Calibration: Coherences to Qualities

What this page does

The theory fixes the form of the correspondence between $\Gamma$ and experience; it leaves its constants free, exactly as the Standard Model leaves the electron mass free (what UHM does not explain). This page collects how those constants are measured: which observables enter, how each is mapped onto components of $\Gamma$, which protocols the corpus already specifies, which ones are proposed here for the first time [Pr], and what result would count against the theory. It reports no data.

Two calibrations, not one

1. The measurement calibration takes a substrate to $\hat\Gamma$. For a brain it is the reconstruction $\pi_{\mathrm{bio}}$ (protocol); for an artificial system, the map $G: \mathrm{AIState} \to \mathcal{D}(\mathbb{C}^7)$ (measurement protocol). Its free parameters $\theta$ — weights, observation-model coefficients, regulariser weights — are not given by the theory. Registry row C31 states the division: $G_2$-uniqueness of the construction is [T]; the specific correspondences "EEG band ↔ dimension" are [H].

2. The phenomenal calibration takes $\hat\Gamma$ to named qualities. It has two parts:

• the metric map $f$ from perceived dissimilarity to the Fubini–Study distance $d_{\mathrm{FS}}$. The enriched Yoneda theorem [T] makes the quality space testable only after $f$ is fixed; "with $f$ only assumed monotone, the test is ordinal and weaker";
• the anchoring: which ray $[\lvert q\rangle]$ is red. The functor distinguishes states up to at most a finite group of relabellings of the axes — its kernel lies inside the 192 elements of the frame group $\Gamma_{\!\text{oct}}$ (1344 elements) that keep the $E$-axis (Corollary 3 [T]); within that, which ray carries which name is measured, not derived. Whether two subjects' quality spaces are related by an inversion stays open (relational identity).

Neither part can be settled by proof. Both are settled by fitting on data where the answer is independently known and testing on data that did not enter the fit.

Observables and where they enter $\Gamma$

Observable	Typical measure	Component of $\Gamma$ it bears on	Source	Status of the mapping
Presence / absence report	immediate or delayed report	ground truth for the verdict $\mathrm{Cons}(\hat\Gamma)$ — inference data only	substitution theorem	[T] as a statement about test design
Intensity rating	magnitude estimation	spectrum $\lambda_i$	falsifiability, predictions 1, 3	open prediction
Discrimination	$d'$, just-noticeable difference	$d_{\mathrm{FS}}$ between rays at fixed spectrum	isospectral discrimination	open prediction
Similarity judgement	pairwise dissimilarity matrix	$d_{\mathrm{FS}}$ through $f$	metric relations; enriched Yoneda	geometry [T]; identification of experiences with rays [I]
Metacognition	meta-$d'$, confidence calibration	reflection $R$, self-model quality $R_\varphi$	phenomenology map; gate theorem T-252 [T]	bound [T]; correspondence [H]
Valence, arousal	rating scales, circumplex	$\mathrm{sign}(dP/d\tau)$, $\lvert dP/d\tau\rvert$	emotional taxonomy, C.1	[C]
EEG spectral power	band power	populations $\gamma_{kk}$	Step 1	[H] (C31)
Cross-frequency coupling	phase–amplitude coupling	moduli $\lvert\gamma_{ij}\rvert$	Step 2	[H] (C31)
Phase locking	complex phase-locking values	phases, hence Fano holonomies $H_p$	Step 3; SUB-3	[H]
TMS-evoked complexity	$\mathrm{PCI}_{\max}$	an independent verdict ($\mathrm{PCI}_{\max} > 0.31$), not a number to match	Step 5	concordance test [Pr]
fMRI slow components	number of independent slow features	opacity rank of the Gap operator	F-ISF	[H]

Two cautions carry over from the sources. Observables are defined in incommensurable units, so each enters as a percentile against a declared reference ensemble that is published with the result (Lesson 1). And $\Gamma$ is built from functional indices, never from raw signal statistics, because signals with an atypical carrier (the hypersynchronous delta EEG of awake children with Angelman syndrome) mislead any carrier-level measure (Lesson 3).

The design rule: prediction data and inference data

Kleiner and Hoel separate the data a theory predicts from (prediction data: here, the signals that enter $\hat\Gamma$) from the data an experimenter infers experience from (inference data: reports and behaviour). The corpus has a theorem on where UHM stands between their two horns (position against the substitution argument, [T] with part (v) [H]):

• a reconstruction whose $\theta$ is fitted on report-labelled sessions tests nothing on those sessions — its agreement with the labels holds by construction;
• after $\theta$ is frozen, the verdict depends on prediction data alone, and reports count as evidence only inside a declared domain $D_{\mathrm{nat}}$ (intact adult brains, natural sleep–wake states, standard anaesthetics).

Every protocol below therefore follows the pre-registration SUB-1…SUB-6 of that section: $\theta$ frozen on wakefulness only; no viability penalty in confirmatory runs ($\lambda_2 = 0$ — with the default $\lambda_2 = 100$ the estimator returned $\hat P = 2/7$ for every sub-threshold state of the uniform family, so P8.2 could not be observed); phases from EEG, never from reaction times; verdicts registered before unblinding.

Protocols

K1. Threshold concordance — existing protocol

Claim. In $D_{\mathrm{nat}}$, $P(\hat\Gamma_{\mathrm{wake}}) > 2/7$ (P8.1) and $P(\hat\Gamma_{\mathrm{NREM3}}) < 2/7$ (P8.2), and the verdict $\mathrm{Cons}(\hat\Gamma)$ agrees with $\mathrm{PCI}_{\max} > 0.31$ on the same sessions (P8.4 in concordance form, SUB-5) — table of P8 predictions.

Data. The sessions of Casarotto et al. (2016): 150 subjects, 540 TMS-evoked potential sets. The decisive rows are REM sleep (8 subjects) and ketamine anaesthesia (6 subjects) — consciousness without behaviour at the time, out of sample once $\theta$ is frozen on wakefulness.

Measure of what the decisive rows can show. If all 14 of them come out concordant, the one-sided 95 % lower bound on the concordance rate in that class is $0.05^{1/14} = 0.807$; with the 8 REM subjects alone it is $0.688$. The 14 subjects can corroborate; they cannot establish a rate above about 0.8.

Decision. Cohen's $\kappa \geq 0.8$ corroborates, $\kappa < 0.4$ falsifies (SUB-5 [Pr]). Current status: untested — no $\pi_{\mathrm{bio}}$ session exists (decision protocols).

K2. The two exits — existing protocol

Among sessions with $\mathrm{PCI}_{\max} \leq 0.31$, responses that stay local are predicted to have $\hat\Phi < 1$, and responses that spread as a stereotyped global wave $\hat P > 3/7$ ($\hat R < 1/3$) — SUB-6 [H]. The window has two edges, so a low complexity has two UHM signatures. This compares prediction data with prediction data, so the substitution argument does not touch it.

K3. Metric calibration of quality space — proposed here [Pr]

Claim under test. Perceived dissimilarities are a monotone function of $d_{\mathrm{FS}}$ between the rays that carry the qualities (prediction 4).

Protocol. (1) A stimulus set of $m$ items in one modality; full pairwise dissimilarity ratings from each subject, twice (test–retest). (2) In the same sessions, per-stimulus $\hat\Gamma$ from $\pi_{\mathrm{bio}}$ with frozen $\theta$, and its eigenrays. (3) Fit a monotone $f$ on a random half of the stimuli; predict the ordering of dissimilarities among the held-out half from $d_{\mathrm{FS}}$ alone.

Pass criteria (from the falsifiability page): Spearman $\rho_S(d_{\mathrm{perceived}}, d_{\mathrm{FS}}) > 0.6$; monotonicity violations below 10 % of pairs; MDS stress below 0.1.

What it calibrates. The fitted $f$ is the constant the enriched Yoneda test needs; once $f$ is fixed, the realisability test of the structure page becomes metric rather than ordinal.

Limit. Step (2) needs rays from neural data, which in turn needs a validated $\pi_{\mathrm{bio}}$; until then only the behavioural half — whether similarity data admit a complex-projective geometry at all — can be run, and it belongs to the structure page.

K4. Intensity and quality dissociate — existing criteria

Two predictions of the falsifiability page separate the two parameters of experience: states with the same spectrum and different eigenvectors should differ in quality and not in intensity (spectra within $0.01$, $d_{\mathrm{FS}} > 0.05$ rad); a change of context $\Gamma_{-E}$ at fixed $\rho_E$ should change quality and not intensity ($\lvert\Delta P\rvert < 0.05$, report difference at $p < 0.01$). The mathematical basis is that the spectrum carries six numbers and the eigenvector data carry the other 42 (T-300 [T]).

K5. Affect calibration — proposed here [Pr]

Claim under test. Valence is $\mathrm{sign}(dP/d\tau)$ and arousal is $\lvert dP/d\tau\rvert$ (C.1 [C]; its condition — that $dP/d\tau$ is a viability signal — is a semantic postulate).

Protocol. Within-subject time series: continuous valence and arousal ratings during an affect-inducing sequence, and $d\hat P/d\tau$ from $\pi_{\mathrm{bio}}$ with frozen $\theta$. Pass: sign agreement between rated valence and $d\hat P/d\tau$ above the rate obtained after circularly shifting the rating series (the null keeps both autocorrelations and breaks the alignment), pre-registered at $p < 0.01$. Fail: no agreement above the shifted null.

K6. Metacognition and the self-model — existing correspondence, sharpened [H]

The phenomenology map predicts that metacognitive sensitivity (meta-$d'$) tracks reflection $R$. The gate theorem (T-252 [T]) gives the correspondence a form: any decision read through the self-model $\varphi$ loses at most $2\sqrt{3/7}\,\sqrt{P(1 - R_\varphi)}$ of accuracy. The testable consequence [H]: across sessions, the gap between first-order accuracy and metacognitive accuracy grows with $\sqrt{\hat P(1 - \hat R_\varphi)}$. A flat relation falsifies the correspondence, not the theorem.

K7. Adaptation dynamics — existing criteria

Intensity follows $\mathcal{Q}(t) \sim \log(\lambda_{\max}(t)/\langle\lambda_{\max}\rangle_\tau)$ (prediction 3): correlation above 0.7, slope in $[0.8, 1.2]$, adaptation period between 100 and 1000 ms. The falsifiability page lists it as "consistent" with the Weber–Fechner law; a law that many theories share does not discriminate between them, so a pass here corroborates little.

K8. Regeneration and $E$-coherence — existing protocol, underpowered as written

Prediction 2 [T] ($\kappa \propto \mathrm{Coh}_E$) is tested by correlating $\widehat{\mathrm{Coh}}_E$ with recovery rate after a standard stressor, with $n \geq 85$ and a predicted $r > 0.3$ (prediction 2): at $n = 85$ a true $r = 0.3$ is detected with power 0.80 (two-sided $\alpha = 0.05$, Fisher $z$). The protocol read $n \geq 30$ until 2026-09-26; at $n = 30$ the power is 0.36, and a null result would have said almost nothing.

Controls

Control	What it guards against	Source
$\theta$ frozen on wakefulness; no NREM, anaesthesia, REM or ketamine label in the fit	a verdict that reproduces its own training labels	SUB-1
$\lambda_2 = 0$ in confirmatory runs	an estimator that contains the predicate	SUB-2
Phases from EEG, not reaction times	inference data leaking into prediction data	SUB-3
Axis relabelling: repeat the analysis under the 192 elements of $\Gamma_{\!\text{oct}}$ that keep the $E$-axis	a result that depends on a labelling the functor may not see	Corollary 3
Label-shuffle and circular-shift nulls	alignment produced by autocorrelation	standard
Test–retest of every behavioural matrix	an unstable ground truth	Console V0-VAL
Cross-anchor agreement (self-report against wearable on shared sectors)	two instruments estimating different objects	Console V1-VAL
Negative control: a planetary index must not modulate $\hat P$	a pipeline that finds structure anywhere	Console V1-VAL; T-257
Blind raters for any behavioural scoring	expectation effects	test E10

Statistics

• Pre-registration. Hypotheses, pass and fail thresholds, sample sizes, exclusion rules and the reference ensemble are registered before data are unblinded (SUB-4). A test that was not pre-registered counts as exploration, not as corroboration or refutation (the rule of the in-silico suite).
• Power for correlations (two-sided $\alpha = 0.05$, power 0.8, Fisher $z$): $r = 0.3$ needs $n = 85$; $r = 0.5$ needs $n = 29$; $r = 0.6$ needs $n = 20$.
• Power for concordance. With chance agreement 0.5 and a true $\kappa = 0.8$, the half-width of the 95 % interval for $\kappa$ is about 0.20 at 35 sessions, 0.17 at 50 and 0.12 at 100. Separating the corroboration threshold 0.8 from the falsification threshold 0.4 needs about 35 sessions or more.
• Dependent pairs. A dissimilarity matrix over $m$ stimuli has $m(m-1)/2$ entries (4278 for 93 colours), but they are not independent: significance comes from permutation of stimulus labels (Mantel-type tests), not from the pair count.
• Many channels. Tests run over 21 channels or 7 lines form a pre-declared family, corrected by Holm or false-discovery-rate control.
• Effect sizes. Every result is reported with its effect size and confidence interval; paired designs use the Wilcoxon test, as the falsifiability page specifies.

Falsification criteria

Result	What it refutes	Level (three-level system)
$\hat P < 2/7$ in healthy waking subjects, or $\hat P > 2/7$ in N3, with $\theta$ frozen (P8.1, P8.2)	the window as the criterion of consciousness in $D_{\mathrm{nat}}$	structural
$\kappa < 0.4$ between $\mathrm{Cons}(\hat\Gamma)$ and $\mathrm{PCI}_{\max} > 0.31$ (SUB-5)	the concordance claim	structural
Local low-complexity responses with $\hat\Phi \geq 1$, or global stereotyped ones with $\hat P \leq 3/7$ (SUB-6)	the two-exit reading [H]	local
Two states with identical full invariants and distinguishable experience	supervenience of experience on $(\Gamma, \mathrm{Hist})$ — only jointly with a frozen $\pi_{\mathrm{bio}}$ (refutation criterion)	catastrophic
No monotone relation between perceived dissimilarity and $d_{\mathrm{FS}}$ (K3)	the metric prediction; the identification of quality space with $\mathbb{CP}^{n-1}$ [I] loses its only direct support	structural
$\hat\Gamma$ non-positive or irreproducible across sessions (Prediction 21)	the calibration $\pi_{\mathrm{bio}}$, not the formalism	local

What does not count against the theory. Failing to find the anchor of one named quality — the theory never claimed to derive it. A mismatch in a system outside $D_{\mathrm{nat}}$ — there the theory makes no consciousness claim. A single-point numerical agreement — agreement of one number with one fitted constant tests nothing (the withdrawn "PCI 0.31 ↔ 2/7" is the corpus's own example).

Next: Structure → · Back: Overview