Falsifiability and Predictions

On notation

In this document:

• $\rho$, $\rho_E$ — density matrix, reduced density matrix of the Interiority dimension
• $\Gamma_{-E}$ — context (states of all dimensions except $E$)
• $\lambda_i$ — eigenvalues of $\Gamma$ (intensities)
• L0, L1, L2 — interiority hierarchy levels
• $d_{\mathrm{FS}}$ — Fubini-Study metric
• $R_{\text{th}}$, $\Phi_{\text{th}}$ — threshold values

Falsification Criteria

Experimental Predictions

The extended theory makes testable predictions:

1. Isospectral discrimination

Two states $\rho_1$, $\rho_2$ with $\mathrm{Spec}(\rho_1) = \mathrm{Spec}(\rho_2)$ but $\mathrm{Eigvec}(\rho_1) \neq \mathrm{Eigvec}(\rho_2)$ should yield:

• Identical experience intensity (spectrum determines intensity)
• Distinguishable experience quality (eigenvectors determine quality)

Numerical criteria:

• Spectra 'identical': $\|\mathrm{Spec}(\rho_1) - \mathrm{Spec}(\rho_2)\|_2 < \varepsilon_{\text{spec}} = 0.01$
• Vectors 'distinguishable': $\min_i |\langle v_i^{(1)} | v_i^{(2)} \rangle| < 1 - \varepsilon_{\text{vec}}$, where $\varepsilon_{\text{vec}} = 0.1$
• Quality 'distinguishable': $d_{\text{FS}}([|q_1\rangle], [|q_2\rangle]) > \varepsilon_{\text{qual}} = 0.05$ rad

Test: Create isospectral neural states, measure phenomenal reports.

2. Contextual modulation

Changing context $\Gamma_{-E}$ with fixed $\rho_E$ should alter the quality of experience without changing intensity.

Numerical criteria:

• $\rho_E$ 'fixed': $\|\rho_E^{(1)} - \rho_E^{(2)}\|_F < \varepsilon_{\rho} = 0.02$
• Context 'changed': $\|\Gamma_{-E}^{(1)} - \Gamma_{-E}^{(2)}\|_F > \delta_{\Gamma} = 0.1$
• Intensity 'constant': $|\mathrm{Tr}((\rho_E^{(1)})^2) - \mathrm{Tr}((\rho_E^{(2)})^2)| < \varepsilon_P = 0.05$
• Quality 'changed': phenomenal report distinguishable with $p < 0.01$ (statistical test)

Test: Modulate context (attention, mood) at constant stimulus, measure changes in perceptual quality.

3. Adaptation dynamics

Experiential content (levels L1–L2) should follow the adaptation law:

$$\mathcal{Q}(t) \sim \log\left(\frac{\lambda_{\max}(t)}{\langle\lambda_{\max}\rangle_\tau}\right)$$

where:

• $\mathcal{Q}(t)$ — subjective experience intensity at time $t$
• $\lambda_{\max}(t)$ — maximum eigenvalue of $\Gamma(t)$
• $\langle\lambda_{\max}\rangle_\tau$ — average over adaptation period $\tau$

Interpretation

This prediction follows from the fact that perception encodes changes relative to baseline (Weber-Fechner law), not absolute values.

Numerical criteria:

• Correlation $r(\mathcal{Q}_{\text{measured}}, \mathcal{Q}_{\text{predicted}}) > r_{\min} = 0.7$
• Regression slope $\beta \in [0.8, 1.2]$ (close to 1)
• RMSE $< \sigma_{\mathcal{Q}} / 2$ (error less than half the standard deviation)
• Adaptation period $\tau \in [100, 1000]$ ms (typical range)

Test: Measure the temporal dynamics of adaptation, compare with prediction.

4. Metric relations

Distances in phenomenal space (L1) should correspond to the Fubini-Study metric:

$$d_{\mathrm{perceived}}(q_1, q_2) \sim d_{\mathrm{FS}}([|q_1\rangle], [|q_2\rangle])$$

where $[|q\rangle] \in \mathbb{P}(\mathcal{H}_E)$ — equivalence class in projective space.

Numerical criteria:

• Spearman correlation $\rho_S(d_{\text{perceived}}, d_{\text{FS}}) > 0.6$
• Monotonicity: violations $< 10\%$ of the total number of pairs
• Metric consistency: $|d(a,b) + d(b,c) - d(a,c)| < \varepsilon_{\triangle} = 0.15$ (triangle inequality)
• MDS reconstruction: stress $< 0.1$ when mapping to $\mathbb{R}^k$

Test: Build a phenomenal quality map (L1), compare with predicted geometry.

Refutation Criterion

The theory is falsified if:

$$\exists \rho_1, \rho_2 : \mathcal{I}(\rho_1) = \mathcal{I}(\rho_2), \text{ but } F(\rho_1) \neq F(\rho_2)$$

where:

• $\mathcal{I}(\rho) := (\mathrm{Spec}(\rho), \mathrm{Eigvec}(\rho), \Gamma_{-E}, \mathrm{Hist})$ — full invariant
• $F: \mathbf{DensityMat} \to \mathbf{Exp}$ — experience functor

That is, if two states with identical full invariants (spectrum + eigenvectors + context + history) yield distinguishable experience.

Gauge precision [T]

The $G_2$-rigidity theorem [T] refines the notion of 'identity': two states $\rho_1, \rho_2$ are considered physically identical if $\rho_2 = U\rho_1 U^\dagger$ for some $U \in G_2$. The full invariant $\mathcal{I}(\rho)$ is defined on the space $\mathcal{D}(\mathbb{C}^7)/G_2$ (34 parameters). The eigenvectors in the table below implicitly assume a fixed $G_2$-gauge; under gauge change $v_i \to Uv_i$, but the inner products $|\langle v_i^{(1)} | v_i^{(2)} \rangle|$ are $G_2$-invariant.

Operational tolerances:

Invariant component	'Identity' criterion
Spectrum	$\|\mathrm{Spec}(\rho_1) - \mathrm{Spec}(\rho_2)\|_2 < 0.01$
Eigenvectors	$\forall i: \lvert\langle v_i^{(1)} \vert v_i^{(2)} \rangle\rvert > 0.99$
Context	$\|\Gamma_{-E}^{(1)} - \Gamma_{-E}^{(2)}\|_F < 0.02$
History	$d_{\text{edit}}(\mathrm{Hist}_1, \mathrm{Hist}_2) < 0.05 \cdot \lvert\mathrm{Hist}\rvert$

Interiority	'Distinguishability' criterion
Phenomenal report	Statistically distinguishable ($p < 0.01$, Wilcoxon test)
Behavioural marker	AUC > 0.7 in discrimination task

Practical criterion

For experimental verification it is sufficient to compare the spectrum and eigenvectors (without history): if $\mathrm{spec}(\rho_1) = \mathrm{spec}(\rho_2)$ and $|q_i^{(1)}\rangle = |q_i^{(2)}\rangle$, but $\mathcal{F}(\rho_1) \neq \mathcal{F}(\rho_2)$, the theory is falsified.

Note on operationalisation

The full invariant $\mathcal{I}(\rho) = (\mathrm{Spec}, \mathrm{Eigvec}, \Gamma_{-E}, \mathrm{Hist})$ is a theoretical ideal. Operational realisation:

• Spec(ρ): measurable via quantum state tomography
• Eigvec(ρ): measurable via full tomography (neural correlates)
• Γ_{-E}: approximately measurable via partial trace — discarding the E-component
• Hist: approximated via time correlators $\langle O(\tau)O(0) \rangle$ (two-point functions, accessible via fMRI/EEG)

The falsification criterion is strict in the theoretical sense and approximate in the experimental sense. This is the standard situation for theories with directly unobservable objects (cf. the wave function in QM).

See also: КК falsification criteria — additional operational criteria for the applied theory.

Current Empirical Status

Prediction	Status	Comment
Isospectral discrimination	Open	Requires neurophenomenological experiments
Contextual modulation	Partially confirmed	Consistent with attention influence data
Adaptation dynamics	Consistent	Consistent with Weber-Fechner law
Metric relations	Open	Requires phenomenal space mapping (L1)
Functional purity	Programme	$P > P_{\text{crit}}$ for $\geq 90\%$ of functioning systems
P-quality correlation	Programme	Correlation of $P$ with functional quality: $r > 0.5$
F-m_t: $m_t \approx 173$ GeV	Consistent	Observation: $172.57 \pm 0.29$ GeV
F-Cabibbo: $\theta_{12} \approx 13°$	Consistent	Observation: $12.96°$ ($\|V_{us}\| = 0.2243$)
F-δ_CP: $\delta_{\text{CP}} \approx 64°$	Consistent (${\sim}0.8\sigma$)	Observation: $69° \pm 4°$, $\sigma_{\mathrm{comb}} \approx 6.4°$
F-Gap-1: Gap_intra < Gap_inter	Open	Requires ISF analysis of fMRI
F-ISF: 6–12 ISF components	Open	Requires systematic fMRI analysis
F-ξ: $\xi_F \sim 160$ pc	Open	Testable through LSS surveys
F-nEDM: $d_n = 0$ (T-99)	Consistent	$\|d_n\| < 1.8 \times 10^{-26}$ e·cm (PSI 2020)
F-τ_p: $\tau_p \sim 6.7 \times 10^{37}$ years	Open	Hyper-K: sensitivity $\sim 10^{35}$ years
F-Higgs: $\delta\lambda/\lambda \sim 10^{-2}$–$10^{-3}$	Open	Awaiting FCC-hh

Falsifiable predictions from Fano integration

Source

Predictions are derived from the integration of Fano geometry with Gap dynamics, Gap thermodynamics, and RG flow. Each prediction is assigned a rigour status in accordance with the registry.

F-Gap-1: Intra-triplet Gap below inter-triplet

$$\langle \mathrm{Gap}_{\mathrm{intra}} \rangle < \langle \mathrm{Gap}_{\mathrm{inter}} \rangle$$

The mean Gap within Fano triplets is lower than between them. Coherences belonging to the same Fano line are more transparent (closer to $\mathrm{Gap}=0$) than coherences connecting different lines.

Testability: ISF components (independent slow features) in fMRI. Intra-triplet correlations should systematically exceed inter-triplet correlations.

Status: [H] Hypothesis — consequence of Gap semantics and G₂-covariance.

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F-Gap-2: Block transparency by Fano triplets

Coherences within the same Fano line are more strongly correlated, forming a block structure in the coherence matrix $\Gamma$. The Fano dissipator preserves triplet coherences ([T], G₂-structure), generating distinguished block transparency.

Testability: Correlation analysis of the coherence matrix — 7 blocks of $3 \times 3$ (by Fano lines) should be statistically separated from off-block elements.

Status: [T] Theorem — consequence of theorems 10.1–10.3 (Fano channel preserves coherences, status registry).

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F-ξ: Fano correlation length

$$\xi_F \sim 160 \; \text{pc}$$

The correlation length of Fano structure in large-scale structure. The scale is determined by RG suppression of the cubic coupling $\lambda_3$ and the phase diagram of the Gap potential.

Testability: Large-scale structure of the Universe — correlation function on scales $\sim 100$–$200$ pc. Absence of a preferred scale $\sim 160$ pc falsifies the prediction.

Status: [T] Theorem — theorems 9.1–9.2 (status registry).

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F-τ_p: Proton lifetime

$$\tau_p \sim 6.7 \times 10^{37} \; \text{years}$$

The proton lifetime, computed from the masses of $X,Y$-leptoquarks via the Gap hierarchy.

Testability: Hyper-Kamiokande experiment (sensitivity up to $\sim 10^{35}$ years). Current Super-K limit: $\tau_p > 2.4 \times 10^{34}$ years. The prediction lies 2–3 orders of magnitude above Hyper-K sensitivity — direct detection of decay at this $\tau_p$ is unlikely, but detection of decay at $\tau_p < 10^{36}$ years falsifies the prediction.

Note on testability

The prediction $\tau_p \sim 10^{37}$–$10^{38}$ years exceeds the sensitivity of Hyper-K ($\sim 10^{35}$ years for $p \to e^+\pi^0$) by 2–3 orders of magnitude. Direct verification is impossible in the foreseeable future. Indirect constraints are possible via neutron-antineutron oscillations.

Status: [H] Hypothesis — depends on the precision of the $M_X$ computation (proton decay).

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F-m_t: Top quark mass from the Pendleton-Ross fixed point

$$m_t \approx 173 \; \text{GeV}$$

The top quark mass is derived from the quasi-IR Pendleton-Ross fixed point. The unique Fano-Higgs line $\{A, E, U\}$ admits a tree-level Yukawa coupling only for the third generation; the RG evolution of this coupling is attracted to the fixed point that fixes $m_t$.

Testability: Already consistent with observations ($m_t^{\text{exp}} = 172.57 \pm 0.29$ GeV). The prediction is falsified by a significant shift in the experimental value.

Status: [T] Theorem — theorem 5.1 (status registry, Yukawa hierarchy).

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F-ISF: ISF components in fMRI

$$N_{\text{ISF}} \in [6, 12]$$

The number of ISF components (independent slow features) in fMRI data is determined by the opacity rank of the Gap operator. At full transparency (all $\mathrm{Gap}(i,j) = 0$) the rank is 0 and all 21 coherences are active; at full opacity the rank is maximal (21). For biologically realistic regimes the rank is $\sim 9$–$15$, giving $21 - 15 = 6$ to $21 - 9 = 12$ active independent components.

Testability: ISF component analysis of fMRI data. Systematic detection of $N_{\text{ISF}} < 6$ or $N_{\text{ISF}} > 12$ falsifies the prediction. The dependence of $N_{\text{ISF}}$ on the state of consciousness (wakefulness / sleep / anaesthesia) should correlate with the rank of the Gap operator.

Status: [H] Hypothesis — consequence of Gap dynamics and the interiority hierarchy.

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F-Neural: Neural correlates of L-levels [C with bridge assumption]

The form of scaling relations (threshold at $P = 2/7$, monotonic dependence of $\Phi$ on connectivity) is derived [C with bridge assumption]. Numerical coefficients are empirical. Experimental protocol: fMRI/EEG during anaesthesia$\leftrightarrow$wakefulness transitions to verify the threshold.

Testability: Measurement of the $\Phi$ jump under pharmacological control of anaesthesia depth (sevoflurane, propofol). Prediction: existence of a sharp transition $P \approx 2/7$, not gradual sliding. The $\Phi(\text{connectivity})$ dependence is monotonic.

Status: [C with bridge assumption] — the scaling form is derived from theory; numerical coefficients require empirical calibration.

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F-Higgs: Higgs self-coupling deviation

$$\frac{\delta\lambda}{\lambda_{\text{SM}}} \sim O(10^{-2} \text{–} 10^{-3})$$

The octonionic correction to the Higgs sector modifies the Higgs self-coupling at the level of $\sim 1\%$–$0.1\%$ relative to the Standard Model prediction.

Testability: FCC-hh collider (sensitivity to $\delta\lambda/\lambda_{\text{SM}} \sim$ several percent). If FCC-hh measures $\lambda_{hhh}$ with $\sim 5\%$ precision and detects a deviation of order $1\%$ — that is confirmation. Absence of deviations at precision $\ll 0.1\%$ — falsification.

Status: [H] Hypothesis — depends on non-perturbative computations in the Higgs sector.

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F-δ_CP: CKM CP-phase from the Fano phase

$$\delta_{\text{CP}} \approx 64° \pm 5°$$

The CKM matrix CP-phase is derived from the geometric phase of the Fano plane. Observed value: $\delta_{\text{CP}}^{\text{exp}} = 69° \pm 4°$. At combined uncertainty $\sigma_{\mathrm{comb}} = \sqrt{5^2 + 4^2} \approx 6.4°$ the discrepancy is $5°/6.4° \approx 0.8\sigma$.

Testability: Refinement of the experimental value at LHCb and Belle II. The prediction is falsified if $\delta_{\text{CP}}^{\text{exp}}$ shifts beyond $\sim 2\sigma$ from $64°$ (i.e. beyond $[54°, 74°]$).

Status: [H] Hypothesis — depends on the Fritzsch texture and loop corrections.

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F-Cabibbo: Cabibbo angle from RG suppression of the Fano angle

$$\theta_{12} \approx 13°$$

The Cabibbo angle is derived from RG suppression of the fundamental Fano angle $2\pi/7 \approx 51.4°$. Observed value: $\theta_{12}^{\text{exp}} \approx 13.0°$.

Testability: Consistent with current data ($|V_{us}| = 0.2243 \pm 0.0005$, corresponding to $\theta_{12} \approx 12.96°$). The prediction is falsified by a significant revision of $|V_{us}|$.

Status: [H] Hypothesis — depends on loop corrections and RG flow.

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F-nEDM: Neutron EDM ($\theta_{\mathrm{QCD}} = 0$ exactly)

$$d_n = 0 \quad \text{(exactly)}$$

Prediction [T] (T-99): $\theta_{\mathrm{QCD}} = 0$ exactly (structural proof), not $\theta < 10^{-10}$. Neutron electric dipole moment:

$$d_n = \frac{e \cdot m_q}{m_n^2} \cdot \theta_{\mathrm{QCD}} = 0$$

Current experimental limit: $|d_n| < 1.8 \times 10^{-26}$ e·cm (PSI 2020). Future experiments (n2EDM, nEDM@SNS) will reach sensitivity $\sim 10^{-28}$ e·cm.

Falsification: Detection of $d_n \neq 0$ at any level → direct refutation of T-99.

Difference from axion solution: The axion allows $\theta \sim m_a / f_a \cdot T \sim 10^{-18}$ — non-zero, albeit ultra-small. Gap theory predicts a strict zero.

Status: [T] Theorem — T-99 (status registry, confinement).

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Summary table of predictions

Code	Prediction	Falsification criterion	Experiment	Status
F-Gap-1	$\langle\mathrm{Gap}_{\mathrm{intra}}\rangle < \langle\mathrm{Gap}_{\mathrm{inter}}\rangle$	Systematically $\mathrm{Gap}_{\mathrm{intra}} \geq \mathrm{Gap}_{\mathrm{inter}}$	fMRI (ISF)	[H]
F-Gap-2	Block transparency by Fano triplets	Absence of block structure in coherences	fMRI	[T]
F-ξ	$\xi_F \sim 160$ pc	Absence of preferred scale $\sim 160$ pc	LSS surveys	[T]
F-τ_p	$\tau_p \sim 6.7 \times 10^{37}$ years	$\tau_p < 10^{36}$ years	Hyper-K	[H]
F-m_t	$m_t \approx 173$ GeV	Significant shift in $m_t^{\text{exp}}$	Colliders	[T]
F-ISF	6–12 ISF components	$N_{\text{ISF}} \notin [6, 12]$	fMRI	[H]
F-Neural	Threshold $P = 2/7$, monotonic $\Phi$(connectivity)	Gradual transition without threshold	fMRI/EEG (anaesthesia)	[C with bridge]
F-Higgs	$\delta\lambda/\lambda_{\text{SM}} \sim 10^{-2}$–$10^{-3}$	No deviations at precision $\ll 0.1\%$	FCC-hh	[H]
F-δ_CP	$\delta_{\text{CP}} \approx 64° \pm 5°$	$\delta_{\text{CP}}^{\text{exp}} \notin [54°, 74°]$	LHCb, Belle II	[H]
F-Cabibbo	$\theta_{12} \approx 13°$	Significant revision of $\|V_{us}\|$	Kaon experiments	[H]
F-nEDM	$d_n = 0$ (T-99: $\theta_{\mathrm{QCD}} = 0$ exactly)	$d_n \neq 0$ at any level	n2EDM, nEDM@SNS	[T]

Status of predictions

Predictions marked [T] are based on rigorously proved theorems (see status registry). The octonionic bridge is fully closed [T] (T15). Predictions marked [H] require additional computations or contain gaps in the physical arguments.

Completeness of Theory

The theory is complete in the following sense:

1. Self-sufficiency: Requires no external postulates or references
2. Universality: Applicable to structural aspects of self-referential systems — from quantum to cognitive
3. Internal consistency: Contains no contradictions
4. Operationality: Can be computationally implemented
5. Explanatory power: Resolves traditional philosophical problems
6. Falsifiability: Makes testable predictions about the structure of experience
7. Formal rigour: Key theorems proved (7D minimality, operator φ, functor F)
8. Compatibility with QM: The nonlinear regenerative term $\mathcal{R}$ does not violate the no-signalling constraint — proved via the CPTP property of $\varphi$ (conditions NS1-NS3)
9. Ensemble independence: Evolution is defined on $\Gamma$ (density matrix), not on wave functions — does not depend on decomposition
10. Computational consistency: The nonlinearity $\mathcal{R}$ does not provide acceleration beyond BQP

Vulnerability analysis

Systematic analysis of five main vulnerabilities of the theory (2026):

#	Vulnerability	Initial status	Result	New status
1	$\dim = 7$ as postulate	Not empirically verified	15+ independent derivations [T]: Theorem S (minimality) + octonionic derivation + T15 (bridge)	Closed (theoretically)
2	$D_{\mathrm{diff}} \geq 2$ [C]	Conditional theorem	T-129 [T]: $\Phi_{\mathrm{th}} = 1$ from first principles → T-151 [T]: $D_{\min} = 2$ unconditionally	Closed (fully)
3	$R = 1/(7P)$ counterintuitive	Requires empirical verification	Algebraic identity [T], physical interpretation, T-124 [T] (non-emptiness of Goldilocks zone)	Closed (theoretically)
4	No experiments	157+ theorems without lab verification	~30 testable predictions, 5 post-hoc coincidences (F-m_t, F-Cabibbo, F-δ_CP, F-nEDM, Weber-Fechner)	Confirmed (requires experiment)
5	Quantum nature of $\Gamma$	Tegmark decoherence	T-132 [T] (necessity of complex $\gamma_{ij}$) + T-153 [T] (substrate closure), but Tegmark argument not fully addressed	Partially open

Summary: 3 of 5 vulnerabilities closed theoretically; 1 is fundamentally experimental; 1 is deeply open (quantum nature of $\Gamma$).

Theory Boundaries

Philosophy of boundaries

Acknowledging boundaries is not a weakness, but a strength of a scientific theory. A theory that claims to explain everything without exception is most likely unscientific.

Structural Boundaries (what is not proved)

Question	Status	Comment
Why 7 dimensions?	Minimality proved	But not uniqueness
Values of constants $\omega_i$, $J_{ij}$, $\gamma_k$	Empirical	Not derived from axioms
Uniqueness of $\Gamma$	Not proved	Other 'universes' possible
Uniqueness of partition $\{A,S,D,L,E,O,U\}$	Proved [T]	All 7 dimensions are functionally unique (A,S,D,L,U — algebraically; E,O — via κ₀)

Physical Boundaries

Question	Status	Comment
Einstein equations	[T] Derived	Spectral action (T-65); $M^4$ derived (T-120)
Standard Model	Structure [T], parameters partially	$G_2 \to SU(3)_C \times SU(2)_L \times U(1)_Y$ [T]; specific masses — partially
Spacetime dimensionality $3+1$	[T] Derived	Sectoral decomposition + Connes reconstruction (T-119, T-120)
Constants $c$, $G$, $\hbar$	$G$ [T] derived, $c$, $\hbar$ not explained	$G_N = 3\pi/(7f_2\Lambda^2)$ (T-65); $c$, $\hbar$ — fundamental

Phenomenal Boundaries (what is taken as axiom)

1. Categorical gap: The theory does not explain why mathematical structures are 'felt.' The identity of being and experience — Axiom Ω⁷, not a theorem.

2. Qualia calibration: The correspondence between specific eigenvalues/eigenvectors and specific qualities of experience is established empirically.

Qualia calibration — an empirical question

Which specific $[|q\rangle] \in \mathbb{P}(\mathcal{H}_E)$ corresponds to 'red' is an empirical question, not a theoretical defect. This is analogous to how the electron mass is not derived from the Standard Model. The structure of experience (spectral decomposition) is the unique functor compatible with the axiomatics, but the specific calibration is determined experimentally.

3. Absolute qualia: The question of the existence of context-independent qualia remains open.

4. Thresholds L2: $R_{\text{th}} = 1/3$ [T] — derived from triadic decomposition ($K = 3$ types of dynamics from axioms) + Bayesian dominance. $\Phi_{\text{th}} = 1$ [T] — unique self-consistent value at $P_{\text{crit}} = 2/7$ (T-129).

Categorical Boundaries

1. $\mathbf{Exp}$ is not a topos: It is proved that the category $\mathbf{Exp}$ is not a topos — there is no internal logic of experiential content.

2. Functor $F$ is non-invertible: One cannot uniquely recover $\rho$ from experiential content — different states may yield 'identical' experience.

3. Problem of time: The category $\mathbf{DensityMat}$ is static; time requires an external parameter.

Status of Boundaries

These boundaries are not a deficiency, but an acknowledgement:

• The theory describes structure, not the question of 'why this particular structure'
• Some questions may be beyond any possible explanation
• Honest acknowledgement of boundaries is a mark of a mature theory

Comparison with physics: Physics does not explain why the laws of nature exist — it describes their structure. Analogously, UHM describes the structure of experience, acknowledging the boundaries of explanation.

Octonionic Falsification Criteria

The structural derivation through octonions generates additional testable predictions:

Prediction	Falsification criterion	Status
Fano symmetries of coherences	7 triplets $(e_i, e_j, e_k)$ of the Fano plane should be distinguishable in the structure of coherences $\gamma_{ij}$	[T]
$G_2$-covariance	The dynamics of $\Gamma$ must be covariant with respect to $G_2 \subset SO(7)$, not the full $SO(7)$	[T]
Associator anomalies	Triple interactions of dimensions should exhibit non-associativity: $[x, y, z] \neq 0$	[T]
Hamming threshold	Structure $H(7,4)$: system is viable with loss of up to 3 of 7 coherences (error correction)	[T]

Bridge [T] — fully closed (T15)

The connection (AP)+(PH)+(QG)+(V) → P1+P2 is established via the complete formal chain T15 (12 steps, all [T]). T11–T13 prove the former condition (МП). All octonionic predictions are consequences of the structural derivation [T].

Research programme

Boundaries do not mean a halt to development. Open directions:

Direction	Goal	Priority
Quantum gravity	Derive $g_{\mu\nu}$ from $\Gamma$	High
Experimental validation of thresholds	Verify $R_{\text{th}} = 1/3$, $\Phi_{\text{th}} = 1$ empirically	High
Isospectral experiments	Test prediction 1 with numerical tolerances	High
ISF analysis of fMRI	Verify F-Gap-1, F-Gap-2, F-ISF	High
Non-perturbative computations	Refine F-Higgs, F-τ_p	High
Correlation length $\xi_F$	Verify F-ξ through LSS surveys	Medium
Connection with Hoffman	Prove equivalence with the theory of conscious agents	Medium
$\infty$-topos	Construct $\infty$-topos on $\mathbf{Exp}$	Low
Standard Model	Close the derivation of $\mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1)$ from the Gap hierarchy	Long-term

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Related documents:

• Glossary — definitions of terms
• Status registry — complete registry of results with classification [T]/[H]/[P]/[I]/[D]
• Axiom Ω⁷ — ∞-topos $\mathrm{Sh}_\infty(\mathcal{C})$ as primitive
• Mathematical apparatus — formal definitions of $\Gamma$, $d_{\mathrm{FS}}$
• Interiority hierarchy — levels L0→L1→L2→L3→L4, thresholds $R_{\text{th}}$, $\Phi_{\text{th}}$, $R^{(n)}_{\text{th}}$
• Categorical formalism — functor $F$, categories $\mathbf{DensityMat}$ and $\mathbf{Exp}$
• 7D minimality theorem — proof of $N = 7$
• Structural derivation via octonions — P1+P2 → $\mathbb{O}$ → N=7
• Formalisation of operator φ — CPTP channels
• Theorems — formal results
• CC predictions — CC-specific falsification criteria
• Fano selection rules — Fano selection rule for Yukawa couplings
• Gap semantics — dual-aspect semantics of 49 elements
• Gap dynamics — Gap operator, bifurcations, non-Markovian dynamics
• Gap thermodynamics — information geometry, potential $V_{\text{Gap}}$
• RG flow of Gap — $\beta$-functions, fixed points, RG suppression of $\lambda_3$
• Higgs sector — uniqueness of the line $\{A,E,U\}$, Higgs mass
• CKM matrix — Fritzsch texture, Cabibbo angle, CP phase
• Yukawa hierarchy — Pendleton–Ross fixed point, $m_t$
• Proton decay — $X,Y$-leptoquarks, $\tau_p$
• Dark matter — $O$-sector relic, $\xi_F$
• G₂ structure — covariance of the Fano dissipator