A Deliberately Constrained Third Path
Theories of consciousness divide into mechanism-driven proposals (Integrated Information Theory, Global Workspace Theory, predictive processing) and structure-driven proposals (geometric or topological substrates, neural-population dynamics). The mechanism-driven proposals offer compelling axiomatic stories. The structure-driven proposals produce numbers but often rely on fitted parameters, learned weights, or domain-specific calibration.
This paper takes a deliberately constrained third path. Once a substrate is chosen, we ask which neuroscience phenomena it is consistent with under no shape parameter tuning, no learned weights, no subject-level measurement fitting, and no neural-data-fitted shape parameters.
The 600-cell regular 4-polytope V600, treated as a graph with H4 Coxeter symmetry. Once this is selected, the vertex set (|V| = 120 on the unit 3-sphere), uniform vertex degree (12 by H4 transitivity), and Laplacian spectrum are forced by the construction. The response operator Cφ = LM + φ−2I is fully fixed once the graph is constructed.
The 600-cell has been studied in pure mathematics for over a century. To our knowledge it has not been proposed before as an empirical candidate substrate for consciousness-linked signatures. This paper does not derive that it must be the substrate; it asks what survives if it is taken as one.
Six Drug/Sleep EEG Signatures
Four conditions × 800 ticks at deterministic seed 42, on the recurrent layer above the same Cφ. Per-condition observables (avalanche power-law α, integrated-information Φ, modality-switching ratio, intensity variance, continuity) are tested against literature-derived thresholds.
| # | Signature | Reference | Predicted | Observed | Verdict |
|---|---|---|---|---|---|
| 1 | NREM-N3 variance ratio (vs Wake) | Sleep-EDFx W→N3 | ~0.365 | 0.463 | PASS |
| 2 | Propofol switching ratio | OpenNeuro ds005620 | [1.5, 5.0] | 1.83× | PASS |
| 3 | Propofol continuity drop | Brodbeck 2012 | > 0.020 | +0.066 | PASS |
| 4 | Propofol Φ collapse (IIT direction) | Tononi 2008 | collapse | 0.33× Wake | PASS |
| 5 | Recovery deterministically identical to Wake | protocol | identical | identical | PASS |
| 6 | Wake cascade-α in SOC band | prior pipeline / Sleep-EDFx | SOC band | 2.252 | PASS |
Wake cortical-avalanche power-law exponent α = 2.252, 95% CI [1.82, 2.86] (R² = 0.956).
This CI three-way overlaps the real Sleep-EDFx EEG CI [2.50, 2.53] (n = 30 subjects) and the prior aria-chess cascade-pipeline CI [2.73, 3.25]. Pairwise overlapping; the substrate's power-law exponent is consistent with both an external EEG dataset and an independent prior pipeline.
Eighteen Preregistered Correspondences
Eighteen substrate/neuroscience correspondences were preregistered with thresholds frozen on 2026-04-18 — before any of the validation runs in this paper. The tally:
17/18 at standard methodology. 18/18 after a documented N=20 deep-dive on the residual high-variance interaction test (P4: context-rotation × partial-emission cascade). No preregistered threshold has been modified.
The original 2026-04-20 reading was 15/18 — a methodology-limited reading on the high-variance interaction term, not a content failure. The closure of the three gaps (P3 N=5, P4 N=20, P13 LOO/state-reset) is documented transparently in the validation log. The open prereg-exact P10 20-permutation rerun is acknowledged as still pending.
Strong-coupling architectural finding
Two cascade mechanisms in the recurrent layer — context rotation (C) and partial emission (P) — are causally identifiable within the factorial ablation model. They exhibit strong synergy: the interaction term ΔCP = +0.190 at N=20 (95% bootstrap CI [+0.143, +0.239]; 0/2000 resamples at or below zero) is comparable in magnitude to the P main effect of −0.218.
The original 3-seed estimate (+0.044) was an underpowered estimate on a high-per-seed-variance term (std = 0.089 at N=20). N≈20 is contributed as a planning scale for similar cascade matrices — recommended as a preregistration-practice consideration, not a finding.
Cross-Domain Selectivity
The substrate exhibits selective amplification in the two cross-domain tasks tested, and serves as an H4-transitive deterministic null reference for cortical functional connectivity:
+40.6pp lift
4-category position classification on 8-D V2 features. Leave-one-out at canonical depth n=25 ticks: raw 53.1% → substrate-routed 93.8%. Prereg threshold >= +15pp on 5-fold CV.
−4.4pp lift
Utterance classification at raw 87.5%. Within preregistered neutrality bounds (|·| < 10pp). The substrate routes selectively, not universally.
Outside biological range
Full-cohort descriptive: −11.58σ on degree homogeneity, +79.78σ on participation ratio (with node-count caveat), +6.80σ on clustering. ARIA is a deterministic null reference, not cortex.
The HCP σ-distances license "outside the biological distribution", not "cortex has drifted from an ideal polytope". The substrate is an H4-transitive deterministic structure; the human cortex is not. The numbers describe how far apart they are on specific graph statistics — nothing more.
Mapping Numerics to Claims
The paper applies an explicit claim-boundary discipline. Each numerical result maps to a strictly bounded language:
"Consistent with"
A result that lands inside its preregistered threshold licenses a "consistent with" claim. Not "matches" or "validates" — consistent.
"Decisively above"
Chess +40.6pp vs the +15pp floor licenses "decisively above prereg", not "proves". An order of magnitude past the threshold is a strong signal, not a proof.
"Outside the distribution"
HCP −11.58σ on degree homogeneity licenses "outside the biological distribution", not "cortex has drifted from a polytope". Statistical distance, not interpretation.
The paper never writes "the substrate is cortex" or "derives consciousness". The discipline is enforced throughout the results section.
Stated Limitations
- Not a uniqueness claim — alternative regular 4-polytopes (24-cell, 120-cell) are an explicit ablation build, not a discharged comparison
- Not a derivation of consciousness — the substrate witness shows quantitative agreement with cortical signatures; it does not establish that the substrate is consciousness
- Not a selection theorem on the adaptive-closure-transport 4-tuple — no Lyapunov function on the reduced flow, no 2I-equivariance audit, no formal edge-space decomposition
- Not a circuit-level model — no identification of which neural populations implement context rotation or partial emission
- Not a derivation of the φ−2 shift — it is a design-level stability clamp, not derived from a closure functional
- The strengthening builds (cross-seed CIs on the recurrent-layer signatures, alternative-polytope ablations, independent N=20 C×P replication, cross-parcellation HCP replication) are listed as open
What This Is, And Is Not
One operator, no parameters tuned to neural data. Four conditions, one deterministic seed. The substrate witness, deliberately constrained — tested, not interpreted.
demo_drug_sleep_v4.py at github.com/vfd-org/closure-kernel-papers. The full validation harness (chess robustness P9–P13, conversation closed-loop, HCP brain functional-connectivity comparison) lives at github.com/VFD-org/aria-chess. MIT licence.