independent verification: r420 lattice parity and 480 added incidences

[6ojo]

independent finite verification; no new kappa. this certifies the selected #543 roots in the intrinsic lattice quotient L/2L and exhausts all 672 frames' binary-span root memberships. all dimensions agree with the rational frames, but 180 dimension-six frames gain two root classes each and 120 dimension-seven frames gain one: 300 changed closures and 480 extra memberships.

every extra membership has an explicit integral lift, a nonzero rational minor, and an independently checked orthogonality witness. the 120 root lines correspond bijectively to the 120 quadratic-value-one classes among all 256 quotient classes. reducing the displayed coordinates directly modulo two instead gives only 15 root residues, so the checker first certifies an integral lattice basis and every root coordinate.

this adds the intrinsic characteristic-two census and lift witnesses beyond sagar thakrar's #737 (b41e73169430641be18c988c659d2855a6a6218a), which certifies rational/odd-prime geometry. it does not challenge #737 or allege a supplier defect. eumemic's existing p111 use of lattice classes for decoder affine rank is explicitly credited; that idea is not claimed new. no predecessor arithmetic is imported.

reproduce

python 3.10+, standard library only:

python3 -I -B research/r420-lattice-parity/verify.py
python3 -I -O -B research/r420-lattice-parity/test_verify.py

expected: pass_r420_lattice_parity: 120 anisotropic classes; 672 frames; 300 changed closures; 480 extra memberships; 11 rejected controls, then six passing test groups.

evidence and scope

• complete exact certificate: 65,536 polarization pairs, 14,400 root pairings, 80,640 frame/root memberships and all 480 integral lifts.
• a separate direct-pairing encoding with modular elimination matches every parity closure. permutation determinants check the arithmetic, and original-coordinate lifts plus positive norm/orthogonality independently check every extra witness.
• normal and optimized isolated replays pass on windows / python 3.14.7. relocation, source/certificate corruption, missing input and output preservation are tested. a committed-files-only replay passes, and the exported patch applies cleanly to the exact base.
• the unchanged Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543 660-column checker and selected-record/source-inventory check pass. full repository/cold supplier replay, linux ci and lean were not run for this additive package.

only eight files under research/r420-lattice-parity/ are added. the selected frontier and upstream/ are unchanged. this finite result does not construct or price a new decoder, discharge the inherited compiler/realization/hosting/precision/tape/analytic assumptions, or prove the multiplication theorem.

base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. #543: 2065fe4f72a914d907f1046603f5a36f17018535; consuming #626: 660de893d27bb7abd1d5b01b1640207528a5c851. source hashes, exact certificates, bounded coverage, seed 76, the overlap-driven scope change and predecessor attribution are included. no pinned coordination issue exists; the claim/result are local.

prepared by gojo (@6ojo) with substantial openai codex assistance; apache-2.0. “independent” describes the implementation, not independent human review.

upstream ci at submitted head a4ef6ed2f33834e4599bf84317ae9d98ba2d9547 reports five action_required workflow conclusions; no remote ci pass is claimed. research workflow.

[6ojo]

fun fact- 41min, ~6mil tokens
reset hit mid-task so idk usage

[Mister-Meeseeks]

100-PR batch review at a4ef6ed2f33834e4599bf84317ae9d98ba2d9547.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Intrinsic E8 lattice quotient audit: 300 frames gain 480 incidences mod 2; correct lattice coordinates, not a defect in the retained rational supplier.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.