Second-wave reference program: exact tori, orientation protocols, and falsifiable sector tests

[LightChainr]

Purpose

Integrate the second-wave reference and protocol layer after PR #15. This PR moves the project from generic finite-size extrapolation toward exact periodic matching checks, orientation-resolved geometries, frozen discriminating experiments, and explicit separation of numerical evidence from operator-level conjecture.

Base: main (PR #15 is already integrated).

Change class and claim level

• Reference/exact code: C1 validated method/control when covered by exact regressions.
• Frozen protocols and prediction files: C0 preregistered tests until evaluated on their reserved targets.
• Theory/operator notes: C0–C2 hypotheses and evidence organization, not canonical claim upgrades.
• Small exact result notes: reproducible reference artifacts, not asymptotic conclusions.

The repository-wide canonical claim levels remain in docs/STATUS.md.

Main additions

Exact finite-torus reference layer

• axis and 45-degree diamond periodic quotients;
• displacement-potential union-find wrapping detection;
• cluster-side versus wrapping-side Mertens–Ziff identity checks;
• exact Bernstein and power-basis matching polynomials on tiny tori;
• Gaussian-circulant geometry/design utilities;
• correction-annihilation and conditioning tools.

Frozen experiment design

• orientation/matching-sector protocols and server queues;
• angular-normalized root-amplitude prediction;
• Gaussian-doubling lineage predictions;
• held-out two-spin-4 and H4/H12 discrimination designs;
• explicit CPU/GPU and information-value gates.

Theory and decision notes

• orientation harmonic derivations;
• matching/rotation/thermal parity decompositions;
• Virasoro level-4 candidate checks;
• no-go and control-model proposals;
• an operator/sector evidence ledger that keeps exact identities, observations, scaling deductions, and LCFT identifications at separate levels.

Automated validation added during governance review

• Python 3.9, 3.11, and 3.13 CI;
• byte-for-byte replay of the frozen width-22--24 preregistration inherited from Add aggressive matching-structure research program and executable audits #15;
• exact finite matching identity at p=0.37 on:
  • axis L=3, all 512 configurations;
  • diamond L=2, all 256 configurations;
• frozen integer power coefficients for those two exact matching polynomials;
• topology/edge-count contracts and exact-enumeration size guard;
• Python-3.9-compatible population counting in the exact enumerators.

Scientific boundary

This PR establishes executable reference methods and frozen tests. It does not establish:

• a unique asymptotic N^-13/8 law;
• H4 rather than H12/H20;
• an x=21/4 LCFT operator identification;
• matching parity of a physical continuum field;
• an exact or closed-form square-site threshold;
• universality or exactness of kappa_3=-5/3;
• success of any GPU production gate.

Several notes cite later server/confirmation evidence and open issues for context. Those references do not import or canonize the raw server results; the result-bearing integration remains PR #21 and is subject to the provenance/covariance gates in #39 and #46.

Merge policy

Use a merge commit so the historical research ancestry remains available to the result-bearing branches stacked above this PR. After merge, PR #21 should be retargeted to main and reviewed as a separate code/result/provenance layer.

[LightChainr]

Governance review completed for the second-wave layer.

Validation now includes:

• CI on Python 3.9, 3.11, and 3.13;
• exact cluster/wrapping matching identity on axis L=3 and diamond L=2;
• frozen integer matching-polynomial coefficients on both topologies;
• geometry and exact-size guards;
• inherited byte-for-byte frozen prediction replay;
• C++17 compilation/self-test job.

The review exposed and fixed Python-3.9 incompatibility in both exact enumeration paths (int.bit_count).

Acceptance boundary:

• exact/reference implementations are accepted as C1 controls;
• prediction and experiment files remain C0 preregistrations until scored;
• LCFT, H4/H12, matching-parity, kappa_3, and asymptotic statements remain hypotheses or provisional interpretations;
• contextual references to server results do not canonize the raw result archive.

Merge with ancestry preserved so the server/result branches can be reviewed as the next separate layer.