Audit P104 cross-axis encoding mismatch and exact boundary transition

[Clear1nsight]

The proposed P104 row encoding does not match the reversed column encoding at the retained two-stage boundary. On constant address functions, a two-unit pivot input produces 48 extra signed-unit Y fields in the row representation and none in the column representation. A common completed C commutes with each encoding separately; it does not cancel their difference.

This package derives the exact literal-slot transition K = S Pi_c L_c S L_r^-1 Pi_r, retaining physical source/target orientation and both dirty-helper banks. A direct common-chart factor word is fully counted (179,712 unit ADD/SUBs, 21,632 halves and restoring doubles each, 19,968 signs and slot swaps each), with physical transports/owners/precision explicitly unpriced. Under PR3954's unchanged named scaffold hypotheses, even free interface work leaves the existing 44,096 rank-mass deficit. Stop native expansion for that contract.

Scope: an exact interface lemma and physical constant-sector counterexample. The canonical caller supplies a two-stage boundary, but does not supply an actual adjacent completed P104 pair. The reversed-column encoding is an explicitly proposed swapped-role contract, not an admitted inverse native word. No supplier, new kappa, runtime gain or frontier change.

Scientific head: afd6bb0a701e9ffd685f27674adaac86687e5f02; root tree 709f05c21826efa6f6fad3cdcaed5069ae5cf546; canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority 6. Two scoped commits add 11 files only under research/p104-encoded-boundary/. Three canonical-main live inputs; no unmerged source dependency.

Verification: primary root/matrix reconstruction and all 208 local inverse basis fields; independent dense all-column checks on four common/varying-chart fixtures and 12 failure controls; six behavioral tests including optimized Git-free read-only export, corrupt/missing source and false results. Registered Python 3.12 replay and exact-public-head publication-byte/source-history preflight pass. Final-head hosted CI passes, as recorded below. No human/kernel audit or selected cold replay claimed.

python3.12 -B scripts/research_package.py --package research/p104-encoded-boundary
python3.12 -B scripts/check_research_commit.py --package research/p104-encoded-boundary --check-source-history

Taken from PR3954's handoff under the coordinated three-scope claim. Main and overlap refreshed; root checked all 662 open PR bodies including drafts and bounded live Discussions. The pre-submission latest-100 delta found new distinct P112 PR3960 and the updated, different PR3577 coefficient-consumer scope. This item excludes sibling private-COPY retirement/coverage studies and PR3956's completed adapter comparison. The next obligation is an actual chronological completed-call pair with matched physical encoding, helper maps and fixed returns, together with a changed favorable complete bill.

Credit Chris R / Clear1nsight's PR3882/3940/3943/3954 representations, caller and gate; ToikY/PR3956 comparison; Rohan Arun/PR1972, Chafik Boukhalfa/PR1991, Adam Gall/PR1940, Josie Elliston/E8, Sagar Thakrar/PR1012, Douglas Colkitt, Dominik Scholz and retained native/compiler/occupancy lineage. New audit by Chris R / Clear1nsight with substantial OpenAI Codex assistance, including separate agent scope and root cross-check. Apache-2.0. No merge or selected-frontier change.

Final-head offline confirmation: all three commands pass under -I -O -B from the official Git-free read-only export, with all 15 exported hashes and modes unchanged. Archive SHA256 52a3d0c1fc9dab45856d3cc11ce443325e9bf316dcac8c17df1d530904981246. The first official cold replay exposed copied read-only modes in destructive-test fixtures; the second commit changes only three lines to make owned temporary copies writable. Scientific inputs, proof and numerical result are unchanged. Hosted run39214265329 passes at final head afd6bb0 on first attempt, testing merge2edcb82477ac3b617abe7bf4e6483b5651256b7e against unchanged main20ecf2891d80b5acf18d980b2164fb44ea7faa90. Planning, all three registered commands and git diff --exit-code pass on hosted Python3.12.15: primary audit, separate104-column/four-chart checker, all12 operator controls and all six behavioral groups. These execution checks preserve the scoped claims and remaining physical/supplier obligations.