neosynaptex

Cross-substrate γ-scaling diagnostics. γ ≈ 1 is treated as a candidate regime marker under active falsification, not a confirmed law and not a definition of intelligence. The canonical statement is in CANONICAL_POSITION.md; the per-claim layering ladder is in docs/CLAIM_BOUNDARY.md.

What it is

neosynaptex is a measurement protocol and Python implementation for estimating a scaling exponent γ between a thermodynamic-cost proxy K and a topological-complexity proxy C on coupled dynamical substrates, under the working ansatz K(C) ~ κ₀ · C^{-γ}. The protocol enforces:

• per-substrate adapter-code hash binding (a drifted adapter refuses to load),
• pre-registered null families (shuffled, IAAFT, AR(1), block-bootstrap, plus the wavelet-phase null in core/nulls/),
• per-substrate prereg + verdict in evidence/replications/registry.yaml,
• a canon-closure overclaim gate (tools/audit/claim_overclaim_gate.py).

There is one anchored proven row (Lemma 1, Kuramoto on dense graphs, γ̂ = 0.9923 numerically); every other substrate row is empirical and substrate-conditional.

Current evidence state

Source of truth: evidence/replications/registry.yaml.

Falsifying / null-result records (reduce, do not extend, the γ ≈ 1 framing):

• binance_btcusdt_1h_pilot_2026_04_14 — γ ≈ 0, r² ≈ 0.001, all nulls indistinguishable. Hourly BTC/USDT log-returns are inconsistent with a γ ≈ 1 marker at this resolution.
• fred_indpro_pilot_2026_04_14 — verdict pending; bounded-secondary, does not license any market criticality claim.
• physionet_nsr2db_n5_multifractal_2026_04_14 — verdict theory_revision. Across n = 5 NSR subjects γ mean = 0.50, std = 0.44, range [0.07, 1.09]. The cardiac substrate is not consistent with universal γ ≈ 1 at the 5-subject pilot level.
• physionet_nsr2db_nsr001_pilot_2026_04_14 — superseded by the multifractal n = 5 result; the n = 1 outlier is retained for record only.
• The EEG MNE eegbci pilot (n = 20) and the within-substrate falsification for stateless-LLM inference (experiments/lm_substrate/) are documented separately and do not pass the cross-substrate convergence claim either.

The single positive within-substrate finding currently on file:

• physionet_chf2db_pathology_contrast_2026_04_14 — verdict support. The 2D (h(q=2), Δh) cardiac fingerprint discriminates n = 5 healthy NSR from n = 5 CHF; Welch t = −4.05, Cohen d = −2.56 on h(q=2). This is a within-cardiac contrast at pilot scale; it does not license clinical, diagnostic, or cross-substrate conclusions.

Net position: γ ≈ 1 has no surviving cross-substrate convergence claim at this commit. It remains a candidate regime marker, falsifiable per substrate.

Repository layout

• neosynaptex.py — engine module: γ-scaling, Jacobian/spectral, phase state and adapter health monitor.
• core/ — measurement primitives: gamma.py, gamma_registry.py, nulls/ (shuffled, IAAFT, AR(1), block-bootstrap, wavelet-phase), iaaft.py, multiverse.py, falsification.py, plus axiom/contract helpers. Approximately 60 modules.
• contracts/ — invariant enforcement (invariants.py, truth_criterion.py, provenance.py, claim_strength.py, fail_closed.py).
• substrates/ — per-substrate adapters and per-substrate READMEs. Current substrates: bn_syn, bridge, cfp_diy, cns_ai_loop, eeg_physionet, eeg_resting, geosync_market, gray_scott, hippocampal_ca1, hrv, hrv_fantasia, hrv_physionet, kuramoto, lotka_volterra, market_crypto, market_fred, mfn, mlsdm, mycelium, physionet_hrv, serotonergic_kuramoto, zebrafish.
• evidence/ — registries and ledgers (gamma_ledger.json, replications/, levin_bridge/, surrogates/, manifests/).
• evl/ — evidence verification ledger.
• experiments/ — replication runners (e.g. lm_substrate/ for the stateless-LLM null result, lemma_1_verification/).
• tests/ — 136 test_*.py files (145 .py files total in tests/).
• tools/audit/ — overclaim gate, replication index check, horizon-trace lint, hash-binding gate.
• docs/ — CLAIM_BOUNDARY.md, REPLICATION_PROTOCOL.md, NULL_MODEL_HIERARCHY.md, MEASUREMENT_METHOD_HIERARCHY.md, plus the archived pre-canon material under docs/archive/.
• formal/ — Coq and TLA+ specifications (skeletons; see formal/coq/bnsyn/README.md and formal/tla/bnsyn/README.md).
• manuscript/ — arXiv submission source for the Kuramoto Lemma 1.
• .github/workflows/ — 21 CI workflow files (overclaim gate, ledger binding, claim-status, replication index, kill-signal coverage, measurement contract, semantic-drift, etc.).

Requirements

Hard runtime dependencies (pyproject.toml):

• Python ≥ 3.10
• numpy >= 2.2.6
• scipy >= 1.15.3

Replication runners and dev tooling additionally need: PyWavelets, wfdb, scikit-learn, pytest, pytest-cov, pytest-timeout, mypy, ruff, import-linter, pyyaml. See pyproject.toml [project.optional-dependencies].

Some replication scripts download external datasets (PhysioNet, FRED, Binance public REST). Network access is not assumed by tests.

Installation

pip install -e .[dev]

Usage

The smallest in-tree demonstration:

from neosynaptex import Neosynaptex
# Adapter classes live under substrates/; see each substrate README for
# the import path and contract.

Replication scripts at the repo root each correspond to one registry entry, e.g.:

python run_btcusdt_replication.py            # falsifying record
python run_nsr2db_hrv_multifractal.py        # theory_revision record
python run_chf2db_hrv_contrast.py            # within-cardiac support record
python run_null_family_screening.py          # null-screen pipeline

Each script writes its artifact under evidence/ or results/. The expected output structure is documented inside the matching prereg under evidence/replications/<slug>/.

Tests

pytest -q

The repo currently ships 136 test_*.py files under tests/. The runtime hash-binding gate refuses to load if the on-disk substrate-adapter SHA-256 does not match the value pinned in evidence/gamma_ledger.json; this is by design and not a test failure. To rebind after an intentional adapter change, follow tools/audit/replication_baseline.json.

Output

• evidence/gamma_ledger.json — pinned per-substrate γ records and adapter hashes (the binding source).
• evidence/replications/registry.yaml — pre-registration index; canonical list of substrate verdicts.
• evidence/proof_chain.jsonl — append-only proof-chain log.
• results/, reports/, figures/ — per-script artifacts.

Notes and limits

• γ ≈ 1 is not validated as a cross-substrate law. Treat any artefact that says otherwise as out-of-canon (see CANONICAL_POSITION.md and the forbidden-phrase list in tools/audit/claim_overclaim_gate.py).
• The CNS-AI-loop substrate is historical-exploratory only; the underlying corpus is non-reproducible. See docs/CLAIM_BOUNDARY_CNS_AI.md.
• Lemma 1 (Kuramoto, dense graphs) is the only proved row. It is a reformulation of Restrepo–Ott–Hunt (2005) and validity depends on the RoH spectral assumptions; non-trivial spectral topologies remain open.
• Pareidolia, mystification and "γ defines intelligence" framings are explicitly forbidden and gated mechanically.

License

AGPL-3.0-or-later. See LICENSE and LICENSE_BOUNDARIES.md.