closure-kernel-papers

A paired-preprint reproducibility bundle for the closure-response operator $C_\varphi = L_M + \varphi^{-2} I$ on the 600-cell, threading two domain-disjoint empirical witnesses on a single fixed operator with no kernel-shape retuning between regimes.

This repository ships two preprints as a single coherent release. They share an operator. Paper A defines and proves it; Paper B is one of the two empirical witnesses below it.

	paper	scope	reproduces
A	aria-closure-kernel — operator witness	The geometry-fixed kernel $C_\varphi$ on $V_{600}$. Discrete-to-continuum agreement, operator-norm identity, multiplicity-weighted shell-radius Pearson correlation.	python3 verify_kernel.py (~1 s)
B	aria-chess — active-regime substrate witness	Eighteen preregistered cortical correspondences and six drug/sleep EEG signatures from the same kernel via a deterministic recurrent-layer trajectory at seed 42.	python3 demo_drug_sleep_v4.py (~30 s)

Headline numbers (already in repro/results.json and re-derivable)

Paper A — operator witness on $V_{600}$

quantity	value
$|V|$, $|E|$, degree	120, 720, 12/12 (uniform)
Laplacian spectrum (multiplicities)	${1, 4, 9, 16, 25, 36, 9, 16, 4}$
$|C_\varphi^{-1}|$ vs $\varphi^2$	$2.618033988749902$ vs $2.618033988749895$
Per-vertex correlation (unweighted)	$0.976202$
Per-vertex correlation ($\varphi$-cocycle, geometric / arithmetic)	$0.888380$ / $0.884364$
Multi-source sweep (120 sources, unweighted) max − min	$\sim 2 \times 10^{-15}$

Paper B — six EEG drug/sleep signatures, single deterministic seed 42

cond      α       95% CI               R²     pass
WAKE      2.252   [1.82, 2.86]         0.956   ✓
SLEEP_N3  3.250   [2.44, 4.14]         0.886   ✓
PROPOFOL  2.758   [2.52, 3.09]         0.931   ✓
RECOVERY  2.252   [1.82, 2.86]         0.956   ✓ (matches WAKE)
═══ TALLY: 6/6 signatures match ═══

WAKE α=2.252, CI [1.82, 2.86] is the three-way overlap with Sleep-EDFx EEG ($n{=}30$, $[2.50, 2.53]$) and the prior aria-chess cascade pipeline CI $[2.73, 3.25]$ — overlapping pairwise.

What this bundle claims (and does not)

A single fixed operator on a single fixed graph appears beneath two domain-disjoint empirical works without kernel-shape retuning. That is the load-bearing claim.

Explicitly not claimed: no derivation of the $\varphi^{-2}$ shift from first principles; no uniqueness of $V_{600}$ among regular 4-polytopes; no kernel-uniqueness on either empirical landing (the b-anomaly AIC tie, free-width-Gaussian alternative, and Mode-B drift caveats are inherited verbatim from that companion repo); no selection theorem on the adaptive-closure-transport 4-tuple; no derivation of consciousness; no circuit-level model. See each paper's §1 claim-boundary box and §9 limitations.

Repository layout

papers/aria-closure-kernel/         # Paper A — operator witness
├── README.md                        # paper claims, files, repro
├── paper/                           # tex + built PDF
└── repro/
    ├── verify_kernel.py             # one self-contained ~470-line script
    └── results.json                 # canonical numerical outputs

papers/aria-chess/                  # Paper B — active-regime substrate witness
├── README.md                        # paper claims, files, repro
├── paper/                           # tex + built PDF
├── brain_mapping_refs/              # frozen preregistration documents (8 files)
└── repro/
    ├── kernel/                      # 6 modules, MIT-headered
    ├── demo_drug_sleep_v4.py        # six EEG signatures, single seed 42
    └── reproduce.sh                 # convenience driver

LICENSE                              # MIT
CITATION.cff                         # both papers as preferred-citation/references
pyproject.toml                       # `pip install -e .` makes `kernel.*` importable

Build the PDFs

Both PDFs are pre-built (papers/*/paper/main.pdf). To rebuild from source:

cd papers/aria-closure-kernel/paper && tectonic main.tex
cd papers/aria-chess/paper          && tectonic main.tex

(Or your favourite LaTeX toolchain. The bibliography uses natbib with plainnat style.)

Reproduce the headline numbers

# install once: numpy + scipy + makes `kernel.*` importable
pip install -e .

# Paper A: ~1 s, no randomness, no external data
cd papers/aria-closure-kernel/repro && python3 verify_kernel.py

# Paper B: ~30 s, deterministic seed 42, no external data
cd papers/aria-chess/repro && ./reproduce.sh

Companion empirical work not in this bundle

Two empirical landings have their own code bases, not bundled here:

• Passive regime — b-anomaly (vfd-b-anomaly): LHCb angular-anomaly fit on five public datasets. Threaded by Paper A §6.
• Active regime — aria-chess (aria-chess): full validation harness (chess robustness P9–P13, conversation closed-loop, HCP brain functional-connectivity comparison). The minimal repro here covers the operator, the geometry, and the six EEG signatures only; larger artifacts (chess engine, training data, HCP data) are not redistributable.

Status

Preprint, not peer-reviewed. April 2026.

License

MIT — see LICENSE.

Citation

See CITATION.cff. BibTeX-equivalent entries are inside each paper's references.bib.