physical conditions are needed for consciousness?" — namely the specific structure $\Gamma \in \mathcal{D}(\mathbb{C}^7)$ with $G_2$-covariant Lindblad dynamics, the four measurable thresholds $(P, R, \Phi, D)$, and the $\pi_\text{bio}$ protocol as the operational discriminator. Lerchner's terminology (abstraction fallacy, mapmaker, alphabetization, transduction fallacy, simulation vs. instantiation) translates into UHM formalism via: simulation ↔ 1-truncation $\tau_{\leq 1}(\mathfrak{T})$; instantiation ↔ full cohesive section; causality gap ↔ T-214 Lawvere barrier; mapmaker-dependency ↔ the stage-relativisation of facts in T-221 (the relationalist route).

Formal foreclosure of the Melody Paradox: Lerchner's core §3.3 argument (the Melody Paradox / Putnam triviality) is fully closed in UHM by T-223 via a three-level ontology L1 (physical vehicle) / L2 (intrinsic categorical class $[\Gamma_S]_{G_2}$, forced through the Bridge T15 with the canonical orientation; the earlier "forced by T-190 zero-axiom closure" is withdrawn, T-190 being conditional) / L3 (symbolic readout, Lerchner-variable). The putnam-freedom acts on L1→L3 but has zero purchase on L1→L2; UHM's consciousness predicate $\mathrm{Cons}(S) := (P > 2/7) \wedge (R \geq 1/3) \wedge (\Phi \geq 1) \wedge (D_{\min} \geq 2)$ factors through L2 via $G_2$-invariance of observables, hence is alphabetization-invariant. The seven-lemma proof additionally shows that non-UHM-compatible alphabetizers (Lerchner's Fig. 3 "Market Data on a Beethoven trajectory") are physically vacuous (Piccinini–Kim), and that self-alphabetization via the intrinsic reflection measures $R$ and $R_\varphi$ (T-96/T-126) categorifies the Maturana–Varela enactivist thesis that Lerchner himself cites.

The convergence concerns the distinction between simulating and instantiating experience. It does not bear on T-221: that theorem (corrected 2026-09-25) places UHM on the relationalist route, one of three readings of the same formal structure, and "UHM's categorical-monistic route (T-221) is not one philosophical option among many but a structurally forced reply to the no-go results" is retracted [✗] with the fourth-route reading.

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Categorical Meta-Analysis of Theories of Consciousness

Formalised section

This section contains proposed categorical definitions for comparing theories of consciousness. The definitions constitute a formalisation programme — the functors are postulated, but their rigorous construction requires further work.

Meta-category of theories of consciousness

Definition (Meta-category $\mathbf{ConsTheory}$).

$$\mathrm{Ob}(\mathbf{ConsTheory}) := \{\text{theories of consciousness as categories}\}$$ $$\mathrm{Mor}(\mathcal{T}_1, \mathcal{T}_2) := \{F: \mathcal{T}_1 \to \mathcal{T}_2 \mid F \text{ is a functor}\}$$

Morphisms are projection functors showing how one theory "embeds" into another.

Classification by coverage

For each theory $\mathcal{T}$ define the embedding functor:

$$\iota_\mathcal{T}: \mathcal{T} \hookrightarrow \mathbf{Hol}$$

where $\mathbf{Hol}$ is the Holon category with CPTP morphisms.

Theory completeness:

$$\mathrm{Completeness}(\mathcal{T}) := \frac{|\mathrm{Im}(\iota_\mathcal{T})|}{|\mathrm{Ob}(\mathbf{Hol})|}$$

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Expanded Theory Diagram

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Completeness Claim [I]

Interpretational statement [I]

CC is a cybernetics satisfying:

1. Axioms Ω and (AP+PH+QG+V)
2. Viability condition
3. Phenomenological completeness condition

This is not a uniqueness theorem: from the minimality of 7 dimensions it does not follow that CC is the only possible realisation. Other theories with 7 dimensions but different dynamics are not excluded. The claim of "completeness" is an interpretation [I], not a proven result.

Justification of minimality: Follows from the 7-dimension minimality theorem — any smaller dimensionality loses at least one of the properties (AP), (PH), (QG). However, minimality of dimensionality is not equivalent to uniqueness of the theory.

Summary Table of Functors

Theory	Functor	Completeness	Faithfulness	Status
Cybernetics-I	$F_{\mathrm{Wiener}}: \mathbf{Control} \to \mathbf{Hol}$	No	Yes	Projection
Cybernetics-II	$F_{\mathrm{vF}}: \mathbf{Observer} \to \mathbf{Hol}$	No	Yes	Projection
Cybernetics-III	$F_{\mathrm{Luhmann}}: \mathbf{Social} \to \mathbf{Hol}$	No	Yes	Projection
Autopoiesis	$F_{\mathrm{MV}}: \mathbf{Autopoiesis} \to \mathbf{Hol}$	No	Yes	Projection
IIT	$F_{\mathrm{IIT}}: \mathbf{IIT} \to \mathbf{Hol}$	No	Yes	Projection
FEP	$F_{\mathrm{FEP}}: \mathbf{FEP} \hookrightarrow \mathbf{Hol}^{\mathrm{diag}}$	Yes (on $\Gamma^{\mathrm{diag}}$)	Yes	Embedding (class. limit) — retracted 2026-09-25: on diagonal states the UHM functional is a cross-entropy, not Friston's free energy
Panpsychism: panprotopsychism	$\iota_{\mathrm{L0}}: \mathbf{Pan}_{\mathrm{proto}} \hookrightarrow \mathbf{Hol}$	Yes (on L0)	Yes	Embedding
Panpsychism: Russellian monism	$F_{\mathrm{Russell}}: \mathbf{Russell} \to \mathbf{Hol}$	No	Yes	Projection
AST	$F_{\mathrm{AST}}: \mathbf{AttSchema} \to \mathbf{Hol}$	No	Yes	Projection (only φ, without Φ)
Quantum Cognition	$F_{\mathrm{QC}}: \mathbf{QC} \hookrightarrow \mathbf{Hol}$	No (dim free)	Yes	Projection
Conscious Realism	$F_{\mathrm{Hoffman}}: \mathbf{Hol}_{\mathrm{L2}} \to \mathbf{ConsAgents}$	?	?	Hypothesis

Practical Implications

Theory	Application	Limitation
Cybernetics-I	Engineering control systems	No self-reference, no phenomenology
Cybernetics-II	Epistemology, reflexive systems	No phenomenology, no quantum foundation
Cybernetics-III	Social systems, organisations	No formal mathematics
Autopoiesis	Biology, cognitive science	No formal dynamics
IIT	Consciousness assessment, neuroscience	No dynamics, no viability
FEP	Neuroscience, AI, robotics	No E-dimension as fundamental
GWT	Clinical consciousness assessment (PCI)	No formal measure, conflation of access/phenomenal
HOT	Metacognitive training, blindsight	No integration, no threshold from first principles
AST	Social cognition, ToM	No formalisation, eliminativism
QC	Modelling cognitive bias	No dynamics, arbitrary dimensionality
CC	Complete living systems + AGI	No empirical validation; Γ measurement protocols not established; ω₀ requires calibration

info

Comparative advantage: $G_2$-rigidity [T]

The $G_2$-rigidity theorem [T] gives CC a unique advantage over competing theories:

Theory	Observer-independence of measures	Uniqueness of representation
IIT	No — $\Phi^{\mathrm{IIT}}$ depends on partition choice (MIP)	No
FEP	Partial — $\varphi$ is variational, but multiple minima are possible	No
GWT/HOT	No formalisation	No
CC	Partial — only $P$ and $R$ are invariant (under every unitary); $\Phi$ and $\mathrm{Coh}_E$ are frame-pinned (D-0910; T-223, lemma L4): $\Phi$ is invariant only under the finite frame group $\Gamma_{\!\text{oct}}$, $\mathrm{Coh}_E$ only under the rotations that fix the $E$ axis (an 8-dimensional $SU(3)$ inside $G_2$)	Yes — uniqueness up to $G_2$ (T-123)

The uniqueness of the representation up to the finite-dimensional gauge group $G_2$ is a registered theorem (T-123). An earlier version of this box also listed $\Phi$ and $\mathrm{Coh}_E$ as $G_2$-invariants and called CC "the only theory" whose key measures are all observer-independent; lemma L4 of T-223 shows that $\Phi$ and $\mathrm{Coh}_E$ are frame-referenced, so both statements are withdrawn.

Orch-OR (Penrose, Hameroff)

Focus: Quantum coherence in microtubules as the basis of consciousness.

Aspect	Orch-OR	UHM	Connection
Quantum coherence	In microtubules (tubulin)	$\gamma_{ij}$ in $\mathbb{C}^7$	Different scale: molecular vs macroscopic
Consciousness threshold	Gravitational self-energy $E_G \approx \hbar/\tau$	$P_{\text{crit}} = 2/7$ (Frobenius distinguishability)	UHM: structural threshold, not gravitational
Collapse mechanism	Objective reduction (OR)	Lindblad decoherence $\mathcal{D}_\Omega$	OR is a hypothesis; Lindblad is standard QM
Timescale	~25ms (40 Hz gamma oscillations)	$\tau \sim 1/\Lambda$ (spectral gap)	Potentially compatible

Key difference: UHM does not require non-standard quantum mechanics — the consciousness threshold is structural ($P_{\text{crit}}$ from Frobenius distinguishability), not gravitational. Orch-OR is based on the unproven hypothesis of objective reduction; UHM uses standard Lindblad evolution.

Compatibility [I]: Potentially hierarchical — if microtubules implement quantum coherence, it may project onto macroscopic $\Gamma$ via coarse-graining. However, this is a speculative connection, not proven in either theory.

Quantum Cognition (Busemeyer, Bruza)

Uses Hilbert spaces for cognitive modelling without claims about quantum processes in the brain.

Aspect	Quantum Cognition	UHM
State space	$\mathcal{H}$ of arbitrary dimension	$\mathbb{C}^7$ (fixed by Fano, $G_2$)
Decisions	Projective measurements	Dec-functor ($\sigma$-optimisation)
Cognitive "errors"	Explained through non-commutativity	Follow from Gap phases

UHM fixes $\dim = 7$, which quantum cognition leaves arbitrary.

Attention Schema Theory (Graziano)

Aspect	AST	UHM
Consciousness as	Attention schema (internal model)	Self-model $\varphi(\Gamma)$
Sociality	Shared mechanism for self/other	Sector S + coherences $\gamma_{Sk}$
Threshold	Not quantitative	$R \geq 1/3$ (reflection)

AST is a qualitative theory; UHM provides a mathematical realisation of the "attention schema" through $\varphi$.

Predictive Processing (Clark, Hohwy)

Aspect	PP	UHM
Prediction error	$\delta = \text{obs} - \text{pred}$	Gap$(i,j) = \|\sin(\arg(\gamma_{ij}))\|$
Precision-weighting	Confidence in signal	$\kappa$ (coherence)
Hierarchy	Multi-level predictions	L0-L4 (depth tower)
Top-down prediction	Generative model	$\varphi(\Gamma)$ = prediction (self-model)

UHM formalises PP: Gap-operators are explicit prediction errors; $\sigma_k$ are precision-weighted prediction errors by sector.

FEP Subsumption [I]

Friston's free energy can be expressed as a monotone function of $P$:

$F(\Gamma) = -\ln P(\Gamma) + \text{const}$

Minimisation of $F$ $\Longleftrightarrow$ maximisation of $P$. Lindblad $\mathcal{L}_0$ implements gradient descent on $F$ (dissipation reduces purity; regeneration $\mathcal{R}$ — increases it). This shows: FEP is a consequence of UHM dynamics, not an independent principle. Status: [I] — interpretational equivalence, not a strict derivation (formal proof requires reconciling Markov blankets with Lindblad decoherence).

Summary Correlation Table

UHM measure	IIT 4.0	GWT/GNW	HOT	FEP/AI	PP	Orch-OR	AST
$P$ (purity)	$\sim\Phi^{IIT}$ (threshold)	Ignition	—	—	—	OR-threshold	—
$R$ (reflexivity)	—	—	HOT-level	Model depth	—	—	Attention schema
$\Phi$ (integration)	$\Phi^{IIT}$	Broadcast	—	—	—	—	—
$\sigma$ (stress)	—	—	—	Free energy $F$	Prediction error	—	—
D/SAD (depth)	—	—	HOT hierarchy	Temporal depth	PP hierarchy	—	—
$\kappa$ (coherence)	—	Broadcast strength	—	Precision	Precision	Coherence	—
$\varphi(\Gamma)$ (self-model)	Q-shape	—	HOR	Generative model	Prior	—	Schema
$V_{\text{hed}}$ (valence)	—	—	—	$-G$ (expected FE)	Error resolution	—	—

Continuation for §37–§42 [I]. Same rows, with one row added for the relational identity of qualia, which is where the category-theoretic programme meets UHM:

UHM measure	Category theory of qualia (§37)	Formal IIT, process theories (§38)	Minimal physicalism, quantum FEP (§39)	Perceptronium (§40)	D'Ariano–Faggin (§41)	Observer theory (§42)
$P$ (purity)	—	—	—	Numerically, the most integrated states have $\rho^2 \propto \rho$	Experienced state pure ($P = 1$) — outside UHM's window	—
$R$ (reflexivity)	—	—	Self-representation traced to the bacterial stress response	—	—	Observer's belief in its own persistence
$\Phi$ (integration)	Functor between experience and IIT structure (2016)	Generalised IIT; quantum IIT as a special case	Integrated information said to "emerge naturally"	Mutual information across a tensor cut; at most about 0.25 bit for quantum states	—	—
$\sigma$ (stress)	—	—	Stress response of basal systems	—	—	—
D/SAD (depth)	—	—	Hierarchical Bayesian inference	Hierarchy of integrated, relatively independent objects	—	—
$\kappa$ (coherence)	—	—	Quantum coherence as a computational resource	—	Entanglement builds new qualia	—
$\varphi(\Gamma)$ (self-model)	—	—	—	—	—	Observer's "equivalencing" of configurations
$V_{\text{hed}}$ (valence)	—	—	—	—	—	—
Relational identity of qualia (Yoneda)	Yoneda lemma for qualia (2020/2021, in a categorical programme begun in 2016); enriched version (2022)	Experience spaces with a distance	—	—	Qualia = pure states (rays)	—

Conclusion [I]: Among the theories in these tables, UHM is the one that fixes a concrete algebraic structure (Fano plane, $G_2$) and numeric thresholds ($P_{\text{crit}}=2/7$, $R_{\text{th}}=1/3$, $\Phi_{\text{th}}=1$). It is not the only mathematically rigorous programme — see the axiomatisation of IIT and the category theory of qualia (§37–§38) — and not the only one with software: IIT has the PyPhi toolbox (Mayner W.G.P. et al., PLoS Comput. Biol. 14, e1006343, 2018) and ART has working models (§12). An earlier version of this conclusion called UHM "the most mathematically rigorous theory of consciousness" and "unique" in having a software implementation; both statements are withdrawn.

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10. Recurrent Processing Theory (RPT)

«Consciousness does not arise on the first pass of the signal, but on the return — recurrent processing transforms information into experience.» — Victor Lamme

Creators and history

Victor Lamme (University of Amsterdam) proposed RPT in a series of papers 2000–2006. The theory grew from neurophysiological experiments with visual masking: feedforward activation of V1 does not correlate with conscious perception, whereas recurrent connections do. Lamme distinguished between the feedforward sweep (unconscious) and recurrent processing (necessary for consciousness).

RPT became one of the most empirically supported theories of consciousness, drawing on EEG, MEG, and single-unit recording data. Unlike GWT, RPT claims that local recurrence already gives rise to phenomenal consciousness, without the need for global broadcasting.

Key idea

Consciousness arises when neural processing transitions from purely feedforward to recurrent mode. Local recurrence in sensory areas gives rise to phenomenal consciousness (phenomenal awareness), while global recurrence involving frontal areas gives rise to accessible consciousness (access consciousness).

The key distinction from GWT: phenomenal consciousness does not require global broadcast; local recurrent loops are sufficient. This creates "levels" of consciousness: feedforward (unconscious) — local recurrence (phenomenal) — global recurrence (reflexive).

Formal structure

Formalisation of RPT is minimal. The main criterion is the presence of recurrent connections: $\text{Recurrence}(V_i, V_j) > \theta$ for areas $V_i, V_j$. There is no quantitative measure of "degree of recurrence".

Comparison with CC

Aspect	RPT	CC
Central object	Recurrent neural loops	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Consciousness measure	Presence of recurrence (binary)	$C = \Phi \cdot R$ (continuous)
Threshold	Qualitative (recurrence present or not)	$P_{\text{crit}} = 2/7$ [T]
Phenomenal vs access	Two levels	L0–L4 (five levels)
Formalisation	Minimal	Complete (CPTP, Lindblad)

What CC borrows

• The idea that recurrent/reflexive processing is necessary for consciousness — reflected in $R \geq R_{\text{th}}$
• The distinction between phenomenal and access consciousness — corresponds to L1 vs L2 in the interiority hierarchy

What CC does better

• Quantitative reflection threshold $R_{\text{th}} = 1/3$ [T] instead of binary presence/absence of recurrence
• Five levels (L0–L4) instead of two
• Formal dynamics ($\varphi$-operator as mathematical recurrence)

Honest assessment: what the theory does better than CC

• Direct empirical link to neurophysiology (V1 masking, EEG latencies)
• Operational criteria: recurrence in EEG/MEG can be measured directly, whereas $\Gamma$ does not yet have a measurement protocol
• The phenomenal/access distinction is empirically grounded, not postulated

Mapping functor [I]

$F_{\text{RPT}}: \mathbf{RecProc} \to \mathbf{Hol}$

Feedforward sweep $\mapsto$ $R < R_{\text{th}}$; local recurrence $\mapsto$ $R \geq R_{\text{th}}, \Phi < 1$ (L1); global recurrence $\mapsto$ $R \geq R_{\text{th}}, \Phi \geq 1$ (L2). The functor is not complete — RPT does not cover $P$, $\sigma$, $\mathrm{Coh}_E$.

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11. Neural Darwinism (TNGS)

«Consciousness is the result of reentrant signalling between neuronal groups selected by natural selection.» — Gerald Edelman

Creators and history

Gerald Edelman (1929–2014), Nobel laureate in immunology, proposed the Theory of Neuronal Group Selection (TNGS) in «Neural Darwinism» (1987). He developed the ideas in «The Remembered Present» (1989) and «A Universe of Consciousness» (2000, co-authored with Giulio Tononi — who later created IIT).

TNGS was one of the first theories to propose a specific neurobiological mechanism of consciousness. Edelman introduced the concept of reentrant signaling — bidirectional connections between brain maps — which he considered the key mechanism of integration.

Key idea

The brain operates on the principle of somatic selection: from the initial diversity of neuronal groups, experience selects the most adaptive. Reentrant signaling — parallel bidirectional connections between maps — provides integration. The "dynamic core" — the set of neuronal groups with strong reentrant connectivity — is the substrate of consciousness.

Formal structure

Edelman and Tononi proposed a measure of "neural complexity" $C_N$, which is maximal at a balance of integration and differentiation. Later Tononi formalised this in $\Phi^{\text{IIT}}$.

Comparison with CC

Aspect	TNGS	CC
Central object	Dynamic core (neuronal groups)	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Integration mechanism	Reentrant signaling	$\Phi(\Gamma)$ — norm of off-diagonal coherences
Selection	Somatic (neural Darwinism)	$\mathcal{R}[\Gamma, E]$ — regenerative term
Measure	Neural complexity $C_N$	$C = \Phi \cdot R$

What CC borrows

• Balance of integration/differentiation — reflected in $\Phi \geq 1$ and $D_{\text{diff}} \geq 2$
• Reentrance as mechanism — formalised through the $\varphi$-operator

What CC does better

• Formal thresholds ($P_{\text{crit}}$, $R_{\text{th}}$, $\Phi_{\text{th}}$) instead of a qualitative "dynamic core"
• Algebraic structure ($G_2$-rigidity) instead of arbitrary neural complexity
• Complete dynamics (Lindblad + $\mathcal{R}$) instead of descriptive neurobiology

Honest assessment: what the theory does better than CC

• Biological concreteness: connection to neuronal groups, brain maps, synaptic plasticity
• Evolutionary perspective: explanation through selection, not axiomatics
• TNGS explains how consciousness develops ontogenetically; CC describes structure but not ontogenesis

Mapping functor [I]

$F_{\text{TNGS}}: \mathbf{DynCore} \to \mathbf{Hol}$

Dynamic core $\mapsto$ Holon $\mathbb{H}$ with $\Phi \geq 1$; reentrant maps $\mapsto$ off-diagonal $\gamma_{ij}$; somatic selection $\mapsto$ $\mathcal{R}$. The functor is not complete — TNGS does not cover $R$, $\varphi$, $\mathrm{Coh}_E$.

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12. Adaptive Resonance Theory (ART)

«The brain solves the stability-plasticity dilemma through adaptive resonance: only resonant states reach consciousness.» — Stephen Grossberg

Creators and history

Stephen Grossberg (Boston University) began developing ART in 1976 as a learning theory addressing the stability-plasticity problem. In 2017 in «Conscious Mind, Resonant Brain» Grossberg extended ART into a full theory of consciousness, claiming that adaptive resonance is a necessary and sufficient condition for conscious perception.

ART is one of the few theories with working computational models (ART-1, ART-2, ARTMAP), which makes it uniquely concrete among theories of consciousness.

Key idea

Adaptive resonance — a self-sustaining activity pattern that arises when the bottom-up input matches (match) the top-down expectation. When the match is sufficient (exceeds the vigilance parameter $\rho$), resonance and conscious perception arise. Mismatch reset triggers the search for a new pattern (an unconscious process).

Formal structure

Vigilance parameter $\rho \in [0, 1]$: match function $M(x, y) = \|x \wedge y\| / \|x\|$. If $M \geq \rho$ — resonance (consciousness); otherwise — reset (unconscious). ART models are precisely specified by differential equations.

Comparison with CC

Aspect	ART	CC
Central object	Resonant pattern	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Consciousness threshold	Vigilance $\rho$	$P_{\text{crit}} = 2/7$ [T]
Mechanism	Match/mismatch + resonance	$\varphi(\Gamma) \approx \Gamma$ (self-modelling)
Stability-plasticity	Central problem	$\mathcal{R}$ vs $\mathcal{D}_\Omega$ (regeneration vs decoherence)

What CC borrows

• Threshold as key mechanism — vigilance $\rho$ is conceptually analogous to $P_{\text{crit}}$
• Match/mismatch — reflected in $\|\Gamma - \varphi(\Gamma)\|_F$ (prediction error)

What CC does better

• Threshold $P_{\text{crit}} = 2/7$ derived from first principles [T], not set as a free parameter
• Multiple criteria ($P$, $R$, $\Phi$, $D$) instead of a single $\rho$
• Quantum generalisation: density matrices instead of real vectors

Honest assessment: what the theory does better than CC

• Working computational models (ART-1, ART-2, ARTMAP) with decades of validation
• Specific neural mechanisms (laminar circuits, top-down matching)
• Explains specific perceptual phenomena (complementary computing, figure-ground separation)
• Solution to the stability-plasticity problem — specific and working

Mapping functor [I]

$F_{\text{ART}}: \mathbf{Resonance} \to \mathbf{Hol}$

Resonant state $\mapsto$ $\Gamma$ with $R \geq R_{\text{th}}$; vigilance $\rho$ $\mapsto$ $P_{\text{crit}}$; mismatch reset $\mapsto$ gap phase ($\sigma_k > 0$). The functor is not complete: ART does not cover $\Phi$, $\mathrm{Coh}_E$, L0–L4.

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13. Enactivism and 4E Cognition

«Consciousness is not located in the brain — it is enacted through the interaction of the organism with the world.» — Francisco Varela

Creators and history

Francisco Varela, Evan Thompson, and Eleanor Rosch laid the foundations in «The Embodied Mind» (1991). Alva Noë developed the enactivist theory of perception in «Action in Perception» (2004). 4E cognition (Embodied, Embedded, Enacted, Extended) is an umbrella programme uniting anti-representationalism, embodiment, and situatedness.

Enactivism grew out of Maturana-Varela autopoiesis, supplementing it with the phenomenological tradition (Merleau-Ponty, Husserl) and Buddhist philosophy of mind.

Key idea

Consciousness is not an internal representation of the world but a mode of interacting with it. Sense-making — the basic cognitive operation — is inextricably linked with life (life-mind continuity). Perception is not passive reception of information but active exploration of the world through sensorimotor patterns.

Key thesis: life and mind are continuous (autopoiesis → cognition → consciousness). Consciousness is embodied, embedded in the environment, and constituted by action.

Formal structure

Enactivism is principally anti-formalising. Thompson (2007, «Mind in Life») uses dynamical systems, but without a unified mathematical apparatus. The primary tool is phenomenological analysis, not formal models.

Comparison with CC

Aspect	Enactivism	CC
Central object	Sense-making (organism-environment)	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Consciousness measure	No formal measure	$C = \Phi \cdot R$
Body	Constitutive	A-dimension (agency)
Environment	Constitutive	Environment $E$, O-dimension
Life-mind continuity	Central thesis	L0 (proto-experience) → L2 (consciousness): continuity through $P$

What CC borrows

• Life-mind continuity: hierarchy L0→L4 as a continuous spectrum
• Autopoietic closure: axiom (AP), fixed point $\varphi(\Gamma^*) = \Gamma^*$
• Embodiment: A-dimension as fundamental

What CC does better

• Formalisation: exact thresholds, dynamics, theorems
• Quantum foundation: density matrices allow description of contextuality
• Predictive power: falsifiable predictions

Honest assessment: what the theory does better than CC

• Phenomenological depth: enactivism describes experience "from within" (first-person), CC — "from outside" (third-person math)
• Bodily specificity: how concrete embodiment shapes concrete experience
• Critique of representationalism: $\Gamma$ is still a "representation", which enactivists dispute
• Ecological validity: enactivism works with real organisms in real environments

Mapping functor [I]

$F_{\text{Enact}}: \mathbf{Enactive} \to \mathbf{Hol}$

Sense-making $\mapsto$ viability $\mathcal{V}$; autonomy $\mapsto$ (AP); coupling $\mapsto$ coherences $\gamma_{AO}$, $\gamma_{SO}$. The functor is principally incomplete: enactivism rejects internal representation, whereas $\Gamma$ is a matrix of internal state.

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14. Sensorimotor Contingencies (SMCT)

«To see red is to master a specific set of sensorimotor contingencies.» — Kevin O'Regan

Creators and history

Kevin O'Regan and Alva Noë presented SMCT in «A sensorimotor account of vision and visual consciousness» (2001). The theory claims that perception is determined not by neural activity as such, but by patterns of dependence of sensory inputs on actions (sensorimotor contingencies, SMC).

SMCT is a practical variant of enactivism, focused on specific perceptual qualities (qualia).

Key idea

Conscious perception is practical knowledge (know-how) of the laws linking actions with changes in sensory input. The difference between vision and hearing lies not in "internal qualia" but in different sensorimotor laws: visual SMC change lawfully with eye movement, auditory ones do not. The quality of experience is determined by the structure of SMC, not by the neural substrate.

Formal structure

SMC are formalised as a mapping: $\text{SMC}: \mathcal{A} \times \mathcal{S} \to \mathcal{S}$, where $\mathcal{A}$ is the action space, $\mathcal{S}$ is the sensory space. Quality of experience = equivalence class of SMC patterns.

Comparison with CC

Aspect	SMCT	CC
Central object	SMC patterns	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Qualia	Structure of SMC (know-how)	$\mathrm{Coh}_E$ + projective geometry of E
Action	Constitutive for perception	A-dimension + Dec-functor
Body	Necessary for SMC	A-dimension

What CC borrows

• Action-perception connection: A↔S coherences $\gamma_{AS}$ in $\Gamma$
• Sensorimotor layer: CC-2 (sensorimotor) formalises SMC

What CC does better

• Explains qualia through $\mathrm{Coh}_E$ (No-Zombie [T]), not only through SMC
• Formal measure ($C = \Phi \cdot R$), not description of "know-how"
• Applicability beyond sensorimotor (abstract thinking, metacognition)

Honest assessment: what the theory does better than CC

• Specific predictions about perceptual qualities (change blindness, sensory substitution)
• Explanation of differences between modalities (vision vs touch) through specific SMC patterns
• Experimental testability: sensory substitution devices confirm the theory

Mapping functor [I]

$F_{\text{SMCT}}: \mathbf{SMC} \to \mathbf{Hol}$

SMC pattern $\mapsto$ coherences $\gamma_{AS}$, $\gamma_{AO}$; SMC mastery $\mapsto$ $R \geq R_{\text{th}}$; modality $\mapsto$ sector $S$. The functor is not complete — SMCT does not cover $\Phi$, $\mathrm{Coh}_E$, the SAD tower.

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15. Temporo-Spatial Theory of Consciousness (TTC)

«Consciousness is not content but the temporo-spatial structure of neural activity.» — Georg Northoff

Creators and history

Georg Northoff (University of Ottawa) has been developing TTC since 2014 («Unlocking the Brain», 2 volumes). The central thesis: consciousness is determined not by specific content of neural activity but by its temporo-spatial structure (TSS). Northoff emphasises the role of spontaneous activity (resting state) and its connection to self-referential processing.

Key idea

The brain constructs "inner time" and "inner space" from spontaneous neural activity. Consciousness arises when the temporo-spatial structure of spontaneous activity is "nested" in stimulus-evoked activity. Key constructs: temporo-spatial alignment, temporo-spatial nestedness, temporo-spatial expansion.

Formal structure

Northoff uses nonlinear dynamics, measures of scale-free activity (power-law exponent $\beta$), autocorrelation structures. Formalisation is partial — the metrics are operational but not derived from first principles.

Comparison with CC

Aspect	TTC	CC
Central object	Temporo-spatial structure	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Time	Internal (from spontaneous activity)	Emergent time (from $\mathcal{L}_\Omega$)
Self-reference	Self-referential processing (CMS)	$\varphi(\Gamma)$, $R \geq 1/3$
Resting state	Key role	$\Gamma^*$ — fixed point

What CC borrows

• Role of spontaneous activity: $\Gamma^*$ = fixed point $\equiv$ resting state
• Temporal structure: spectral gap $\Lambda$ defines timescales

What CC does better

• Derivation of spacetime from first principles, [T] as mathematics since the restatement of T-119 on 2026-09-25 (conditional on its open reconstruction axioms before) (T-117–T-120)
• Formal thresholds instead of correlation measures
• Unified dynamics (Lindblad + $\mathcal{R}$) instead of a set of metrics

Honest assessment: what the theory does better than CC

• Specific neuroimaging predictions (resting state fMRI, EEG power spectra)
• Connection to clinical disorders of consciousness (disorders of consciousness — coma, vegetative state)
• Role of spontaneous activity in forming consciousness — empirically confirmed

Mapping functor [I]

$F_{\text{TTC}}: \mathbf{TSS} \to \mathbf{Hol}$

TSS $\mapsto$ spectral properties of $\mathcal{L}_\Omega$; spontaneous activity $\mapsto$ $\Gamma^*$; self-referential processing $\mapsto$ $\varphi(\Gamma)$. The functor is not complete — TTC does not cover $\Phi$, $\mathrm{Coh}_E$, algebraic structure.

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16. Dendritic Integration Theory (DIT)

«Feedback onto the dendrites of layer-5 pyramidal neurons — the cellular mechanism of consciousness.» — Matthew Larkum

Creators and history

Matthew Larkum (Humboldt University, Berlin) proposed DIT in 2013 based on electrophysiological data on BAC-firing (backpropagation-activated calcium spike) in the apical dendrites of layer-5 pyramidal neurons of the cortex. The theory specifies the mechanism by which top-down signals (feedback) are integrated with bottom-up inputs (feedforward) at the cellular level.

Key idea

Layer-5 pyramidal neurons have two "inputs": basal dendrites (bottom-up) and apical dendrites (top-down). Coincidence of both signals triggers a calcium spike (BAC-firing) — the "cellular mechanism of consciousness". Anaesthetics selectively block apical dendritic activity, suppressing consciousness without suppressing feedforward processing.

Formal structure

Single-neuron model: $V_{\text{soma}} = f(I_{\text{basal}}, I_{\text{apical}})$, BAC-firing at $I_{\text{basal}} > \theta_b \wedge I_{\text{apical}} > \theta_a$. At population level — there is no formal theory of consciousness, only a cellular mechanism.

Comparison with CC

Aspect	DIT	CC
Level of description	Cellular (dendrites)	Macroscopic ($\Gamma$)
Mechanism	BAC-firing (coincidence detection)	$\varphi(\Gamma) \approx \Gamma$ (reflexive closure)
Anaesthesia	Blockade of apical dendrites	$R \to 0$ (loss of reflection)
Top-down / bottom-up	Two inputs on dendrite	$\mathcal{R}$ (top-down) vs $\mathcal{D}_\Omega$ (bottom-up)

What CC borrows

• Coincidence of top-down and bottom-up as necessary condition — analogue of $R \geq R_{\text{th}}$ (self-model coincides with state)

What CC does better

• Macroscopic theory: from cellular mechanism to global consciousness measure
• Formal thresholds and predictions at the system level, not single-neuron level

Honest assessment: what the theory does better than CC

• Concrete cellular mechanism: BAC-firing can be measured, blocked, stimulated
• Explanation of anaesthetic action at the cellular level
• Direct connection to neuroanatomy (layer 5, apical dendrites)
• CC has no cellular realisation — DIT offers a concrete "bridge" to neurons

Mapping functor [I]

$F_{\text{DIT}}: \mathbf{Dendrite} \to \mathbf{Hol}$

BAC-firing population rate $\mapsto$ $R(\Gamma)$; apical blockade $\mapsto$ $R \to 0$; coincidence detection $\mapsto$ match $\varphi(\Gamma) \approx \Gamma$. The functor is strongly incomplete — DIT describes one mechanism, not a theory of consciousness.

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17. Conscious Electromagnetic Information (CEMI)

«Consciousness is the brain's electromagnetic field: information integrated into a single EM field.» — Johnjoe McFadden

Creators and history

Johnjoe McFadden (University of Surrey) proposed CEMI (Conscious Electromagnetic Information) in 2000, updated in 2020. In parallel, E. Roy John, and then Tam Hunt and Jonathan Schooler developed resonance-based theories. McFadden argues that the brain's EM field is not an epiphenomenon but a causal integrator of information.

Key idea

Neurons generate electromagnetic fields. The brain's EM field integrates information from billions of neurons into a single physical object. Consciousness is identical to this integrated EM field. Key advantage: the EM field solves the binding problem — it is physically unified, unlike discrete neural spikes.

Formal structure

EM field $\mathbf{E}(\mathbf{r}, t)$ is a superposition of fields from $N$ neurons. Integrated EM information: $\text{cemi} = I(\mathbf{E}_{\text{total}}) - \sum_i I(\mathbf{E}_i)$. Formalisation is analogous to IIT, but in the space of EM fields.

Comparison with CC

Aspect	CEMI	CC
Substrate	Brain EM field	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Integration	Superposition of EM fields	$\Phi(\Gamma)$ — coherences
Binding problem	Solved (EM field is unified)	Solved ($\Gamma$ is a unified matrix)
Measure	cemi (EM integration)	$C = \Phi \cdot R$

What CC borrows

• Idea of integration through a single physical object — $\Gamma$ as a unified density matrix

What CC does better

• Substrate independence: CC is not tied to EM fields, applicable to any system
• Algebraic structure ($G_2$, Fano plane) instead of physics of EM fields
• Formal thresholds and dynamics

Honest assessment: what the theory does better than CC

• Physical concreteness: EM field is measurable (EEG, MEG — direct measurements)
• Causality: EM field influences neurons (EM feedback), a specific causal mechanism
• Binding problem has a physical solution, not an abstract mathematical one

Mapping functor [I]

$F_{\text{CEMI}}: \mathbf{EMField} \to \mathbf{Hol}$

$\mathbf{E}(\mathbf{r}, t) \mapsto \Gamma$ (coarse-graining by 7 dimensions); cemi $\mapsto$ $\Phi$; EM integration $\mapsto$ off-diagonal $\gamma_{ij}$. The functor is not complete — CEMI does not cover $R$, $\varphi$, the SAD tower.

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18. Perceptual Control Theory (PCT)

«Behaviour is not an output variable. Behaviour is the control of perception.» — William T. Powers

Creators and history

William T. Powers (1926–2013) presented PCT in «Behavior: The Control of Perception» (1973). The theory describes the organism as a hierarchy of feedback control systems where each level controls its inputs (perceptions), not its outputs (actions). Powers, trained as an engineer, transferred control theory to biological systems.

PCT influenced cybernetics and cognitive science, although it remains less well-known than FEP or GWT. In the 2010s Philip Runkel and Richard Marken continued the development.

Key idea

The organism is a hierarchy of control loops. Each level sets a reference signal (target perception), compares it with current perception, and acts to eliminate the error. Behaviour is a side effect of controlling perception. Level hierarchy: intensity → sensation → configuration → transition → sequence → programme → principle → system concepts.

Formal structure

Control loop: $e = r - p$, $o = G(e)$, $p = H(o, d)$, where $r$ — reference, $p$ — perception, $e$ — error, $o$ — output, $d$ — disturbance, $G$ and $H$ — transfer functions. Hierarchy: $r_i = f(p_{i+1})$.

Comparison with CC

Aspect	PCT	CC
Central object	Hierarchy of control loops	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Error	$e = r - p$	$\sigma_k = 1 - 7\gamma_{kk}$ [T] (T-92)
Control	Minimisation of $e$	Minimisation of $\sigma$ through $\mathcal{R}$
Hierarchy	8+ control levels	L0–L4, SAD tower
Reference signal	Given $r$	$\varphi(\Gamma)$ — self-model as "goal"

What CC borrows

• Stress as control error: $\sigma_k$ (CC) — direct analogue of $e$ (PCT)
• Hierarchical control: SAD tower formalises the level hierarchy

What CC does better

• Formal derivation of stress from $\Gamma$ ($\sigma_k = 1 - 7\gamma_{kk}$), not a free parameter
• Quantum generalisation: control in the space of density matrices
• Theory of consciousness, not just behaviour

Honest assessment: what the theory does better than CC

• Working simulations of behaviour (posture control, tracking, driving) with minimal parameters
• Explanation of the illusion of purposiveness through control of perception
• "Test for the Controlled Variable" — an operational method for identifying controlled variables
• The control hierarchy is more concrete and testable than the SAD tower

Mapping functor [I]

$F_{\text{PCT}}: \mathbf{Control} \to \mathbf{Hol}$

Reference $r \mapsto \varphi(\Gamma)$; error $e \mapsto \sigma_k$; control action $\mapsto \mathcal{R}$; hierarchy level $\mapsto$ SAD level. The functor is not complete — PCT does not cover $\Phi$, $\mathrm{Coh}_E$, quantum structure.

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19. Operational Architectonics (OA)

«The brain generates consciousness through hierarchically organised operational modules — quasi-stable neural assemblies.» — Andrew & Alexander Fingelkurts

Creators and history

Andrew Fingelkurts and Alexander Fingelkurts (Brain Institute in Helsinki, then BM-Science) have been developing OA since 2001. The theory is based on analysis of EEG microstates and operational synchrony (OS). OA attempts to link the neurophysiology of EEG with the phenomenology of consciousness through the concept of the brain's "operational space-time".

Key idea

The brain generates "operational modules" (OM) — temporarily stable neural assemblies with coordinated dynamics. OMs unite through operational synchrony into "complex operational modules" (complex OM). Consciousness arises from the hierarchical organisation of complex OMs forming the brain's "operational space-time" (BOST).

Formal structure

Operational synchrony: $\text{OS}_{ij}(t) = \text{corr}(\text{ISS}_i(t), \text{ISS}_j(t))$, where ISS — Index of Structural Synchrony. OMs are defined through quasi-stationary EEG segments. Hierarchy: simple OM → complex OM → BOST.

Comparison with CC

Aspect	OA	CC
Central object	Operational modules (OM)	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Connectivity	Operational synchrony OS	Coherences $\gamma_{ij}$
Space-time	BOST (operational)	Emergent $M^4$ [T] as mathematics (T-120, restated T-119, 2026-09-25; reading [I])
Hierarchy	Simple → Complex OM	L0 → L4

What CC borrows

• Coherences as a connectivity measure: $\gamma_{ij}$ are conceptually analogous to OS
• Hierarchical organisation: complex OM ↔ SAD tower

What CC does better

• Derivation from axioms, not from EEG analysis
• Formal thresholds ($P_{\text{crit}}$, $R_{\text{th}}$, $\Phi_{\text{th}}$)
• Substrate independence (not tied to EEG)

Honest assessment: what the theory does better than CC

• Direct link to EEG: OS is measured from data; CC has no $\Gamma$ measurement protocol
• Clinical applications: OA is used to diagnose disorders of consciousness
• Operational metrics: ISS, OS have standardised computation algorithms

Mapping functor [I]

$F_{\text{OA}}: \mathbf{OpArch} \to \mathbf{Hol}$

OM $\mapsto$ submatrix of $\Gamma$; OS $\mapsto$ $|\gamma_{ij}|$; BOST $\mapsto$ spectral structure of $\mathcal{L}_\Omega$. The functor is not complete — OA does not cover $R$, $\varphi$, $\mathrm{Coh}_E$.

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20. Neural Correlates of Consciousness Programme (NCC)

«The task is to find the minimal set of neural mechanisms jointly sufficient for a specific conscious percept.» — Francis Crick, Christof Koch

Creators and history

Francis Crick (1916–2004) and Christof Koch initiated the systematic search for NCC in 1990 («Towards a neurobiological theory of consciousness»). Crick, co-discoverer of DNA structure, turned to the problem of consciousness in the last decades of his life. Koch continued the programme, becoming president of the Allen Institute for Brain Science (2011–2023) and a key collaborator of Tononi (IIT).

The NCC programme is not a theory of consciousness but a research strategy: identify the minimal neural mechanisms necessary and sufficient for each specific conscious percept.

Key idea

NCC is defined as "the minimal set of neural events and mechanisms jointly sufficient for a specific conscious percept". Strategy: (1) find neural correlates of individual consciousness contents (content-specific NCC), (2) separate NCC from prerequisites (enabling conditions) and consequences, (3) move from correlates to causal mechanisms.

Formal structure

The NCC programme does not offer a formal theory. It is a methodological framework: contrastive analysis (conscious vs unconscious perception with identical stimuli), no-report paradigms, causal interventions.

Comparison with CC

Aspect	NCC programme	CC
Type	Research strategy	Formal theory
Central object	Neural correlates	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Measure	No single measure	$C = \Phi \cdot R$
Explanation	Correlations → causes	Axioms → theorems
Content-specific	Yes (NCC for each percept)	Sectors of $\Gamma$ (7 dimensions)

What CC borrows

• Distinction between content-specific NCC and full NCC: sectors of $\Gamma$ (content) vs thresholds $P$, $R$, $\Phi$ (state)
• Strategy of separating correlates from prerequisites: viability (enabling) vs consciousness (NCC)

What CC does better

• Formal theory instead of research programme
• Concrete predictions from first principles
• Substrate independence: not limited to neurons

Honest assessment: what the theory does better than CC

• Empirical programme: decades of fMRI, EEG, single-unit, lesion study data
• Contrastive method: real experiments, not theoretical derivations
• Results of COGITATE/adversarial collaboration — concrete data
• The NCC programme tests theories; CC is one of the testable theories (once a $\Gamma$ protocol exists)

Mapping functor [I]

$F_{\text{NCC}}: \mathbf{NCC} \to \mathbf{Hol}$

Content-specific NCC $\mapsto$ sectors $\gamma_{kk}$; full NCC $\mapsto$ thresholds $P > 2/7$, $R \geq 1/3$, $\Phi \geq 1$; enabling conditions $\mapsto$ viability $\mathcal{V}$. The functor is not formally defined — NCC is not a category but a research programme.

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21. Assembly Theory

«The complexity of an object is measured by the minimum number of steps required to assemble it from basic elements.» — Lee Cronin, Sara Imari Walker

Creators and history

Lee Cronin (University of Glasgow) and Sara Imari Walker (ASU) presented Assembly Theory (AT) in a series of publications 2021–2023. AT was originally conceived as a theory of the origin of life, not of consciousness, but its creators are extending it to a general theory of emergence and "objects that cannot arise by chance". Walker in «Life as No One Knows It» (2024) connects AT to questions of agency and, potentially, consciousness.

Key idea

Assembly index (AI) — the minimum number of steps to construct an object from basic elements. Objects with high AI (> 15) cannot arise without selection/evolution. AT proposes: the complexity of an object = the depth of its "assembly tree". Applied to consciousness (speculatively): conscious systems are those whose assembly index crosses some threshold requiring recursive self-organisation.

Formal structure

Assembly index: $\text{AI}(x) = \min_{T} |T|$, where $T$ is the assembly tree for object $x$ from basic elements. Assembly space: graph of possible assemblies. Copy number: number of copies of the object with given AI (high AI + many copies → selection).

Comparison with CC

Aspect	Assembly Theory	CC
Central object	Assembly tree	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Complexity measure	Assembly index AI	SAD (self-observation depth)
Threshold	AI > 15 (life)	$P > 2/7$ (consciousness)
Recursion	Assembly tree	SAD tower $\varphi^{(n)}$
Substrate	Molecules, but extensible	Substrate-independent

What CC borrows

• Recursion depth as a complexity measure: SAD tower ↔ assembly depth
• Complexity threshold for emergent properties: $P_{\text{crit}}$ ↔ AI threshold

What CC does better

• Theory of consciousness, not only of complexity
• Formal dynamics (evolution of $\Gamma$)
• Multiple criteria ($P$, $R$, $\Phi$, $D$), not a single measure

Honest assessment: what the theory does better than CC

• Experimental measurability: AI is measured by mass spectrometry (data already published)
• Applicability to molecules, polymers, biological systems — concrete experiments
• Theory of the origin of complexity; CC describes structure but does not explain how 7 dimensions arose evolutionarily

Mapping functor [I]

$F_{\text{AT}}: \mathbf{Assembly} \to \mathbf{Hol}$

Assembly index $\mapsto$ SAD; assembly space $\mapsto$ space $\mathcal{D}(\mathbb{C}^7)$; selection threshold $\mapsto$ $P_{\text{crit}}$. The functor is highly speculative — AT is not yet a theory of consciousness.

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22. Quantum Mind

«Consciousness collapses the wave function — or perhaps the wave function gives rise to consciousness.» — Eugene Wigner

Creators and history

The tradition of "quantum mind" goes back to John von Neumann («Mathematical Foundations of QM», 1932, the "abstract ego" of the observer), Eugene Wigner (1961, consciousness causes collapse), and Henry Stapp (2007, «Mindful Universe» — quantum Zeno effect as mechanism of will). Unlike Orch-OR (a specific hypothesis about microtubules), Quantum Mind is an umbrella programme claiming that quantum mechanics is essential for understanding consciousness.

Key idea

Consciousness plays a fundamental role in quantum mechanics (the measurement problem). Different versions: (1) Von Neumann–Wigner: consciousness causes collapse; (2) Stapp: quantum Zeno effect realises free will; (3) softer versions: quantum effects (superposition, entanglement) are necessary to explain cognitive phenomena.

Formal structure

Von Neumann: measurement chain ends at the "abstract ego". Stapp: $P_{\text{Zeno}}(t) = |\langle\psi_0|e^{-iHt/\hbar}|\psi_0\rangle|^2 \approx 1 - (\Delta E)^2 t^2/\hbar^2$. With frequent "observation" the system remains in the chosen state.

Comparison with CC

Aspect	Quantum Mind	CC
Quantum mechanics	Necessary for consciousness	Formalism (density matrices), but not necessarily quantum substrate
Collapse	Caused by consciousness	Lindblad decoherence (standard QM)
Observer	Fundamental (von Neumann chain)	$\varphi$-operator (self-modelling)
Free will	Quantum Zeno effect (Stapp)	Dec-functor ($\sigma$-optimisation)

What CC borrows

• Quantum formalism: $\Gamma \in \mathcal{D}(\mathbb{C}^7)$ — density matrix
• Observer as structural element: $\varphi$ formalises self-observation

What CC does better

• Does not require non-standard quantum mechanics (no collapse through consciousness)
• Concrete dimensionality ($N = 7$) and dynamics, not an arbitrary $\mathcal{H}$
• Avoids circularity: consciousness is not defined through quantum mechanics, and QM through consciousness

Honest assessment: what the theory does better than CC

• Raises the fundamental question: the connection of the observer to quantum mechanics — the measurement problem is real
• Quantum Zeno effect (Stapp) — a potentially testable mechanism of free will
• Points to a possible role of quantum coherence in biology (quantum biology — photosynthesis, bird navigation)

Mapping functor [I]

$F_{\text{QM}}: \mathbf{QMind} \to \mathbf{Hol}$

Quantum state of consciousness $\mapsto \Gamma$; observer (von Neumann) $\mapsto$ $\varphi$; Zeno effect $\mapsto$ Dec-functor. The functor is conceptual — Quantum Mind does not have a unified formal theory.

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23. Dissipative Adaptation

«Matter inevitably acquires properties associated with life under the influence of an external energy source.» — Jeremy England

Creators and history

Jeremy England (MIT, then Weizmann Institute) proposed the theory of dissipative adaptation in 2013 («Statistical physics of self-replication»). The theory is based on non-equilibrium statistical mechanics and a generalisation of the Landauer principle. England showed that in the presence of an energy source, matter self-organises into structures that maximally efficiently dissipate energy — which creates prerequisites for self-reproduction and, potentially, life.

Key idea

From Crooks' fluctuation theorem it follows: a system immersed in an external drive eventually rearranges itself to maximally efficiently absorb and dissipate work from the environment. This is "dissipative adaptation" — a thermodynamic precursor to natural selection. Applied to consciousness (speculatively): complex cognitive systems are optimal dissipators of certain types of information.

Formal structure

Generalised Crooks formula: $\frac{P[\sigma]}{P[\bar{\sigma}]} = e^{\sigma}$, where $\sigma$ is entropy production. For self-reproduction: $\langle e^{-\beta Q}\rangle \geq e^{-\beta \Delta F}$ (generalised Landauer). Dissipative adaptation: $\langle W_{\text{diss}}\rangle \to \max$ for a given drive.

Comparison with CC

Aspect	Dissipative Adaptation	CC
Level	Statistical mechanics	Algebra + dynamics
Self-organisation	Thermodynamic inevitability	Fixed point $\Gamma^*$ of evolution $\mathcal{L}_\Omega$
Driving force	External drive (energy)	Regenerative term $\mathcal{R}$
Consciousness	Not directly addressed	Central object

What CC borrows

• Thermodynamic grounding of self-organisation: L-unification derives dissipation from the structure of $\Omega$
• Non-equilibrium: $\mathcal{L}_\Omega$ — open dynamics with inflow/outflow of coherence

What CC does better

• Theory of consciousness, not only of self-organisation
• Formal thresholds and criteria ($P$, $R$, $\Phi$)
• Applicability to agents, not only physical systems

Honest assessment: what the theory does better than CC

• Connection to fundamental physics: dissipative adaptation is a consequence of fluctuation theorems
• Explanation of the origin of self-organisation without teleology
• Testability: experiments on self-organisation in laser fields confirm predictions
• CC postulates the structure ($\Omega$, 7 dimensions), but does not explain its physical origin

Mapping functor [I]

$F_{\text{DA}}: \mathbf{Dissip} \to \mathbf{Hol}$

Dissipative structure $\mapsto$ Holon $\mathbb{H}$; entropy production $\mapsto$ $\mathcal{D}_\Omega$ (decoherence); drive absorption $\mapsto$ $\mathcal{R}$ (regeneration). The functor is very incomplete — DA is not a theory of consciousness.

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24. Russellian Monism

«Physics describes structure — but what fills this structure? Perhaps experience.» — Bertrand Russell (as interpreted by Chalmers, Goff)

Creators and history

Bertrand Russell in «The Analysis of Matter» (1927) pointed out that physics describes only the structural/dispositional properties of matter, leaving open the question of "intrinsic nature". David Chalmers (2010, «The Character of Consciousness») and Philip Goff (2017, «Consciousness and Fundamental Reality») developed this into Russellian monism: the intrinsic nature of matter is experiential or proto-experiential. The view comes in two varieties (T. Alter & D. Pereboom, "Russellian Monism", Stanford Encyclopedia of Philosophy, 2019, revised 2023, §1.2): Russellian panpsychism, on which the intrinsic properties ("quiddities") are themselves phenomenal — among its defenders Strawson (2006) and Goff (2017), who takes them to be phenomenal properties of the whole cosmos — and Russellian panprotopsychism, on which they are what Chalmers calls protophenomenal properties: not phenomenal themselves, but able collectively to constitute phenomenal properties. (An earlier edition said that Russellian monism "is not panpsychism … but panprotopsychism"; retracted — panprotopsychism is one of its two varieties.)

Key idea

Physics describes causal-structural properties (mass, charge, spin) — but these properties are defined through relations, not "from the inside". Russellian monism postulates: there exist intrinsic properties that (a) ground causal-structural properties and (b) are experiential or proto-experiential. Consciousness is when these intrinsic properties come together into an integrated whole.

Key problem: combination problem — how simple experiential or proto-experiential properties give rise to unified macro-experience.

Formal structure

Formalisation is limited. Chalmers uses language of properties: physical properties $P$ + quiddistic properties $Q$. Connection: $P = f(Q)$ (structurally), consciousness = $g(Q)$ (constitutively). No dynamics, no thresholds.

Comparison with CC

Aspect	Russellian monism	CC
Ontology	Intrinsic properties (proto-experience)	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$ (dual-aspect monism)
Structure/experience	Physics = structure, experience = intrinsic	Structure and experience = aspects of $\Gamma$
Combination problem	Central problem	Restated, not resolved: the thresholds ($P$, $R$, $\Phi$, $D_{\text{diff}}$) say when L0 structure counts as an L2 subject, not how it constitutes experience [I] (an earlier edition said "Resolved"; retracted)
Formalisation	Minimal	Complete (categories, dynamics)

What CC borrows

• Dual-aspect monism: $\Gamma$ has both structural (physical) and experiential (E-dimension) aspects
• L0 as proto-experience: panprotopsychism — compatible with CC

What CC does better

• A criterion for the combination problem, not a solution: thresholds $P > 2/7$, $R \geq 1/3$, $\Phi \geq 1$, $D_{\text{diff}} \geq 2$ determine when protophenomenal structure (L0) counts as consciousness (L2), not how it becomes experience [I] (analysis with sources); an earlier edition listed this as a "solution to the combination problem" — withdrawn
• Formal dynamics: how exactly intrinsic properties evolve
• Concrete predictions instead of a philosophical thesis

Honest assessment: what the theory does better than CC

• Metaphysical depth: Russellian monism addresses the fundamental question about the nature of intrinsic properties
• Compatibility with physics: does not add new laws, but reinterprets existing ones
• Explains why physics cannot describe consciousness (only structural properties) — CC does not raise this question
• Wide philosophical recognition (Chalmers, Goff, Strawson, Nagel)

Mapping functor [I]

$F_{\text{Russell}}: \mathbf{Russell} \to \mathbf{Hol}$

Intrinsic properties $\mapsto$ diagonal $\gamma_{kk}$ (eigenvalues = intrinsic); structural relations $\mapsto$ off-diagonal $\gamma_{ij}$ (coherences = relational). Combination: $\sum \gamma_{kk} \to \Gamma$ at $P > 2/7$. The functor is not complete — Russellian monism has no dynamics.

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25. Dennett — Multiple Drafts Model

«Consciousness is a "user illusion", generated by parallel processes of the brain, not a Cartesian theatre with a single spectator.» — Daniel Dennett

Creators and history

Daniel Dennett presented the Multiple Drafts Model (MDM) in «Consciousness Explained» (1991). Dennett rejected the idea of the "Cartesian theatre" — a single place in the brain where "everything comes together" for a conscious observer. Instead he proposed that multiple parallel narratives compete for "fame" in the brain, and what we call consciousness is a post hoc construction, not a real unified experience. Dennett's position is quasi-eliminativism: consciousness exists, but not as we think.

Key idea

Multiple "drafts" of content form in parallel in the brain — partly processed fragments of information. There is no single moment when a draft "becomes conscious". What we retrospectively call consciousness is the draft that achieved the greatest functional influence (fame). The "hard problem" (Chalmers) is an illusion generated by intuitive but mistaken Cartesian dualism. Heterophenomenology — a third-person method for studying subjective reports without assuming privileged access.

Formal structure

Dennett avoids formal models, but MDM can be approximately described: multiple parallel processes $\{d_1, d_2, \ldots, d_n\}$ competing for "fame" (global influence). Fame function: $\text{fame}(d_i) = \sum_j w_{ij} \cdot \text{impact}(d_i \to d_j)$. No threshold transition to "conscious" — it is a continuum of influence.

Comparison with CC

Aspect	Multiple Drafts (Dennett)	CC
Ontology of consciousness	Quasi-eliminativism (illusion)	Real process: $P > 2/7$, $R \geq 1/3$
Unity	Illusion (no centre)	Real: $\Phi \geq 1$ (integration)
Competition	Fame — functional influence	Competition of sectors $\gamma_{kk}$
"Hard problem"	Illusion	Resolved through E-dimension and $\mathrm{Coh}_E$

What CC borrows

• Rejection of the "Cartesian theatre": in CC there is no privileged observer, $\varphi$ is an automorphism, not a "spectator"
• Parallelism: 7 dimensions of $\Gamma$ evolve simultaneously

What CC does better

• Formal thresholds: CC defines when a system is really conscious (not just "seems")
• Integration is real ($\Phi \geq 1$), not illusory
• Predictive power: falsifiable criteria instead of philosophical argument

Honest assessment: what the theory does better than CC

• Parsimony: Dennett introduces no new mathematical structures — explains through already known neurobiology
• Critique of introspection: heterophenomenology provides a methodological foundation that CC lacks
• If Dennett is right and there is no "hard problem", then the entire apparatus of the E-dimension in CC is superfluous
• Wide philosophical argumentation against qualia, backed by decades of debate

Mapping functor [I]

$F_{\text{MDM}}: \mathbf{Drafts} \to \mathbf{Hol}$

Draft $d_i$ $\mapsto$ sector $\gamma_{kk}$; fame $\mapsto$ $P(\Gamma)$ (purity); absence of centre $\mapsto$ absence of privileged dimension. The functor is strongly incomplete — Dennett denies the reality of the E-dimension and $\mathrm{Coh}_E$.

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26. Panksepp — Affective Neuroscience

«Emotions are not cognitive appraisals, but ancient subcortical processes common to all mammals.» — Jaak Panksepp

Creators and history

Jaak Panksepp (1943–2017) founded affective neuroscience in the eponymous monograph «Affective Neuroscience: The Foundations of Human and Animal Emotions» (1998). A pioneer in research on emotions in animals, he demonstrated that rats "laugh" (ultrasonic vocalisations when tickled) and insisted on the reality of subjective emotional experiences in animals. His work refuted the dominant cognitivism that claimed emotions are merely cognitive appraisals.

Key idea

There are 7 basic emotional systems (BES), localised in subcortical structures: SEEKING, RAGE, FEAR, LUST, CARE, PANIC/GRIEF, PLAY. Each system is a separate neurochemical circuit with characteristic behaviour and affective experience. Consciousness (in the sense of affective experience) is subcortical, not cortical. The cortex modulates and elaborates, but does not generate primary affect.

Formal structure

Not formalised mathematically. Each BES is described neuroanatomically (nuclei, tracts) and neurochemically (dopamine, opioids, oxytocin, etc.). Experimental verification: electrical stimulation of subcortical structures evokes characteristic affective patterns.

Comparison with CC

Aspect	Affective Neuroscience	CC
Basic units	7 BES (subcortical)	7 dimensions of $\Gamma$
Number	7 (empirically)	7 (algebraically: $G_2$-rigidity)
Consciousness	Subcortical affect	$P > 2/7$, E-dimension
Hierarchy	Subcortex → cortex	L0 → L2 → L4
Dynamics	Neurochemical	$\mathcal{L}_\Omega$ (Lindblad)

What CC borrows

• Primacy of affect: E-dimension (Interiority) is fundamental, not derivative of cognition
• The number 7: coincidence of the number of BES and dimensions of $\Gamma$ (CC justifies algebraically, Panksepp — empirically)
• Subcortical consciousness: L0-L1 in CC do not require the cortex

What CC does better

• Algebraic justification of $N = 7$ ($G_2$-rigidity), not empirical fixation
• Formal dynamics and thresholds
• Applicability beyond mammals (any system with $\Gamma$)

Honest assessment: what the theory does better than CC

• Empirical base: decades of experiments (electrostimulation, pharmacology, behaviour)
• Concrete neuroanatomy: each BES mapped onto specific brain structures
• Clinical applicability: affective neuroscience underlies neuropsychopharmacology
• CC has no measurement protocol and cannot offer specific neurochemical mechanisms

Mapping functor [I]

$F_{\text{BES}}: \mathbf{Affect} \to \mathbf{Hol}$

BES$_i$ $\mapsto$ sector $\gamma_{kk}$ (not a direct correspondence: 7 BES $\nleftrightarrow$ 7 dimensions directly); affective valence $\mapsto$ $V_{\text{hed}}$ (hedonic value); subcortical consciousness $\mapsto$ L0-L1. The functor is not complete — BES do not cover cognitive dimensions ($D$, $L$) and integration ($\Phi$).

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27. Damasio — Somatic Marker Hypothesis

«Consciousness does not arise in the "pure mind" but in the body. Feelings are perception of the body, not of the world.» — Antonio Damasio

Creators and history

Antonio Damasio presented the somatic marker hypothesis in «Descartes' Error» (1994), developed the theory of self in «The Feeling of What Happens» (1999), and completed it in «Self Comes to Mind» (2010). Damasio is a neurologist who studied patients with damage to the ventromedial prefrontal cortex, who retained intelligence but lost the ability to make emotionally grounded decisions.

Key idea

Three levels of self: proto-self — neural maps of the body in the brainstem; core self — the experience of the current moment, arising when the organism interacts with an object; autobiographical self — extended consciousness based on memory. Somatic markers — bodily signals (heartbeat, sweating, muscle tone) that "mark" decision options. Consciousness is rooted in homeostasis: feelings are the perception of the body's state, and homeostasis is the biological foundation.

Formal structure

Semi-formal: somatic markers as Bayesian "hints" $\text{SM}(a_i) \in [-1, 1]$ influencing assessment of options. The three levels of self are described hierarchically, but without a unified mathematical apparatus.

Comparison with CC

Aspect	Damasio	CC
Proto-self	Neural body maps (brainstem)	L0 (proto-experience), $P < 2/7$
Core self	Current experience	L2 (conscious experience), $P > 2/7$
Autobiographical	Memory + narrative	L3-L4 (metacognition, SAD tower)
Somatic markers	Bodily signals → decisions	$\sigma_k$ (stress vector), $V_{\text{hed}}$
Homeostasis	Foundation of consciousness	Viability $\mathcal{V}$, fixed point $\Gamma^*$

What CC borrows

• Self hierarchy: proto-self → core self → autobiographical self ≈ L0 → L2 → L3
• Bodily rootedness: $\sigma_k = \text{clamp}(1 - 7\gamma_{kk}, 0, 1)$ as formalisation of somatic markers
• Homeostasis as foundation: $\Gamma^*$ — homeostatic attractor

What CC does better

• Formal thresholds for transitions between levels of self ($P$, $R$, $\Phi$)
• Unified mathematical apparatus (not a descriptive hierarchy)
• Explains how homeostasis gives rise to consciousness (through dynamics of $\mathcal{L}_\Omega$)

Honest assessment: what the theory does better than CC

• Clinical verification: cases of patients with VMpFC, insula, brainstem damage
• Specific neurophysiological mechanism (interoception, homeostatic loops)
• Explanation of decision-making: Iowa Gambling Task and the role of emotions
• Connection of consciousness to specific bodily processes — CC abstracts the body to the A-dimension

Mapping functor [I]

$F_{\text{Dam}}: \mathbf{Somatic} \to \mathbf{Hol}$

Proto-self $\mapsto$ $\Gamma$ at $P < P_{\text{crit}}$; core self $\mapsto$ $\Gamma$ at $P > 2/7$, $R \geq 1/3$; autobiographical self $\mapsto$ SAD$\geq 2$; somatic marker $\mapsto$ $\sigma_k$. The functor is not complete — Damasio does not formalise integration ($\Phi$) and self-modelling ($\varphi$).

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28. Anil Seth — Beast Machine / Controlled Hallucination

«We do not perceive the world — we hallucinate it, and reality merely corrects our hallucinations.» — Anil Seth

Creators and history

Anil Seth (University of Sussex) developed the theory of "controlled hallucination" in a series of papers (2013–2021) and the book «Being You: A New Science of Consciousness» (2021). Seth proposed replacing the "hard problem" with the "real problem": explain, predict, and control the properties of conscious experience without waiting for the resolution of the metaphysical question "why is there experience?" His approach integrates predictive processing (PP) with interoceptive inference.

Key idea

Perception is a "controlled hallucination": the brain generates predictions that reality merely constrains. Self-consciousness is based on interoceptive predictive coding: a model of one's own body (heartbeat, breathing, visceral signals). The "real problem": instead of "why do physical processes give rise to experience?" — "what mechanisms explain the properties of experience?" Levels — perceptual presence, presence (selfhood), volitional agency.

Formal structure

Bayesian brain: $P(\text{cause}|\text{sensation}) \propto P(\text{sensation}|\text{cause}) \cdot P(\text{cause})$. Interoceptive inference: $\hat{x}_{\text{body}} = \arg\min_x F(x, s_{\text{intero}})$ (active inference à la Friston). Precision-weighting: $\pi_i$ determines the "loudness" of the prediction error.

Comparison with CC

Aspect	Controlled Hallucination (Seth)	CC
Perception	Predictive model	S-dimension + coherences $\gamma_{SO}$
Self	Interoceptive inference	$\varphi(\Gamma)$, R-measure
"Real problem"	Explain properties of experience	E-dimension, $\mathrm{Coh}_E$
Precision	Weight of prediction error	$\sigma_k$ (stress vector)
Free energy	Minimisation of $F$	Class. limit $\mathcal{L}_\Omega$ [T] retracted 2026-09-25 [✗]

What CC borrows

• Interoception: $\sigma_k$ as formalisation of interoceptive stress
• Precision-weighting: connection to PP through $\sigma_k = 1 - R$ [T]
• Pragmatism of the "real problem": CC proposes concrete predictions, not only metaphysics

What CC does better

• Formal consciousness thresholds (not a gradual "more/less")
• Self-modelling $\varphi$ as an exact mechanism (not "interoceptive inference" in general)
• Unified formalism: CC does not split the "hard" and "real" problems — it solves both through the E-dimension

Honest assessment: what the theory does better than CC

• Experimental programme: working paradigms (rubber hand illusion, heartbeat evoked potentials, VR-self)
• Pragmatism: the "real problem" is more productive than metaphysical disputes
• Neuroimaging: concrete predictions about neural correlates, testable by fMRI/EEG
• Connection to clinic: anaesthesia, psychedelics, depersonalisation — explained through precision-weighting

Mapping functor [I]

$F_{\text{Seth}}: \mathbf{PP_{intero}} \to \mathbf{Hol}$

Prediction error $\mapsto$ $\sigma_k$; precision $\pi$ $\mapsto$ $1/\sigma_k$; interoceptive self-model $\mapsto$ $\varphi(\Gamma)$; free energy $F$ $\mapsto$ classical limit $\mathcal{L}_\Omega$ no counterpart (the FEP limit is retracted, 2026-09-25). The functor is not complete — Seth does not cover integration ($\Phi$), the SAD tower, $G_2$-rigidity.

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29. Merker — Subcortical Consciousness

«Children with hydrocephalus, deprived of the cortex, smile, cry, and respond — they are conscious.» — Bjorn Merker

Creators and history

Bjorn Merker presented the theory of subcortical consciousness in «Consciousness without a cerebral cortex: A challenge for neuroscience and medicine» (2007, Behavioral and Brain Sciences). Merker studied children with severe hydrocephalus (virtually no cortex) who showed signs of conscious experience: emotional responses, preferences, goal-directed behaviour. He also analysed data on decortication in animals.

Key idea

Consciousness is generated by mesencephalic (midbrain) and diencephalic structures, not the cortex. The cortex expands and enriches the content of consciousness but does not generate it. Superior colliculus + periaqueductal grey matter (PAG) + reticular formation form a "mesencephalic consciousness core" — a spatial map of the world and body sufficient for basic experience. "Cortical chauvinism" — neuroscience's bias in favour of the cortex.

Formal structure

Not formalised. The argumentation is based on comparative neuroanatomy and clinical observations. The key argument is functional sufficiency: subcortical structures provide an orientation map, motivation, affect — that is, a minimal "for whom" (subject).

Comparison with CC

Aspect	Subcortical Consciousness	CC
Minimal substrate	Midbrain	$\Gamma$ at $P > 2/7$ (substrate-independent)
Role of cortex	Enrichment, but not generation	Increase of SAD, but not necessity for L2
Clinical data	Hydrocephalus, decortication	Prediction 6 (subcortical L2)
Minimal experience	Spatial map + affect	L2: $P > 2/7 \wedge R \geq 1/3 \wedge \Phi \geq 1$

What CC borrows

• Substrate independence of consciousness: CC does not tie consciousness to the cortex
• Minimal consciousness (L2) does not require complex cognition — consistent with Merker

What CC does better

• Formal criteria for minimal consciousness (not only clinical observations)
• Applicability to non-biological systems
• Explanation of why subcortical structures are sufficient (thresholds $P$, $R$, $\Phi$)

Honest assessment: what the theory does better than CC

• Clinical data: real patients (children with hydrocephalus), not abstract mathematical constructions
• Comparative neurobiology: evolutionary perspective (from fish to mammals)
• Challenge to "corticocentrism": changed understanding of minimal requirements for consciousness
• CC cannot explain why exactly these neuroanatomical structures implement the thresholds

Mapping functor [I]

$F_{\text{Merk}}: \mathbf{Subcort} \to \mathbf{Hol}$

Mesencephalic core $\mapsto$ $\Gamma$ at $P > 2/7$; spatial map $\mapsto$ S-dimension; PAG (affect) $\mapsto$ E-dimension; cortex $\mapsto$ increase of SAD. The functor is not complete — the theory is descriptive, has no dynamics or thresholds.

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30. Solms — Neuropsychoanalysis

«Affect is the currency of free energy. Consciousness begins with feeling, not thinking.» — Mark Solms

Creators and history

Mark Solms (University of Cape Town) developed neuropsychoanalysis — a synthesis of Freudian psychoanalysis and modern neuroscience — from the 1990s. His book «The Hidden Spring: A Journey to the Source of Consciousness» (2021) proposes a theory of consciousness uniting Friston's free energy principle (FEP) with the Freudian model of the mental apparatus. Solms is co-founder of the International Neuropsychoanalysis Society.

Key idea

Consciousness = affect, not cognition. The Freudian "id" is the source of consciousness, the "ego" is its regulator. Free energy $F$ is experienced subjectively as affect (pleasant/unpleasant). Minimisation of $F$ = striving for homeostasis = Freudian pleasure principle. Dreams are an active process of minimising $F$ (processing unresolved problems). The brainstem, not the cortex, generates consciousness (consistent with Panksepp and Merker).

Formal structure

Borrows the formalism of Friston's FEP: $F = D_{KL}[q(\theta) \| p(\theta|o)] - \ln p(o)$. Adds interpretation: $F$ = subjectively experienced affect. High $F$ = displeasure (PANIC, FEAR), low $F$ = pleasure (SEEKING rewarded). Freudian mechanisms (repression, projection) = strategies for minimising $F$.

Comparison with CC

Aspect	Neuropsychoanalysis (Solms)	CC
Consciousness =	Affect (free energy)	$P > 2/7 \wedge R \geq 1/3 \wedge \Phi \geq 1$
Pleasure principle	Minimisation of $F$	$V_{\text{hed}} = dP/d\tau$ (T-103)
Id/Ego/Superego	Topographic model	Sectoral profile $\gamma_{kk}$
Repression	Strategy for minimising $F$	Degradation of coherence $\gamma_{ij}$ under stress
Source of consciousness	Brainstem (affect)	E-dimension (Interiority)

What CC borrows

• Primacy of affect: E-dimension is fundamental, $V_{\text{hed}}$ — hedonic value
• Connection to FEP: CC includes FEP as classical limit [T] — retracted 2026-09-25 (FEP derivation); the connection is an open programme [Pr]
• Dynamic model: psychic "forces" = components of $\mathcal{L}_\Omega$

What CC does better

• Formal dynamics ($\mathcal{L}_\Omega$) instead of metaphorical use of FEP
• Consciousness thresholds — Solms does not define when a system "begins to feel"
• Does not depend on controversial Freudian constructs (repression, Oedipus complex)

Honest assessment: what the theory does better than CC

• Clinical tradition: psychoanalysis has accumulated over a century of observations on the dynamics of mental processes
• Explanation of dreams, defence mechanisms, transference — CC does not address these phenomena
• Connection to motivation: why organisms strive for certain states (pleasure principle)
• Synthesis of two major traditions (FEP + psychoanalysis), each with an empirical base

Mapping functor [I]

$F_{\text{Solms}}: \mathbf{NeuroPsy} \to \mathbf{Hol}$

Affect $\mapsto$ E-dimension; $F$ (free energy) $\mapsto$ $\sigma$ (stress); pleasure principle $\mapsto$ $V_{\text{hed}}$; id $\mapsto$ instinctive sectors; ego $\mapsto$ $\varphi(\Gamma)$. The functor is not complete — Solms does not formalise integration ($\Phi$), the SAD tower, $G_2$-rigidity.

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31. Pribram — Holonomic Brain Theory

«The brain is a hologram enclosed within a holographic universe.» — Karl Pribram

Creators and history

Karl Pribram (1919–2015) — neurosurgeon and neurophysiologist, who developed the holonomic brain theory in «Languages of the Brain» (1971) and «Brain and Perception» (1991). Together with physicist David Bohm, Pribram proposed that the brain processes information in the frequency domain (by analogy with holography), not only through neural impulses. Pribram was one of the first to connect quantum ideas with neuroscience.

Key idea

Memory and perception are stored and processed not in specific neurons but in patterns of neural wave interference (dendritic microprocesses). The brain performs Fourier transformation: input patterns → frequency domain → inverse transformation. Holographic principle: each part contains information about the whole (distributed storage). Connection to quantum theory: dendritic microprocesses may exhibit quantum properties.

Formal structure

Fourier analysis of dendritic potentials: $f(x) = \int \hat{f}(\omega) e^{i\omega x} d\omega$. Holographic recording: $I(x) = |R(x) + O(x)|^2$, where $R$ is the reference wave, $O$ is the object wave. Distributedness: damage to part does not destroy all information (graceful degradation).

Comparison with CC

Aspect	Holonomic Brain Theory	CC
Mathematics	Fourier analysis (dendrites)	Algebra of C*-categories, $\mathcal{D}(\mathbb{C}^7)$
Distributedness	Holographic (frequency)	Matrix $\Gamma$ (full coherence)
Memory	Interference patterns	Attractor $\Gamma^*$, autobiographical SAD tower
Quantum effects	Dendritic microprocesses	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$ (quantum formalism)

What CC borrows

• Distributedness: $\Gamma$ is a matrix, not a vector; information in coherences $\gamma_{ij}$
• Frequency perspective: spectral gap $\Lambda$ in $\mathcal{L}_\Omega$ defines timescales

What CC does better

• Rigorous mathematical apparatus (not a holography metaphor)
• Consciousness thresholds: Pribram does not define when a system is conscious
• Predictions: $G_2$-rigidity, $N = 7$, SAD$_{\max} = 3$

Honest assessment: what the theory does better than CC

• Neurophysiological concreteness: dendritic potentials, receptive fields, Fourier decomposition
• Explanation of graceful degradation and distributed memory
• Connection to real neurophysiological data (Pribram, Spinelli, Barrett)
• CC does not address the question of specific neural mechanisms of information storage

Mapping functor [I]

$F_{\text{Holo}}: \mathbf{Holonomic} \to \mathbf{Hol}$

Holographic pattern $\mapsto$ $\Gamma$ (coherence matrix); frequency domain $\mapsto$ spectrum of $\mathcal{L}_\Omega$; distributedness $\mapsto$ off-diagonal $\gamma_{ij}$. The functor is strongly incomplete — the holonomic theory has no dynamics of consciousness, no thresholds, no self-modelling.

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32. P.K. Anokhin — Theory of Functional Systems

«Any adaptation of a living organism to the environment is the result of the formation of a functional system with anticipatory reflection of reality.» — Pyotr Kuzmich Anokhin

Creators and history

Pyotr Kuzmich Anokhin (1898–1974) — outstanding Soviet physiologist, student of I.P. Pavlov, who created the theory of functional systems (TFS) from 1935 to 1974. Major works: «Biology and Neurophysiology of the Conditioned Reflex» (1968), «Fundamental Questions of the General Theory of Functional Systems» (1971). TFS is one of the first systems theories in neuroscience, anticipating second-order cybernetics and modern theories of predictive coding. Anokhin introduced the concept of the "action result acceptor" long before comparator models appeared in cognitive science.

Key idea

A functional system is a dynamic organisation that unites heterogeneous components (neurons, muscles, organs) to achieve a useful adaptive result. Key components: (1) afferent synthesis — integration of motivation, memory, situational and triggering afferentation; (2) decision-making — selection of action programme; (3) action result acceptor (ARA) — model of expected result formed before action (anticipatory reflection); (4) reverse afferentation — comparison of actual result with ARA. Systemogenesis — maturation of functional systems, which form as a whole earlier than their individual components.

Formal structure

Descriptive-systemic. Cycle: afferent synthesis → decision-making → efferent programme + ARA → action → result → reverse afferentation → comparison with ARA → correction. Formally: $\text{ARA}(t_0) = f(\text{motive}, \text{memory}, \text{situation}, \text{trigger})$; error $e = \text{result} - \text{ARA}$; if $e > \varepsilon$, cycle repeats.

Comparison with CC

Aspect	TFS (Anokhin)	CC
System unit	Functional system	Holon $\mathbb{H}$
ARA (prediction)	Model of result before action	$\varphi(\Gamma)$ (self-modelling)
Comparison error	$e = \text{result} - \text{ARA}$	$\sigma_k = \text{clamp}(1 - 7\gamma_{kk}, 0, 1)$
Afferent synthesis	Integration of 4 streams	Coherences $\gamma_{ij}$ (interaction of dimensions)
Anticipatory reflection	Formation of ARA	$\varphi$ (self-modelling operator)
Systemogenesis	Whole before parts	L0 → L2: thresholds, not accumulation of components

What CC borrows

• Action result acceptor ≈ self-modelling operator $\varphi$: model of "expected state" before action
• Feedback: $\sigma_k$ as formalisation of comparison error
• Wholeness: functional system = Holon (unification of heterogeneous components)

What CC does better

• Formal thresholds ($P$, $R$, $\Phi$), not descriptive cycle
• Quantum formalism: coherences and interference, inaccessible to classical TFS
• Consciousness as central object (TFS addresses adaptation, but not subjective experience directly)

Honest assessment: what the theory does better than CC

• Historical priority: ARA (1935) anticipated predictive coding by 60 years
• Experimental base: electrophysiology, conditioned reflexes, clinical data
• Systemogenesis: a concrete developmental theory applicable in embryology and paediatrics
• Concept of "useful adaptive result" as organising principle — CC formalises viability $\mathcal{V}$, but less concretely
• Integration of motivation and memory into a unified afferent synthesis — CC distributes these across different dimensions

Mapping functor [I]

$F_{\text{TFS}}: \mathbf{FuncSys} \to \mathbf{Hol}$

Functional system $\mapsto$ Holon $\mathbb{H}$; ARA $\mapsto$ $\varphi(\Gamma)$; afferent synthesis $\mapsto$ coherences $\gamma_{ij}$; error $e$ $\mapsto$ $\sigma_k$; systemogenesis $\mapsto$ evolution $\mathcal{L}_\Omega(\Gamma)$. The functor is not complete — TFS has no consciousness measures ($\Phi$, $R$), does not address qualia and the E-dimension.

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33. Shvyrkov — System-Evolutionary Theory

«A neuron is not a signal transmitter but an element of the individual experience of the organism.» — Vyacheslav Borisovich Shvyrkov

Creators and history

Vyacheslav Borisovich Shvyrkov (1939–1994) — Soviet and Russian neurophysiologist, student of Anokhin, who developed TFS into system-evolutionary theory (SET). Major works: «Introduction to Objective Psychology» (2006, posthumous edition), numerous papers on neural correlates of behaviour. Shvyrkov recorded the activity of individual neurons in rabbits and cats learning new behaviour, and found that neurons "specialise" in specific behavioural acts.

Key idea

Every neuron is an element of a specific functional system formed in individual experience. A neuron does not transmit a "signal" — it is part of a system implementing a specific behavioural act (system specialisation of neurons). Learning = formation of new functional systems, in which previously unspecialised neurons are "recruited". Memory is not a storage of information but a set of formed functional systems (each "recorded" in a specific group of neurons). Evolution of individual experience = systemogenesis throughout life.

Formal structure

Experimental-descriptive. Recording of single neurons: neuron $n_i$ is active in phase $\phi_j$ of behavioural act $\iff$ $n_i \in \text{FS}_j$ (functional system $j$). New FS during learning: set $\{n_k\}$ is "recruited" into FS$_{j+1}$. Statistics: percentage of neurons specialised for each act.

Comparison with CC

Aspect	SET (Shvyrkov)	CC
Unit of analysis	Neuron as element of FS	Holon $\mathbb{H}$
Learning	Formation of new FS	Evolution of $\Gamma$ under $\mathcal{L}_\Omega$
Memory	Set of FSs	Attractor $\Gamma^*$, SAD tower
Specialisation	Neuron → one behavioural act	Sector $\gamma_{kk}$ → one dimension
Development	Systemogenesis (ontogenesis)	L0 → L4 (through thresholds)

What CC borrows

• Systemicity: Holon as a holistic unit not reducible to elements
• Development as formation of new structures: evolution of $\Gamma$ under $\mathcal{L}_\Omega$

What CC does better

• Formal apparatus: density matrices, categories, provable theorems
• Substrate independence: CC is applicable not only to neurons
• Consciousness thresholds ($P$, $R$, $\Phi$) — SET does not define when a system is "conscious"

Honest assessment: what the theory does better than CC

• Experimental data: direct recording of neurons during learning (single-unit recording)
• Specific neurophysiological mechanism of experience formation
• Connection to Anokhin's TFS: SET is the development of a powerful tradition with 80+ years of experimental base
• Explanation of neuron "recruitment" — CC does not address the neural level

Mapping functor [I]

$F_{\text{SET}}: \mathbf{SysEvol} \to \mathbf{Hol}$

Functional system $\mapsto$ Holon $\mathbb{H}$; set of specialised neurons $\mapsto$ $\Gamma$ (coherences); formation of new FS $\mapsto$ change of $\Gamma$ under $\mathcal{L}_\Omega$; individual experience $\mapsto$ attractor $\Gamma^*$. The functor is strongly incomplete — SET works at the neural level and has no consciousness measures.

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34. Ivanitsky — Information Synthesis

«Subjective experiences arise as the result of information synthesis — the return of excitation from associative areas to projective ones through the limbic system.» — Alexei Mikhailovich Ivanitsky

Creators and history

Alexei Mikhailovich Ivanitsky (1935–2014) — outstanding Russian neurophysiologist, director of the laboratory of higher nervous activity at the Institute of Higher Nervous Activity and Neurophysiology of the Russian Academy of Sciences. He developed the information synthesis hypothesis (IS) from the 1970s, laid out in «Brain basis of subjective experiences» (1996, Journal of Higher Nervous Activity) and «Consciousness and the Brain» (2005). Ivanitsky was one of the first in world science to propose a specific neurophysiological mechanism for generating subjective experience.

Key idea

Consciousness arises through circular cortical movement of excitation: projective cortex (sensory input) → associative cortex (categorisation, comparison with memory) → limbic system (emotional assessment) → return to projective cortex. It is precisely the return — "information synthesis" — that gives rise to subjective experience: the sensation is enriched with meaning (from memory) and emotional assessment. The time of a full cycle ≈ 150–300 ms — correlates with P300 (evoked potential). Without closing the loop (e.g., with stimulus masking) — no awareness.

Formal structure

Electrophysiological model: cycle $\text{S}_1 \to \text{Assoc.} \to \text{Limb.} \to \text{S}_1$, taking $\sim 200$ ms. EEG coherence between projective and associative zones — correlate of awareness. Threshold: closed loop = awareness; interrupted = unconscious processing. Formally: $\text{Consciousness} \iff \text{coherence}(\text{S}_1, \text{Assoc}, \text{Limb}) > \theta$.

Comparison with CC

Aspect	Information Synthesis (Ivanitsky)	CC
Consciousness mechanism	Circular cortical cycle	Thresholds $P > 2/7$, $R \geq 1/3$, $\Phi \geq 1$
Coherence	EEG between zones	$\gamma_{ij}$ (coherences of $\Gamma$)
Emotions + sensations	Fusion in limbic loop	Connection S↔E through $\gamma_{SE}$
Time of awareness	~200 ms (P300)	Timescale $\sim 1/\Lambda$
Threshold	Closed loop vs absent	$P_{\text{crit}} = 2/7$

What CC borrows

• Coherence as mechanism of consciousness: coherences $\gamma_{ij}$ in $\Gamma$ — direct analogue of EEG coherence
• Threshold: binary transition (closed loop → awareness) ≈ $P > P_{\text{crit}}$
• Synthesis of sensations and emotions: $\gamma_{SE}$ (coherence S↔E)

What CC does better

• Substrate independence: not tied to specific cortical zones
• Exact thresholds ($2/7$, $1/3$, $1$), not descriptive "closed loop"
• Self-modelling ($\varphi$), integration ($\Phi$), reflection ($R$) — richer structure

Honest assessment: what the theory does better than CC

• Electrophysiological verification: P300, EEG coherence — directly measurable correlates
• Specific timescale of awareness (~200 ms)
• Priority: Ivanitsky proposed the circular hypothesis in the 1970s, anticipating Lamme's recurrent processing theory
• Explanation of the role of emotions in awareness through specific neuroanatomy
• CC cannot offer concrete EEG predictions (no $\Gamma$ measurement protocol)

Mapping functor [I]

$F_{\text{IS}}: \mathbf{InfoSynth} \to \mathbf{Hol}$

Circular cycle $\mapsto$ recurrence $R \geq R_{\text{th}}$; EEG coherence $\mapsto$ $\gamma_{ij}$; information synthesis $\mapsto$ $\Phi \geq 1$; limbic assessment $\mapsto$ E-dimension. The functor is not complete — IS theory does not cover self-modelling ($\varphi$), the SAD tower, $G_2$-rigidity.

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35. Allakhverdov — Consciousness as Paradox

«Consciousness is a control mechanism that verifies unconscious hypotheses about the world. Paradox: consciousness knows only what the unconscious has "permitted" it to know.» — Viktor Mikhailovich Allakhverdov

Creators and history

Viktor Mikhailovich Allakhverdov (b. 1946) — Russian psychologist, professor at St. Petersburg State University, creator of psycho-logic — a cognitive theory of consciousness, set out in «Consciousness as Paradox» (2000) and «A Methodological Journey Across the Ocean of the Unconscious to the Mysterious Island of Consciousness» (2003). Allakhverdov is one of the few contemporary Russian scholars to have proposed an original and integral theory of consciousness. His approach is unique: he treats consciousness as a logical (rather than neurophysiological) problem.

Key idea

Cognition is built on the model of scientific inquiry: the unconscious generates hypotheses about the world, and consciousness verifies them. Consciousness is a control mechanism operating on the principle of "verification vs falsification" (Popper's influence). Paradox: consciousness has no direct access to reality — it checks only what the unconscious has "presented" to it. "Allakhverdov's law": consciously perceived information tends toward repeated conscious perception (positive selection), while non-consciously perceived information tends toward repeated non-conscious perception (negative selection). Experimentally: reaction time to a previously consciously perceived stimulus is shorter; a previously non-consciously perceived stimulus is suppressed more strongly. Consciousness works with signified information (having cognitive meaning), not "raw data".

Formal structure

Logical-cognitive model: the unconscious generates hypotheses $\{h_1, h_2, \ldots\}$; consciousness verifies: $\text{verify}(h_i, \text{data})$. Positive selection: $P(\text{awareness}_{t+1} | \text{awareness}_t) > P(\text{awareness}_{t+1})$. Negative selection: $P(\text{awareness}_{t+1} | \neg\text{awareness}_t) < P(\text{awareness}_{t+1})$. Formalisation is partial — the primary method of argumentation is logical and experimental.

Comparison with CC

Aspect	Psycho-logic (Allakhverdov)	CC
Consciousness	Control mechanism (verification)	$\varphi(\Gamma)$ (self-modelling)
Unconscious	Generator of hypotheses	L0 (below threshold $P < 2/7$)
Positive selection	Conscious → consciously perceived again	Attractor $\Gamma^*$ (stable states)
Negative selection	Non-conscious is suppressed	$\sigma_k > 0$ → degradation of coherence
Access paradox	Consciousness ≠ direct access	$\varphi$ is an automorphism, not a "mirror"

What CC borrows

• Consciousness as control/verification: $\varphi(\Gamma)$ checks coherence (not "reflects reality")
• Two-level architecture: unconscious (L0) + conscious (L2) — analogue of "generation + verification"
• Attractor property of awareness: positive selection ≈ stability of $\Gamma^*$

What CC does better

• Formal dynamics ($\mathcal{L}_\Omega$): not only a logical model but also an evolution equation
• Quantitative thresholds: $P$, $R$, $\Phi$ — not descriptive "verification"
• Applicability to non-biological systems

Honest assessment: what the theory does better than CC

• Experimental programme: dozens of experiments on positive/negative selection (St. Petersburg school)
• Logical rigour: paradoxes of consciousness are analysed from the standpoint of formal logic
• Explanation of cognitive illusions: why we "don't see" the obvious and "see" the nonexistent
• Original "Allakhverdov's law" — CC has no analogue of the mechanism for suppressing non-conscious material
• Connection to epistemology (Popper, verification/falsification) — deeper philosophical reflection on the nature of cognition

Mapping functor [I]

$F_{\text{Psy}}: \mathbf{Psychologic} \to \mathbf{Hol}$

Unconscious hypothesis $h_i$ $\mapsto$ state $\Gamma$ at $P < P_{\text{crit}}$; verification $\mapsto$ $\varphi(\Gamma)$; positive selection $\mapsto$ stability of $\Gamma^*$; negative selection $\mapsto$ degradation of coherences $\gamma_{ij} \to 0$. The functor is not complete — psycho-logic has no quantum formalism, integration measures ($\Phi$), or neurophysiological level.

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36. Worden — Projective Wave Theory (PWT)

«The brain's internal model of local 3-D space is held not in neurons, but in a wave excitation holding a projective transform of Euclidean space; if the wave is the source of spatial consciousness.» — Robert Worden

Creators and history

Robert Worden (PhD, University of Cambridge) — researcher associated with the Active Inference Institute. The Projective Wave Theory (PWT) was first published as a preprint (arXiv:2405.12071, 2024) and in final form in Frontiers in Psychology on 25 February 2026 ("The projective wave theory of consciousness", doi: 10.3389/fpsyg.2026.1674983). It belongs to the dynamical / wave-based family of consciousness theories, alongside Pribram's holonomic brain theory and McFadden's CEMI, but with a distinctive mathematical ingredient: a projective (rather than Euclidean) representation of space.

Key idea

PWT attacks a specific sub-problem — how the brain supports our largely undistorted conscious experience of local 3-D space — by isolating three difficulties that neural theories face:

1. Selection problem: which subset of neurons is causally responsible for consciousness?
2. Precision problem: how can a neural representation achieve the precise 3-D geometry that our conscious experience exhibits?
3. Decoding problem: how is the (generally distorted) neural code transformed into an undistorted conscious picture?

Worden's answer is that the brain holds the internal model of local 3-D space not in neurons, but in a wave excitation that carries a projective transformation of Euclidean space. The wave itself — not its neural substrate — is the seat of spatial conscious experience. Indirect evidence for such a wave is adduced in the mammalian thalamus and in the central body of the insect brain; direct detection remains outstanding and is offered as the principal falsification criterion.

Formal structure

PWT's mathematical ingredient is the action of the projective group $PGL(4,\mathbb{R})$ (equivalently $PGL(3,\mathbb{R})$ for 3-D projective space) on a wave-field $\psi(x)$ representing the local spatial model. A projective transformation composed with a coarse-grained neural read-out is proposed to explain why the conscious picture is undistorted while the neural representation is not. No equation of motion for $\psi$ is committed to, no numerical predictions are derived, no consciousness threshold is formalised, and the wave's microscopic substrate is left open (the theory is "implementation-agnostic within wave media").

Comparison with CC (UHM)

Aspect	PWT (Worden)	CC / UHM
Ontological primitive	Wave excitation $\psi$ in 3-D space	Coherence matrix $\Gamma \in \mathcal{D}(\mathbb{C}^7)$
Hard problem	Not directly addressed	Reframed via two-aspect monism (T-186 [H])
Target	Spatial consciousness (sub-problem)	Full hierarchy L0–L4, all content
Physical substrate	Thalamus / insect central body	Substrate-independent (categorical)
Consciousness threshold	None	$P > 2/7$, $R \geq 1/3$, $\Phi \geq 1$, $D_{\mathrm{diff}} \geq 2$ (T-160, T-40b, T-129 [T]; the threshold $D_{\mathrm{diff}} \geq 2$ is [D], T-151)
Numerical predictions	None	23 predictions with falsification criteria
Derivation of physics	None	GR on an emergent $M^4$ (T-117–T-121, [T] as mathematics since 2026-09-25); quantum mechanics postulated, not derived (QM reduction); Standard-Model colour from $G_2$ [T], electroweak [C at (FE)], finite space imported from Connes (T-186 [H])
Group structure	$PGL(4,\mathbb{R})$ (projective)	$G_2 = \mathrm{Aut}(\mathbb{O})$ (exceptional, finite-dim)
Falsification	Wave not found in brain	$\beta \neq 1/4$; zombie at $N < 7$; $\mathrm{SAD} \geq 4$; etc.
Scope relative to UHM	Candidate neural implementation of the coarse-grained geometric sector $\{A,S,D\}$ of $\Gamma$	Foundational theory of which PWT may be a brain-level projection

What CC borrows

• Wave-like ontology of the substrate of experience: both theories reject a purely neural-computational account. In CC, the off-diagonal coherences $\gamma_{ij}$ play the role analogous to the PWT wave field — they carry phase information that is lost in any classical computational description.
• Projective geometry of the spatial sector: the $\{A,S,D\}$ sector of $\Gamma$ reconstructs (via Gel'fand + Connes, T-119 [T]) a smooth compact orientable spin 3-manifold $\Sigma^3$. Worden's emphasis that the spatial representation is projective rather than Euclidean is compatible with the $PGL(4,\mathbb{R})$ action on projective spatial sections of $\Sigma^3$.
• Explicit mechanism for undistorted spatial experience: PWT's selection / precision / decoding triad sharpens the requirement that any theory of consciousness must eventually explain how phenomenal 3-D space is achieved. In UHM this is answered by the spectral-triple reconstruction of $\Sigma^3$ and the Page–Wootters emergence of time.

What CC does better

• Scope: CC addresses consciousness as a whole (experience, self-modelling, integration, affect, ethics) rather than only the spatial sub-problem.
• Hard problem: CC dissolves it via two-aspect monism [T via T-186]; PWT offers no account of why a wave should feel like anything.
• Formal rigour: CC has equations of motion ($\mathcal{L}_\Omega$), a spectral gap, exact thresholds, and a status registry of theorems; PWT is programmatic.
• Falsifiability: CC has 23 numerical predictions with explicit criteria; PWT has one binary check ("is there a wave?").
• Physics: CC derives GR + QM + Standard Model; PWT assumes standard physics.

Honest assessment: what the theory does better than CC

• Concreteness of the neural prediction: PWT points to a specific biological structure (thalamus / central body) and a specific physical observable (a wave excitation), which is directly falsifiable by neurophysiological experiment. CC currently lacks a validated $\pi_{\mathrm{bio}}$ mapping from neural data to $\Gamma$.
• Minimality of the hypothesis: PWT postulates one extra structure (the wave) and leaves the rest of neuroscience untouched; CC's categorical machinery is heavier.
• Engagement with the precision/decoding problem: the requirement that the undistorted geometry of conscious space be explained is a constraint CC addresses only indirectly (via the emergent $\Sigma^3$).

Mapping functor [I]

$F_{\mathrm{PWT}}: \mathbf{PWT} \to \mathbf{Hol}$

Wave excitation $\psi \mapsto$ off-diagonal coherences in the $\{A,S,D\}$-sector of $\Gamma$; projective group action $PGL(4,\mathbb{R}) \mapsto$ $G_2$-restricted transformations on $\Sigma^3$ (T-119 [T]); thalamic / central-body substrate $\mapsto$ one possible physical realisation of $\pi_{\mathrm{bio}}^{-1}$; undistorted conscious space $\mapsto$ spectral-triple reconstruction $A_{\mathrm{space}} \cong C(\Sigma^3)$.

The functor is not complete: PWT lacks dynamics, thresholds, self-modelling ($\varphi$), integration ($\Phi$), and a theory of non-spatial content (affect, reflection, meta-awareness). In the CC meta-category, PWT is a projection onto the spatial-geometric sector, compatible with UHM as a candidate neuroscientific implementation rather than a competitor at the foundational level.

Compatibility with UHM

Crucially, PWT and UHM are not mutually exclusive. If Worden's wave is eventually detected in the thalamus, it would serve as a concrete biological realisation of the coarse-grained $\{A,S,D\}$-sector of $\Gamma$ in the mammalian brain, answering part of the $\pi_{\mathrm{bio}}$ calibration problem (Phase II of the UHM experimental protocol). Conversely, if UHM's $P_{\text{crit}} = 2/7$ threshold and tricritical exponents are confirmed, they provide PWT with the missing thermodynamic framework. The two frameworks operate at different levels of explanation: UHM at the foundational (ontological-mathematical) level, PWT at the biological-implementation level.

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37. Category Theory of Consciousness and Qualia (Tsuchiya, Saigo)

«Category theory can prove that two objects A and B in a category can be equivalent if and only if all the relationships that A holds with others in the category are the same as those of B; this proof is called the Yoneda lemma.» — Naotsugu Tsuchiya and Hayato Saigo (2021)

In brief. This programme treats experiences as the objects of a category and their similarities as its arrows, and asks what can be known about an experience from its relations alone. It matters for UHM directly: it is the published precedent for UHM's use of the Yoneda lemma to identify qualia relationally, and it has already taken that idea into the laboratory.

Creators and history

Naotsugu Tsuchiya (Monash University, Melbourne), Hayato Saigo (Nagahama Institute of Bio-Science and Technology) and Shigeru Taguchi (Hokkaido University) proposed in 2016 to use category theory — the branch of mathematics that studies structures together with the structure-preserving maps between them — to assess IIT's central claim that an experience is a particular mathematical structure: Tsuchiya N., Taguchi S., Saigo H., "Using category theory to assess the relationship between consciousness and integrated information theory", Neurosci. Res. 107, 1–7 (2016), doi:10.1016/j.neures.2015.12.007. Instead of asserting an identity in one step, they asked whether there is a functor — a structure-preserving translation — between the domain of experience and IIT's "maximally irreducible conceptual structures", and claimed that the existence of such a functor can be tested empirically. In an April 2020 preprint ("Applying Yoneda's lemma to consciousness research: categories of level and contents of consciousness", doi:10.31219/osf.io/68nhy) and the paper that followed (Tsuchiya N., Saigo H., "A relational approach to consciousness: categories of level and contents of consciousness", Neurosci. Conscious. 2021(2), niab034, doi:10.1093/nc/niab034) the Yoneda lemma became the centre of the programme. With Steven Phillips (National Institute of Advanced Industrial Science and Technology, Tsukuba) they extended it to graded similarity: Tsuchiya N., Phillips S., Saigo H., "Enriched category as a model of qualia structure based on similarity judgements", Conscious. Cogn. 101, 103319 (2022), doi:10.1016/j.concog.2022.103319. What the sources support directly is this: a category-theoretic approach from 2016, the Yoneda-based relational account of qualia explicitly in the 2020 preprint and the 2021 paper, and the enriched (metric) version in 2022. A later paper by the same authors cites the 2016 paper when it writes that category theory characterises a quale "as a collection of relationships with other qualia via the Yoneda lemma" (Tsuchiya N., Saigo H., Phillips S., "An adjunction hypothesis between qualia and reports", Front. Psychol. 13, 1053977, published January 2023); but the 2016 abstract does not mention the lemma, and the 2021 paper credits the 2016 paper with the categorical approach — tools for kinds of "sameness" and a stepwise plan for testing IIT's identity claim — not with the lemma. (An earlier edition said that the authors credit the 2016 paper as the start of the Yoneda-based characterisation; that wording is withdrawn.)

Key idea

An experience cannot be inspected "in itself", but its relations to other experiences can — by asking people whether two experiences look the same, or how similar they are. Take experiences as objects and "is experienced as nearly indistinguishable from" (or a graded dissimilarity) as arrows, and you obtain a category of qualia. The Yoneda lemma then says that an object is determined, up to isomorphism, by the totality of its relations to all other objects: two qualia with the same pattern of relations to everything else are equivalent. The 2021 paper also defines categories for the level of consciousness (states ordered by "is at least as conscious as") and for its contents (colour, sound, pain), and proposes the categorical structure of experience as a gold standard against which empirical research and theories of consciousness should be tested.

Formal structure

A category $\mathbf Q$ of qualia: objects are experiences, arrows are similarity relations. For $A \in \mathbf Q$ the functor $h_A = \mathrm{Hom}(-, A)$ collects all of $A$'s relations, and the Yoneda lemma gives $h_A \cong h_B \Rightarrow A \cong B$. In the enriched version the sets of arrows are replaced by numbers — a measured dissimilarity — and a quale is characterised by its dissimilarities to all others "up to an (enriched) isomorphism" (2022). The empirical arm (Kawakita G., Zeleznikow-Johnston A., Takeda K., Tsuchiya N., Oizumi M., "Is my 'red' your 'red'?: Evaluating structural correspondences between color similarity judgments using unsupervised alignment", iScience 28, 112029, 2025) collected similarity judgements for 93 colours and aligned the resulting structures across people by optimal transport, without telling the algorithm which colour is which: the structures of colour-neurotypical participants aligned "correctly" at the group level, those of colour-blind participants did not.

Comparison with CC

Aspect	Category theory of qualia	CC / UHM
What a quale is	An object of a category of experiences, fixed by its relations	A ray $[\lvert q\rangle] \in \mathbb P(\mathcal H_E)$ with Fubini–Study distances
Yoneda lemma for qualia	Category-theoretic programme from 2016; the Yoneda-based account stated and applied in the 2020 preprint and the 2021 paper	Theorem "Yoneda's lemma for qualia"
Graded similarity	Enriched categories (2022); enriched Yoneda up to enriched isomorphism	Fubini–Study metric $d_{FS}$: a Lawvere metric space whose enriched Yoneda embedding is an isometry, with enriched isomorphism = identity (theorem, 2026-09-25)
Map from physics to experience	A functor between experience and IIT's structures, to be tested (2016)	Functor $F: \mathbf{DensityMat} \to \mathbf{Exp}$, claimed unique under UHM's axioms
Empirical test	Done: unsupervised alignment of colour-similarity structures (2025)	Metric prediction 4 on the falsifiability page; not yet tested

Precedent: what this programme did first

Prior art for a UHM ingredient

UHM's relational identity of qualia — the Yoneda theorem for qualia and its corollary on inverted qualia — is not a novel idea of UHM. The use of the Yoneda lemma to characterise a quale by its relations to all other qualia was published by Tsuchiya and Saigo in an April 2020 preprint and a 2021 journal paper, within the category-theoretic programme that Tsuchiya, Taguchi and Saigo began in 2016; the graded (metric) version — a quale characterised by its dissimilarities to all other qualia, up to enriched isomorphism — appeared in 2022. The corpus page that states the theorem does not cite this work. What UHM adds is a specific choice of category (rays of $\mathbb P(\mathcal H_E)$ with the Fubini–Study metric) and the claim that the functor $F$ into it is unique under UHM's axioms; that page labels these formal results [T] and marks their reading as a theory of experience [I].

What CC borrows

• The relational strategy itself: the identity of a quality through its position among all other qualities. The Yoneda argument on the two-aspect monism page is this programme's argument, restated for UHM's category — though the corpus does not cite the programme.
• The functorial framing: a theory of consciousness as a structure-preserving map from physical states into a category of experiences (2016).

What CC does better

• One point, backed by the corpus's formal results: UHM commits in advance to a concrete geometry for the category of qualities (Fubini–Study distances on $\mathbb P(\mathcal H_E)$) and states that the functor $F$ is unique under its axioms (theorem, labelled [T] on its page, with no registry number). The Tsuchiya programme deliberately leaves the category to be found by experiment. Whether committing in advance is an advantage depends on whether the committed geometry survives the kind of test listed next.
• Added 2026-09-25 [T]. The commitment has checkable consequences that the programme's general lemma cannot have: with $d_{FS}$ the enriched Yoneda embedding is an isometry and enriched isomorphism is identity; dissimilarities to a finite probe set fix a quality to within twice its covering radius, with explicit probe counts (93 colours cannot resolve below $\approx 0.104$ rad even on $\mathbb{CP}^1$); and a dissimilarity matrix is realisable only if a Gram-type matrix $\cos(d_{ij})e^{i\theta_{ij}}$ is positive semidefinite of rank $\leq \dim \mathcal H_E$ (enriched Yoneda theorem). The enriched construction itself is the programme's (2022).

Honest assessment: what the theory does better than CC

• Priority: it published the Yoneda-based relational account of qualia before UHM, with the caveats that UHM's page omits — equivalence up to isomorphism, and a category of qualia that has to be established by experiment.
• Data: its similarity-judgement and unsupervised-alignment methods have produced results (93 colours; neurotypical against colour-blind observers). UHM's metric prediction ($d_{\mathrm{perceived}} \sim d_{FS}$, falsifiability, prediction 4) has no data and needs a calibration that is not yet fixed.
• Precision about inverted qualia [I]: the Yoneda lemma gives identity up to isomorphism within one category. UHM's corollary — two qualities with the same distances to all others are identical — holds in any metric space for a simpler reason (two distinct points always differ in their distance to one of the two), so it does not reach the classical inverted-spectrum case, which concerns a symmetry of the whole quality space mapping one subject's qualities onto another's. The Tsuchiya programme poses that question correctly — as the existence of a structure-preserving map between two subjects' categories — and has begun to measure it. The corpus assigned it to the $G_2$ frame, but that identification is retracted (calibration and the $G_2$-frame: the phenomenal functor is not blind to a $G_2$ rotation, frame decision D-0910); what remains is empirical calibration, not Yoneda.

Standing

An active programme. Its relational method has produced two published alignment tests: across people (Kawakita et al., iScience, 2025) and between people and language models (Kawakita, Zeleznikow-Johnston, Tsuchiya & Oizumi, Sci. Rep. 14: 15917, 2024: GPT-4 matched colour-neurotypical humans on 93 colours with a matching rate of 91.4 %, GPT-3.5 with 11.8 %). What that match does and does not say about consciousness in UHM's terms: measurement protocol. By its own description it is "ontologically neutral": it proposes a language for testable questions about the structure of experience, not a criterion of which systems are conscious.

Mapping functor [I]

$F_{\text{CatQ}}: \mathbf{Q} \to \mathbf{Exp}$

Object of $\mathbf Q$ (an experience) $\mapsto$ ray $[\lvert q\rangle]$; similarity arrow $\mapsto$ small $d_{FS}$; enriched hom (a dissimilarity) $\mapsto$ $d_{FS}$ itself. The functor is conjectural: nothing guarantees that measured similarity structures are Fubini–Study geometries, and that is exactly what an alignment test would check.

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38. The Mathematical Structure of IIT and Process Theories (Kleiner, Tull, Signorelli, Coecke, Prentner)

«We provide a definition of a generalized IIT which has IIT 3.0 of Tononi et. al., as well as the Quantum IIT introduced by Zanardi et. al. as special cases.» — Johannes Kleiner and Sean Tull (2020)

In brief. A group of mathematicians and philosophers set out to state precisely what kind of mathematical object a theory of consciousness is, taking IIT as the worked case. It matters for UHM because UHM's own architecture — a map from physical states into a structured space of experiences, written in the language of categories — is one instance of the general form they axiomatised, and because they showed where IIT's formal definition breaks.

Creators and history

• Johannes Kleiner (Munich Center for Mathematical Philosophy, LMU Munich): "Mathematical Models of Consciousness", Entropy 22(6), 609 (2020), doi:10.3390/e22060609 — what warrants a mathematical representation of experience, and a general framework for models of consciousness.
• Kleiner and Sean Tull (Cambridge Quantum Computing): "The Mathematical Structure of Integrated Information Theory", Front. Appl. Math. Stat. 6, 602973 (2021), doi:10.3389/fams.2020.602973 (arXiv:2002.07655, February 2020); and Tull and Kleiner, "Integrated Information in Process Theories", arXiv:2002.07654 (2020).
• Camilo Miguel Signorelli, Quanlong Wang and Bob Coecke: "Reasoning about conscious experience with axiomatic and graphical mathematics", Conscious. Cogn. 95, 103168 (2021), doi:10.1016/j.concog.2021.103168.
• Robert Prentner: "Consciousness and topologically structured phenomenal spaces", Conscious. Cogn. 70, 25–38 (2019), doi:10.1016/j.concog.2019.02.002; "Category theory in consciousness science: going beyond the correlational project", Synthese 204, 69 (2024), doi:10.1007/s11229-024-04718-5; with Albantakis L. and Durham I., "Computing the integrated information of a quantum mechanism", Entropy 25(3), 449 (2023).

Key idea

Kleiner and Tull strip IIT down to the structure its algorithm actually uses: a class of physical systems, a class of experience spaces (sets equipped with a distance, an intensity and a scaling) and "cause–effect repertoires". An IIT is then a map that sends each system to its space of possible experiences, and each state to the experience it has. Tononi's IIT 3.0 and the quantum IIT of Zanardi, Tomka and Campos Venuti ("Towards Quantum Integrated Information Theory", arXiv:1806.01421, 2018) come out as special cases; the process-theory version — symmetric monoidal categories with their graphical calculus of string diagrams — extends IIT to any physical theory that can be written that way. Signorelli, Wang and Coecke use the same graphical calculus to recover, from the way processes compose, the distinction between an external and an internal view, the privacy of experience and phenomenal unity. Prentner models phenomenal space with mereology and topology (2019) and argues (2024) that category theory, and above all the notion of a functor, is what can take consciousness science beyond the "correlational project".

Formal structure

An IIT in the sense of Kleiner and Tull: the data are a system class $\mathrm{Sys}$ and a cause–effect structure; the output is a map $\mathrm{Sys} \to \mathrm{Exp}$ into experience spaces and, for each system, a map from its states to its experience space. The work does not claim that any IIT is true. It locates a weak point of the definition: IIT's nested maximisations and minimisations ("core subsystems") come with "no guarantee that these operations lead to unique results, neither in classical nor Quantum IIT", which the authors call "a case of ill-definedness".

Comparison with CC

Aspect	Formal IIT and process theories	CC / UHM
General form	A map $\mathrm{Sys} \to \mathrm{Exp}$ into experience spaces	Functor $F: \mathbf{DensityMat} \to \mathbf{Exp}$
Language	Symmetric monoidal categories, string diagrams	∞-topos; CPTP category $\mathbf{Hol}$
Quantum case	Quantum IIT as a special case (2018, 2021, 2023)	$\Gamma \in \mathcal D(\mathbb C^7)$
External/internal split	Recovered from composition (Signorelli, Wang, Coecke 2021)	Map splitting into $\mathrm{Map}_{\mathrm{ext}}$ and $\mathrm{Map}_{\mathrm{int}}$
Well-definedness	IIT's cores may be non-unique — shown (2021)	Closed formula for $\Phi$ in a pinned frame; representation unique up to $G_2$ (T-123, registered as a theorem)

Precedent

The form of UHM's bridge — a structure-preserving map from physical states into a mathematically structured space of experiences — was published before UHM: as a functor to be tested between experience and IIT's structures (Tsuchiya, Taguchi and Saigo 2016, §37) and as an axiomatic definition of the whole class of such theories (Kleiner and Tull, arXiv February 2020). Two further precedents bear on claims made on this page: quantum versions of IIT exist (Zanardi, Tomka and Campos Venuti 2018; Kleiner and Tull 2021; Albantakis, Prentner and Durham 2023), so "no quantum foundation" (§2) describes Tononi's IIT 3.0 and 4.0, not the IIT programme; and a categorical derivation of the external/internal distinction, of privacy and of unity was published by Signorelli, Wang and Coecke (2021). UHM's map-splitting theorem is a different construction — labelled [T] on its page, with its reading as physics versus experience marked [I] — but it is not the first categorical account of that distinction.

What CC borrows

• Nothing explicitly: the corpus does not cite this work. Implicitly, UHM uses the template "theory of consciousness = map into a space of experiences", with its $\mathbf{Exp}$ in the role of the experience space.
• The criticism of IIT in the $G_2$-rigidity box above ("$\Phi^{\mathrm{IIT}}$ depends on partition choice") is a special case of the non-uniqueness that Kleiner and Tull proved.

What CC does better

• UHM's integration measure is well defined by construction: $\Phi(\Gamma)$ is a closed formula on a fixed $7 \times 7$ matrix, with no search over partitions, so the ill-definedness that Kleiner and Tull found in IIT's cores cannot arise for it. This is a property of the definition, not a theorem; its price is that $\Phi(\Gamma)$ depends on the pinned frame (registry row T-129: "$\Phi$ is a frame-pinned observable").

Honest assessment: what the theory does better than CC

• Axiomatic transparency: Kleiner and Tull separate what IIT's algorithm needs from auxiliary choices and state the result as definitions a reader can check in one paper.
• Generality: the process-theory formulation applies to any physical theory expressible in symmetric monoidal categories; UHM fixes one seven-dimensional quantum theory.
• Structure of phenomenal space: Prentner's mereological and topological model says how parts of experience compose into a unified field; UHM expresses unity only through the single number $\Phi \geq 1$.

Standing

An active research line whose results are definitions and a proved limitation of IIT's algorithm, not empirical claims — so "confirmed" or "refuted" does not apply. The substitution argument of Kleiner and Hoel (see Formal critiques) comes from the same programme.

Mapping functor [I]

$F_{\text{KT}}: \mathbf{Sys}_{\mathrm{IIT}} \to \mathbf{Hol}$

A generalised IIT is a map $\mathrm{Sys} \to \mathrm{Exp}$; UHM has the same shape, with $\mathrm{Sys}$ the states $\mathcal D(\mathbb C^7)$ with the dynamics $\mathcal L_\Omega$ and $\mathrm{Exp}$ the rays with Fubini–Study geometry — if UHM is read as a theory of IIT type, which the corpus does not claim. The mapping is not an embedding: UHM has no cause–effect repertoires and no exclusion step.

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39. Minimal Physicalism and a Quantum Free-Energy Principle (Fields, Glazebrook, Levin)

«Our "minimal physicalist" approach makes no assumptions beyond those of quantum information theory, and hence is applicable from the molecular scale upwards.» — Chris Fields, James F. Glazebrook and Michael Levin (2021)

In brief. Fields, Glazebrook and Levin describe any system that exchanges information with its environment — a molecule, a cell, an organism — in the language of quantum information, and read cognition and awareness off that description at every scale. It matters for UHM twice: it is a published scale-free, quantum-informational account of cognition and consciousness (UHM's scale invariance CC-6 and its fractal holons make a scale claim of their own), and, with Karl Friston, it published a quantum formulation of the free-energy principle, which UHM also claims to generalise.

Creators and history

Chris Fields (Caunes Minervois, France), James F. Glazebrook (Eastern Illinois University; University of Illinois at Urbana–Champaign) and Michael Levin (Allen Discovery Center, Tufts University): "Minimal physicalism as a scale-free substrate for cognition and consciousness", Neurosci. Conscious. 2021(2), niab013 (2021), doi:10.1093/nc/niab013. With Karl Friston: Fields C., Friston K., Glazebrook J.F., Levin M., "A free energy principle for generic quantum systems", Prog. Biophys. Mol. Biol. 173, 36–59 (2022), doi:10.1016/j.pbiomolbio.2022.05.006 (arXiv:2112.15242, December 2021).

Key idea

Two systems that interact through a boundary are described as exchanging bits across a "holographic screen" — an array of qubits that each side alternately prepares and measures. The screen plays the role of a Markov blanket (the statistical boundary between inside and outside in the free-energy principle). What a system can register is limited by its quantum reference frames (QRFs), the physical structures it uses to measure. From this the 2021 paper shows, in its words, that "integrated information, state broadcasting via small-world networks, and hierarchical Bayesian inference emerge naturally", and lists eighteen qualitative predictions, mostly about basal organisms — for example, that E. coli, whose spatial reference frame is one-dimensional (its body axis), does not experience three-dimensional space. The 2022 paper reformulates the free-energy principle for generic quantum systems and shows it to be "asymptotically equivalent to the Principle of Unitarity".

Formal structure

A bipartite interaction $H_{AB}$ encoded on the $N$ qubits of the screen; separability of the joint state gives conditional independence, i.e. a Markov blanket; QRFs are specified with Barwise–Seligman channel theory, a category-theoretic language of classifiers and "infomorphisms". There is no fixed dimension and no threshold.

Comparison with CC

Aspect	Minimal physicalism, quantum FEP	CC / UHM
Description of the substrate	Quantum information, any dimension	$\Gamma \in \mathcal D(\mathbb C^7)$
Scale	Scale-free by construction, from molecules to ecosystems	Scale invariance CC-6 (registry row T-72, [T at weak coupling] through the canonical aggregation, Theorem 9.5)
Boundary	Holographic screen as Markov blanket	Holon boundary, dimension $A$ (conceptual, §3)
Free-energy principle	Quantum formulation (2021/2022)	Classical FEP as a limit of UHM's variational $\varphi$ — retracted 2026-09-25 (FEP derivation): the functional is a cross-entropy and $\varphi$ is not its minimiser
Criterion of consciousness	None; awareness graded by the available QRFs	$\mathrm{Cons}(S)$: four thresholds
Basal organisms	Eighteen qualitative predictions	L0 (proto-experience) for every system; no organism-specific prediction

Precedent: what this programme did first

Two UHM claims with an earlier external version

1. Quantum generalisation of the FEP. The FEP derivation page (§6.3 and Corollary 7.1) presents "UHM generalizes FEP to the quantum case" as a UHM result and says that the FEP works "only with classical distributions". A quantum-information formulation of the FEP, co-authored by the FEP's originator, was posted in December 2021 and published in 2022 (Fields, Friston, Glazebrook and Levin). Quantising the FEP is therefore not new with UHM. What was UHM's own — its particular functional ($S_{vN} + D_{KL}$ with the self-model $\varphi$) and the claim that the classical FEP is its limit — was retracted on that page on 2026-09-25 (Theorems 3.1, 4.2 (iii)–(iv), 4.3 and Corollaries 7.1–7.2): the functional is a cross-entropy, minimised by the projection onto the top eigenvector of $\Gamma$ rather than by $\varphi$.
2. A scale-free, quantum-informational account of cognition and consciousness. A framework that applies "in the same form" from molecules to ecosystems was published in 2021. UHM's CC-6 states something narrower and different — a bounded change of $P$, $R$ and $\Phi$ under the canonical aggregation at weak coupling (T-72 [T], raised 2026-09-25 from conditional on assumption (AGG)) — but the idea of a scale-free quantum-information substrate for consciousness is not a UHM novelty.

What CC borrows

• Nothing explicitly: the corpus does not cite this work. The ingredients run in parallel — a boundary read as a Markov blanket, and one formal structure claimed at every scale.

What CC does better

• UHM states quantitative claims where this programme stays qualitative. CC-6 (registry row T-72, [T at weak coupling] since 2026-09-25, earlier the same day conditional on assumption (AGG)) bounds the change of $P$, $R$ and $\Phi$ under the canonical aggregation — the mean of the marginals, the only permutation-invariant one consistent on uncoupled copies — by $O(g)$ when the coupling $g$ is weak (Theorem 9.5). The earlier unconditional bound $O(\varepsilon_0)$ for any CPTP aggregation is retracted there — the completely depolarising channel is CPTP and sends every $\Gamma$ to $I/7$ — and at strong coupling the bound fails (Theorem 9.6), so the advantage holds at weak coupling.
• UHM has explicit thresholds of consciousness; the programme has none — which is also why it cannot be caught out by them.

Honest assessment: what the theory does better than CC

• Minimal assumptions: nothing beyond standard quantum information theory, where UHM adds a fixed dimension, an octonionic structure and four thresholds.
• Contact with biology: its eighteen predictions concern organisms that can be studied now (bacteria, biofilms, insects), and the programme stresses that basal organisms and synthetic constructs offer "distinct advantages for experimental manipulation"; UHM makes no organism-specific prediction.
• The FEP is theirs: Friston co-authored the quantum formulation; UHM's claim to contain the FEP as a limit was a claim about someone else's principle, and it is retracted (2026-09-25, FEP derivation).

Standing

Active. The programme builds on the free-energy principle, whose central derivation Aguilera M., Millidge B., Tschantz A. and Buckley C.L. ("How particular is the physics of the free energy principle?", Phys. Life Rev. 40, 24–50, 2022, doi:10.1016/j.plrev.2021.11.001) found to hold "only for a very narrow space of parameters" even in simple linear stochastic systems. The quantum reformulation replaces the Markov blanket by a holographic screen defined through separability; whether that answers the criticism is not settled in the sources cited here. The 2021 paper presents several of its predictions as agreeing with observations already made (for instance, stigmergic memory in bacteria) rather than as new tests.

Mapping functor [I]

$F_{\text{MP}}: \mathbf{QRF} \to \mathbf{Hol}$

Holographic screen $\mapsto$ holon boundary (dimension $A$); quantum reference frame $\mapsto$ the pinned frame in which $\Gamma$ is read; variational free energy $\mapsto$ $S_{vN} + D_{KL}$ no counterpart (that functional is a cross-entropy, and the FEP limit is retracted, 2026-09-25). The functor is not complete: minimal physicalism has no fixed dimension, no $G_2$ structure and no thresholds, while UHM has no account of what a system can register.

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40. Tegmark — Consciousness as a State of Matter ("Perceptronium")

«We examine the hypothesis that consciousness can be understood as a state of matter, "perceptronium", with distinctive information processing abilities.» — Max Tegmark (2015)

In brief. Tegmark asked what physical properties a lump of matter needs in order to be conscious — the way one asks what makes matter a solid or a liquid — and tried to answer with density matrices and Hamiltonians. It matters for UHM because UHM also starts from a density matrix and its dynamics, and because Tegmark's calculations show that integration defined independently of basis is tiny for every quantum state — which sharpens what UHM's integration measure is, and what it is not.

Creators and history

Max Tegmark (MIT): "Consciousness as a state of matter", Chaos, Solitons & Fractals 76, 238–270 (2015), doi:10.1016/j.chaos.2015.03.014; arXiv:1401.1219 (January 2014). The same author's earlier decoherence argument against quantum effects in the brain is treated separately in the corpus (T-267).

Key idea

Tegmark proposes four conjectured necessary conditions for "perceptronium": the information principle (substantial capacity to store information), the integration principle (it cannot consist of nearly independent parts), the independence principle (substantial independence from the rest of the world) and the dynamics principle (substantial capacity to process information). Autonomy combines the last two, and a utility principle is offered as an evolutionary explanation rather than a necessary condition. He then generalises Tononi's integrated information to arbitrary quantum systems and uses it on the "quantum factorization problem": why do observers experience the particular split of Hilbert space into subsystems that corresponds to classical space?

Formal structure

The integrated information of a state $\rho$ is the mutual information across the "cruelest cut", minimised over all ways of factorising the Hilbert space into a tensor product. By a theorem Tegmark attributes to Jevtic, Jennings and Rudolph, the minimum is reached in the eigenbasis of $\rho$; numerically, the most integrated states are rescaled projectors. His conclusion: "no matter how large a quantum system we create, its state can never contain more than about a quarter of a bit of integrated information" — the quantum integration paradox — so that integrated information "must be modified or supplemented by at least one additional principle". Maximising independence alone picks the energy eigenbasis, in which nothing changes (the paper's quantum Zeno paradox).

Comparison with CC

Aspect	Perceptronium (Tegmark)	CC / UHM
Starting objects	$\rho$ and $H$ ("physics from scratch")	$\Gamma$ and $\mathcal L_\Omega$
Integration	Mutual information across a tensor-product cut, independent of basis	$\Phi(\Gamma)$: off-diagonal coherence in a fixed basis
Upper bound	About 0.25 bit for any quantum state	$\Phi \leq 6$ on any $7 \times 7$ density matrix; $\Phi \leq 2$ inside the consciousness window (see Aaronson)
Which basis?	Open ("quantum factorization problem")	The pinned functional frame; representation unique up to $G_2$ (T-123, registered as a theorem)
Consciousness	Necessary conditions only	$\mathrm{Cons}(S)$: four thresholds

Difference in kind

[I] The two "integrations" are different quantities. Tegmark's needs a tensor-product factorisation $\mathcal H = \mathcal H_1 \otimes \mathcal H_2$, and $\mathbb C^7$ has none because 7 is prime; so Tegmark's measure is not even defined for a single seven-dimensional $\Gamma$, and his quarter-bit bound does not constrain $\Phi(\Gamma)$. Conversely, $\Phi(\Gamma)$ is not a property of the state alone: it vanishes in $\Gamma$'s own eigenbasis and becomes positive only relative to a fixed basis. What Tegmark calls the factorisation problem therefore returns in UHM as the question of the frame. The corpus answers it with its $G_2$-uniqueness theorem plus the frame decision D-0910 (registry row T-129: "$\Phi$ is a frame-pinned observable") — by axiom and convention, not by deriving the basis from a Hamiltonian, as Tegmark asks.

What CC borrows

• Nothing explicitly: the corpus cites Tegmark only for the decoherence argument (T-267). In parallel: the starting point "only $\rho$ and its dynamics", and consciousness as a phase of matter — UHM's T-160 (registered as a theorem) places a phase transition at $P = 2/7$.

What CC does better

• A definite answer to "which basis": T-123 (uniqueness of the representation up to $G_2$, registered as a theorem) together with the pinned frame; Tegmark leaves the question open. Whether an answer by axiom and convention counts as better is itself debatable.
• Quantitative thresholds, where Tegmark gives necessary conditions only.

Honest assessment: what the theory does better than CC

• Checked calculations with a negative result: the quarter-bit bound is a precise no-go for basis-independent integration in quantum states, and Tegmark states the paradoxes of his own proposal openly.
• The factorisation problem is posed, not assumed: UHM's integration means something only in a basis it fixes; Tegmark shows why the choice of basis cannot be taken for granted.
• Links to established physics: error-correcting codes, criticality in condensed matter, Quantum Darwinism.

Standing

A programmatic paper. By its author's own conclusion, the integration principle as defined fails for quantum states and needs "at least one additional principle"; it has not been developed into a testable criterion of which systems are conscious.

Mapping functor [I]

$F_{\text{Teg}}: \mathbf{Perceptronium} \to \mathbf{Hol}$

Information principle $\mapsto$ $D_{\mathrm{diff}} \geq 2$; integration principle $\mapsto$ $\Phi \geq 1$ (a different quantity, as above); independence and dynamics $\mapsto$ autonomous $\mathcal L_\Omega$ with regeneration; factorisation problem $\mapsto$ the choice of frame. Not a projection in the usual sense: the central quantity changes its meaning in translation.

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41. D'Ariano and Faggin — Quantum-Information Panpsychism

«As a result we reach a quantum-information-based panpsychism, with classical physics supervening on quantum physics, quantum physics supervening on quantum information, and quantum information supervening on consciousness.» — Giacomo Mauro D'Ariano and Federico Faggin (2020)

In brief. Two physicists argue that experience is quantum information as lived from inside, and that a quale is a pure quantum state. Of all the external programmes on this page it is the nearest to UHM's identification of experience with a state in the Hilbert-space formalism — and it contradicts UHM on two precise points.

Creators and history

Giacomo Mauro D'Ariano (Department of Physics, University of Pavia) and Federico Faggin (Federico and Elvia Faggin Foundation): "Hard Problem and Free Will: An Information-Theoretical Approach", arXiv:2012.06580 (December 2020); published in F. Scardigli (ed.), Artificial Intelligence Versus Natural Intelligence, Springer, 2022, pp. 145–192, doi:10.1007/978-3-030-85480-5_5. Faggin's book Irreducible: Consciousness, Life, Computers, and Human Nature (Essentia Books, 2024) sets out an idealist version for general readers, in which, in its publisher's words, "nature's most fundamental level is that of consciousness as a quantum phenomenon".

Key idea

The chapter's principles: information is experienced by the system that carries it (P1); experience cannot be shared, even in principle (P2, privacy) — and since only non-classical information cannot be read without disturbing it, the information theory of consciousness must be quantum (P2′); the state of a conscious system is pure (P3, "psycho-purity"), because an experience is one definite thing, whereas a mixture describes only someone else's knowledge of it; experience is made of structured qualia (P4). Hence their statement S1: "Qualia are described by ontic pure quantum states", with new qualia arising by superposition and entanglement. Free will is the unpredictable outcome of a purity-preserving ("atomic") quantum operation. The chapter lists possible tests: the number of qubits involved, complementary observables in cognition, violations of local-realism bounds.

Formal structure

Operational probabilistic theories as the framework, with quantum theory as the chosen instance. The ontic state is the pure state lived from inside; the epistemic state is the generally mixed state predicted from outside. To keep the ontic state pure, its evolution must be atomic (a single Kraus operator).

Comparison with CC

Aspect	D'Ariano–Faggin	CC / UHM
Experience is	Quantum information lived from inside	An aspect of $\Gamma \in \mathcal D(\mathbb C^7)$ (two-aspect monism)
A quale	A pure state (a ray)	A ray $[\lvert q\rangle] \in \mathbb P(\mathcal H_E)$ — an eigen-ray of $\rho_E$; the identification is marked [I] (registry row T-203)
Purity of the experienced state	Pure, $P = 1$	Mixed: the window $2/7 < P \leq 3/7$
Why quantum	Privacy requires information that cannot be copied	$\Gamma$ is "classically realizable" (T-267)
Free will	Outcome of an atomic quantum operation	Dec-functor ($\sigma$-optimisation)
Dimension	Open ("the number of qubits involved")	Fixed: 7

Two points of direct conflict

The programmes contradict each other here

1. Purity. D'Ariano and Faggin require the experienced state to be pure. UHM's consciousness window requires $R \geq 1/3$, i.e. (with $R = 1/(7P)$) $P \leq 3/7$: a pure state has $R = 1/7$ and fails UHM's predicate. The two cannot both be right about the experienced state. They could be reconciled only by reading UHM's $\Gamma$ as D'Ariano and Faggin's epistemic state — knowledge from outside — which is exactly the reading they reject for experience, and which would turn UHM's identity claim into a claim about an observer's knowledge.
2. Why quantum. Their argument for quantum theory is privacy: classical information can be copied and read without disturbance, so it cannot be experience. The corpus holds instead that $\Gamma$ is classically realizable (T-267, registered with theorem and conditional parts) and complex "by algebra, not superposition". By D'Ariano and Faggin's privacy principle, a classically realizable $\Gamma$ could not carry experience.

Precedent

The identification of a quale with a pure quantum state — a ray of a Hilbert space — was published by D'Ariano and Faggin in December 2020 (arXiv) and in 2022 (book chapter), with worked examples (direction qualia on the Bloch sphere). UHM's identification of a quality with a ray $[\lvert q\rangle] \in \mathbb P(\mathcal H_E)$ is therefore not new as a form of identification. UHM's variant — eigen-rays of a mixed $\rho_E$ — is different, and the corpus itself marks it as an interpretation (T-203: mathematical core registered as a theorem, identification as [I]).

What CC borrows

• Nothing explicitly: the corpus does not cite this work. In parallel: experience identified with a state in the Hilbert-space formalism; qualities as rays; the privacy of experience as structural (in UHM through T-214: the bridge to experience cannot be internal to the theory).

What CC does better

• A fixed dimension and explicit thresholds, with a non-empty window (T-124, registered as a theorem). D'Ariano and Faggin leave the number of qubits open and give no criterion separating conscious from non-conscious systems — under their panpsychism, every system that carries information experiences it.

Honest assessment: what the theory does better than CC

• An argument for quantumness: privacy, hence no copying, hence quantum theory. UHM uses the quantum formalism without such an argument and, by T-267, does not need genuinely quantum information at all.
• Named experimental signatures: complementary observables and violations of local-realism bounds in cognition — sharper than anything the corpus offers for the quantum character of $\Gamma$.
• A mechanism for free will stated inside the formalism (an atomic operation), where UHM uses a decision functor.

Standing

A theoretical proposal in a book chapter and a book for general readers; the tests it lists are not reported as performed in the works cited here.

Mapping functor [I]

$F_{\text{DF}}: \mathbf{QInfo}_{\text{ontic}} \to \mathbf{Hol}$

Pure ontic state $\mapsto$ ray $[\lvert q\rangle]$; mixed epistemic state $\mapsto$ $\Gamma$; atomic operation $\mapsto$ Dec-functor. The functor is not structure-preserving on the central point: it sends what one theory calls the experienced state to what the other calls knowledge about it.

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42. Wolfram — Observer Theory

«Consciousness is not about the general computation that brains—or, for that matter, many other things—can do. It's about the particular feature of our brains that causes us to have a coherent thread of experience.» — Stephen Wolfram (2021)

In brief. Wolfram argues that the laws of physics we find are the laws any observer like us must find — an observer who is computationally bounded and lives one sequential thread of experience. It matters for UHM because UHM also ties physics and experience together through the structure of an observer (self-model, emergent time); Wolfram's essays are the most explicit statement that physical law depends on the kind of observer.

Creators and history

Stephen Wolfram: "What Is Consciousness? Some New Perspectives from Our Physics Project" (22 March 2021) and "Observer Theory" (11 December 2023), both published on his own site, writings.stephenwolfram.com — essays, not peer-reviewed papers.

Key idea

In Wolfram's Physics Project the universe is a computationally irreducible rewriting of a hypergraph. An observer is anything that treats many microscopic configurations as equivalent ("equivalencing"), is computationally bounded, and takes itself to persist in time. His claim: "if there's underlying computational irreducibility—plus causal invariance—then any observer who forms their perception of the universe in a computationally bounded way must inevitably perceive the universe to follow the laws of general relativity"; likewise, quantum mechanics is what such an observer sees of the branching ("branchial") structure of histories, and the second law of thermodynamics follows too. Consciousness, in the 2021 essay, is the feature that produces "a coherent thread of experience".

Formal structure

Programmatic: the essays state the claims and refer to the technical documents of the Physics Project. They give no quantitative criterion of consciousness and no test of one.

Comparison with CC

Aspect	Observer theory	CC / UHM
What makes an observer	Computational boundedness, equivalencing, belief in its own persistence	Self-model $\varphi$, reflection $R$
Time	A sequential thread of experience	Emergent time (Page–Wootters)
Physics from	Observer plus computational irreducibility and causal invariance	$\Gamma$ and $\mathcal L_\Omega$ (spectral action and related results)
Criterion of consciousness	None	$\mathrm{Cons}(S)$

Precedent

Wolfram's essays (2021, 2023) state explicitly that the physical laws we find follow from the kind of observer we are. The corpus derives general relativity from a spectral action, not from properties of the observer, so there is no priority collision on that point; the parallel lies only in the role both give to the observer's structure.

What CC borrows

• Nothing explicitly: the corpus does not cite this work.

What CC does better

• A consciousness predicate with numbers, including a non-empty window (T-124, registered as a theorem); Wolfram gives none.

Honest assessment: what the theory does better than CC

• Economy: one idea — boundedness plus persistence — where UHM needs several axioms.
• An explicit link between "one thread of experience" and the emergence of physical law, which UHM does not state.

Standing

Self-published essays within a broader project; not peer-reviewed, and without a test of the claims about consciousness.

Mapping functor [I]

$F_{\text{Obs}}: \mathbf{Observer} \to \mathbf{Hol}$

Equivalencing $\mapsto$ coarse-graining into $\Gamma$; computational boundedness $\mapsto$ the finite dimension 7; persistence $\mapsto$ the fixed point $\Gamma^*$ of $\varphi$. Conceptual only: neither side supplies the arrows.

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Final Comparative Assessment

Before moving to the master table, it is useful to assess the key theories across several criteria. For each criterion: 0 = absent, 1 = partial, 2 = complete.

Criterion	IIT	GWT	FEP	HOT	PP	AST	RPT	ART	CC
Formalism (equations, theorems)	2	1	2	1	1	0	0	2	2
Consciousness threshold (quantitative)	1	1	0	0	0	0	0	1	2
Dynamics (evolution equations)	0	0	2	0	1	0	0	2	2
Phenomenology (qualia, experience)	1	0	0	1	0	1	1	0	2
Self-modelling	0	0	1	1	1	2	0	1	2
Falsifiability	1	1	1	1	1	0	1	1	2
Empirical base	1	2	1	1	1	1	2	2	0
Substrate-independence	2	0	1	1	1	1	0	0	2
Connection to physics	0	0	1	0	0	0	0	0	2
Total	8	5	9	6	5	5	4	9	18

Caveat

This table is a subjective assessment, not a proven result. CC scores maximum on formal criteria but zero on empirical base — which is perhaps the most important criterion. A theory without experimental verification remains a hypothesis, however elegant its mathematics. CC's score for falsifiability should be read together with the formal critiques above: its main criterion is testable only with a fixed reconstruction protocol $\pi_{\mathrm{bio}}$, and its numeric predicate is exposed to the unfolding and substitution arguments.

How CC unifies theories: diagram of projections

Each arrow is a projection: the theory takes part of the CC formalism and ignores the rest. IIT takes $\Phi$ and ignores $R$, $\sigma$, $\varphi$. GWT takes the threshold ($P > 2/7$) and ignores $\Phi$, $R$. HOT takes $\varphi$ and $R$ and ignores $\Phi$, $P$. None takes everything. In this sense CC is a unification, not a competitor.

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Master Table: 42 Theories of Consciousness

#	Theory	Authors	Year	Central object	Consciousness measure	Connection to CC	Functor status
1	Autopoiesis	Maturana, Varela	1980	Autopoietic organisation	No	(AP), $\varphi(\Gamma^*)=\Gamma^*$	Projection
2	IIT	Tononi	2004/2023	Cause-effect structure	$\Phi^{\text{IIT}}$	$\Phi(\Gamma)$	Projection
3	FEP	Friston	2010	Markov blanket	$F$ (free energy)	Class. limit [T] retracted 2026-09-25 [✗]	Embedding open [Pr]
4	GWT	Baars, Dehaene	1988/2001	Global workspace	Broadcasting	$P > 2/7$ (ignition)	Projection
5	HOT	Rosenthal, Lau	2005	Metarepresentation	HOT level	$\varphi$, $R \geq 1/3$	Projection
6	PP	Clark, Hohwy	2013	Prediction error	Precision	$\sigma_k$, $k=1-R$ [T]	Projection
7	AST	Graziano	2013	Attention schema	No	$\varphi(\Gamma)$	Projection
8	Quantum Cognition	Pothos, Busemeyer	2013	$\rho \in \mathcal{D}(\mathcal{H})$	No	$\Gamma \in \mathcal{D}(\mathbb{C}^7)$	Projection
9	Orch-OR	Penrose, Hameroff	1996	Microtubules	$E_G$ (gravitational)	Speculative [I]	Hypothesis
10	RPT	Lamme	2000	Recurrent loops	Recurrence (binary)	$R \geq R_{\text{th}}$	Projection
11	TNGS	Edelman	1987	Dynamic core	$C_N$ (neural complexity)	$\Phi$, $\mathcal{R}$	Projection
12	ART	Grossberg	1976/2017	Resonant pattern	Vigilance $\rho$	$P_{\text{crit}}$, match $\varphi$	Projection
13	Enactivism / 4E	Varela, Thompson, Noë	1991	Sense-making	No	(AP), $\mathcal{V}$	Principally incomplete
14	SMCT	O'Regan, Noë	2001	SMC patterns	No	$\gamma_{AS}$, CC-2	Projection
15	TTC	Northoff	2014	Temporo-spatial structure	BOST metrics	$\Gamma^*$, $\Lambda$	Projection
16	DIT	Larkum	2013	BAC-firing (dendrites)	BAC rate	$R(\Gamma)$	Strongly incomplete
17	CEMI	McFadden	2000/2020	Brain EM field	cemi	$\Phi(\Gamma)$	Projection
18	PCT	Powers	1973	Control loops	Error $e$	$\sigma_k$, $\varphi$	Projection
19	OA	Fingelkurts	2001	Operational modules	OS (synchrony)	$\gamma_{ij}$	Projection
20	NCC	Crick, Koch	1990	Neural correlates	No single measure	Thresholds $P$, $R$, $\Phi$	Not formal
21	Assembly Theory	Cronin, Walker	2023	Assembly tree	Assembly index	SAD, $P_{\text{crit}}$	Speculative
22	Quantum Mind	von Neumann, Wigner, Stapp	1932+	Quantum state	No single measure	$\Gamma$, $\varphi$	Conceptual
23	Dissipative Adaptation	England	2013	Dissipative structure	Entropy production	$\mathcal{D}_\Omega$, $\mathcal{R}$	Very incomplete
24	Russellian monism	Russell, Chalmers, Goff	1927/2010	Intrinsic properties	No	Dual-aspect monism, L0	Projection
25	Multiple Drafts	Dennett	1991	Competing "drafts"	Fame (functional)	$P(\Gamma)$, sectors	Strongly incomplete
26	Affective Neuroscience	Panksepp	1998	7 BES (subcortical)	No single measure	7 dimensions, E, $V_{\text{hed}}$	Projection
27	Somatic Marker	Damasio	1994/2010	Self hierarchy	No single measure	$\sigma_k$, L0→L3, $\Gamma^*$	Projection
28	Beast Machine	Anil Seth	2021	Interoceptive inference	No single measure	$\sigma_k$, $\varphi$, PP [T]	Projection
29	Subcortical Consciousness	Merker	2007	Mesencephalic core	No	L2 without cortex, Pred 6	Projection
30	Neuropsychoanalysis	Solms	2021	Affect as $F$	$F$ (free energy)	E-dim., $V_{\text{hed}}$, FEP [T]	Projection
31	Holonomic Brain	Pribram	1991	Holographic patterns	No	$\Gamma$, $\gamma_{ij}$, spectrum	Strongly incomplete
32	Theory of Functional Systems	P.K. Anokhin	1935/1974	Functional system, ARA	No	$\varphi$, $\sigma_k$, $\mathbb{H}$	Projection
33	System-Evolutionary Theory	Shvyrkov	2006	Neuron = element of experience	No	$\Gamma$, $\mathcal{L}_\Omega$	Strongly incomplete
34	Information Synthesis	Ivanitsky	1996	Circular cortical cycle	EEG coherence	$\gamma_{ij}$, $R$, $\Phi$	Projection
35	Psycho-logic	Allakhverdov	2000	Hypothesis verification	No	$\varphi$, $\Gamma^*$, L0/L2	Projection
36	Projective Wave Theory (PWT)	Worden	2024/2026	Wave $\psi$ with projective $PGL(4,\mathbb{R})$ action	None (binary: wave present/absent)	Coherences $\gamma_{ij}$ in $\{A,S,D\}$, $\Sigma^3$ (T-119)	Projection / candidate neural implementation
37	Category theory of qualia	Tsuchiya, Taguchi, Saigo, Phillips	2016/2021/2022	Category of experiences; similarity as arrows	None (structure, not magnitude)	Yoneda identity of qualia, $d_{FS}$ geometry	Precedent (Yoneda) / conjectural functor
38	Formal IIT; process theories	Kleiner, Tull; Signorelli, Wang, Coecke; Prentner	2019–2024	Map from systems into experience spaces	Generalised $\Phi$	Functor $F$ into $\mathbf{Exp}$; $\Phi(\Gamma)$	Precedent (form of the bridge) / projection
39	Minimal physicalism; quantum FEP	Fields, Glazebrook, Levin (and Friston)	2021/2022	Holographic screen between quantum systems	None (graded by reference frames)	CC-6 scale invariance ([T at weak coupling]); FEP limit (retracted)	Precedent (quantum FEP) / projection
40	Perceptronium	Tegmark	2014/2015	$\rho$ and $H$ with a tensor factorisation	Integrated information across the "cruelest cut"	$\Phi(\Gamma)$ — a different quantity	Different in kind
41	Quantum-information panpsychism	D'Ariano, Faggin	2020/2022/2024	Pure ("ontic") quantum state	None (panpsychist)	Qualia as rays; conflicts on purity and on quantumness	Conflict
42	Observer theory	Wolfram	2021/2023	Computationally bounded observer	None	Observer structure, emergent time	Conceptual

Notes on the master table

• Embedding — the theory is a strict subcase of CC (proven)
• Projection — the theory covers part of CC's structure (incomplete functor)
• Hypothesis — connection is speculative
• Principally incomplete — the theory rejects formalisation (enactivism)
• Not formal — research programme, not a formal theory
• Precedent — the external work published first an ingredient that UHM uses; UHM's version of that ingredient is not novel
• Conflict — the two theories make contradictory claims on a named point
• Different in kind — the shared word (here "integration") names different quantities
• Conceptual — a parallel of ideas with no formal arrows on either side

None of the listed theories covers all components of CC simultaneously: quantum formalism ($\Gamma$), dynamics ($\mathcal{L}_\Omega$), self-modelling ($\varphi$), thresholds ($P$, $R$, $\Phi$), phenomenology ($\mathrm{Coh}_E$), and algebraic rigidity ($G_2$). However, CC in turn has no empirical validation and no measurement protocols for $\Gamma$, which is its main weakness compared to experimental theories (NCC, RPT, ART, Ivanitsky, Anokhin, and the category theory of qualia with its colour-alignment data, §37).

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Related documents:

• FEP derivation from UHM — the claim that FEP is the classical limit of UHM is retracted there (Theorems 3.1, 4.2 (iii)–(iv), 4.3 [✗]); Theorems 4.1 (as an identity) and 5.1 stand
• History of cybernetics — cybernetics of orders I-II-III
• Panpsychism — categorical analysis of variants of panpsychism and Hoffman's conscious realism
• Cognitive hierarchy — K1–K5 levels
• Axiomatics — formal foundations of CC
• Theorems — key results
• Categorical formalism — category $\mathbf{Hol}$, functor $F$
• Interiority hierarchy — levels L0→L1→L2→L3→L4
• Glossary — IIT, FEP, GWT, HOT, AST, QC, conscious realism