Independent verification: R420 compensation rank and minimum-weight kernel

[jsnider3]

This independent verification certifies the accepted PR543 R420 dirty-helper correction matrix: rank 120, nullity 300, minimum nonzero kernel weight 4, with exactly 18 weight-four kernel vectors. No new circuit or kappa is claimed.

The verifier pulls target observables backward through A/scatter/B, independently of the predecessor's forward symbolic interpreter. It checks J=I, V=I and K=D, both products of an explicit 120-by-120 inverse minor, a complete 300-vector kernel basis, and 120 dirty inputs that each isolate one target error when compensation is omitted. The complete D/A/scatter/B/C scalar endpoint also passes on all 660 input columns.

All 87,990 helper-column pairs are checked to exclude kernel weights below four and enumerate every weight-four support. One exact cancellation uses absolute helpers {284, 296, 521, 623}. A separate Boolean interpreter reads the literal source independently and checks all 420 helper-basis directions, plus every nonempty subset of all 18 minimum-weight supports.

A scoped consequence is that a linear factorization of this fixed K through r summaries requires r >= 120. This says nothing about XOR optimality, sequential scratch reuse, or a different supplier.

python3 -I -B research/r420-compensation-rank80/verify.py
python3 -I -O -B research/r420-compensation-rank80/test_verify.py

Expected: PASS_R420_DIRTY_RANK rank=120 nullity=300 distance=4 pairs=87990 isolated_errors=120 controls=10, then seven tests pass. Python 3.10+ standard library only.

Validation passed on Linux x86_64 / Python 3.12.3: normal and optimized runs, byte-identical regenerated certificate, minimal clean export, ten rejecting controls, seven obligation tests, the unchanged PR543 frame/scalar/interface checker, selected-record integrity, review-ledger checks and staged whitespace. Controls include a rank-preserving wrong compensation, a dependent kernel basis, and cleanup damage that leaves K unchanged. Source corruption is rejected; gzip recompression is accepted by decoded payload. Full hosted/native construction, repository-wide suites, Lean and remote CI were not rerun or claimed.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. PR543: 2065fe4f72a914d907f1046603f5a36f17018535. Selected PR626: 660de893d27bb7abd1d5b01b1640207528a5c851. Exact source/blob/payload pins, certificate, proof, validation and local claim are included. Only research/r420-compensation-rank80/ is added. The selected frontier and upstream/ are unchanged; inherited all-size/compiler, common-label/mutable-basis, hosting, precision/tape and analytic obligations remain.

OS assignment seed 80, independent-verification track. No pinned coordination issue existed. The final queue refresh covered 547 open PRs through #728. Concurrent #686/#694 helper-basis and #713/#716 target-basis circuits are credited; this adds a different verification method and explicit rank/kernel evidence for their accepted baseline, without importing or certifying their changes. #612's Lean boundary/B work and #717/#718's different scoped limits are distinguished. This is separate from my #695 CI reconciliation and #712 complex cold-wrapper certificate.

Credit remains with eumemic's PR543 and the original PR493/370/425/472/510 lineage, their preserved notices, and the selected construction authors. Prepared by Joshua Snider, with substantial OpenAI Codex assistance in analysis, implementation, verification and writing. Apache-2.0. Independent implementation does not imply independent human review or a formal proof of integer multiplication.

[Mister-Meeseeks]

100-PR batch review at cf5ff54a358b400a7e69abe941d1d0ad0944b25e.

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

Reviewed scope: Compensation rank/nullity and low-weight kernel census; exact reversed covectors and complete dirty columns, no implemented improved network.

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.