Prove the fixed-contract T74 inherited-correction floor

[petalas]

Summary

research/t74-inherited-centre-floor/
  README.md                 scoped proof and reopening conditions
  verify.py, test_floor.py  independent exact checker and behavior tests
  INPUTS.json, inputs/      two source-bound words and original notices
  RESULT.json               replayable certificate

Resolves the restricted target-support part of PR2696's released Discussion2612 handoff.

The inherited partner sources {33,55,74,85} have an exact correction matrix of determinant -1/16. Under the stated separated-source and fixed target-continuation contract, reassigning only the eight recovered sources cannot cancel its four target rows. With the additional exact line-30 frames, pinned cut incidences and a zero reader per rank-eight centre, the sharp cut bill is 4H7 + 4H1 + 4H8. Both published words attain it.

The zero-reader hypothesis is explicit and necessary for this cut theorem. Changing partner recovery, target coordinates, target frames or the reader contract remains open. This is not a bound on all assignments under changed contracts, a global packing optimum, supplier admission or a new kappa.

Evidence

• Before: omitting the inherited correction leaves eight nonzero partner-source coefficients on targets {23,34,50,108}. A single omitted ADD independently produces the exact nonzero residual on targets 23 and 108.
• After: both provider words pass the independent four-source projection, invertible target-continuation check, chart/frame checks and literal cut invoice. Seven mathematical rejection controls per provider pass.
• Registered offline replay and source metadata/pins pass on Linux/Python 3.12.15. Six behavior tests pass, including actual normal/optimized CLI equality with the retained receipt and corrupt-source rejection before parsing. Python 3.13 produces the identical receipt. Ruff diagnostics and 69 repository research-workflow tests pass.

python3.12 -B scripts/research_package.py --package research/t74-inherited-centre-floor
python3.12 -B -m unittest discover -s tests -p 'test_research_*.py'
ruff check --select E,F,B,I,UP,SIM research/t74-inherited-centre-floor

Exact pending dependency: PR2696 5a42add713e09a8798a84d0be7a8276626d9e785. Started from canonical main c3c94c2e; refreshed main 21ec98bf and live overlap through 2026-10-15 18:21:42 UTC, priority revision 5. Relevant guidance, selected record and dependency head were unchanged. The overlap helper reported complete metadata pagination over 770 open PRs and 1,337 Discussions. This is not a novelty guarantee.

Credit Mason Hale for PR2696 and its words; zxv/2530 for recovery, Tekalign/2436 for lifted compensation, Jeremy Kothe for the words/hosting, and the retained native/bit/owner lineage. Source bytes and notices are unchanged. New work is Apache-2.0.

Only four source columns are audited. Native phases, complete dirty-state correctness, cleanup, hosting, precision, the global invoice, outer inequalities and all-size multiplication obligations are not reverified. No independent human review is claimed. Next work must change a named inherited partner path or target/cut contract and supply its full bill; other A/B or owner-fill improvements are not excluded.

Engineering choices: Build the Lever produced the standalone checker; Prove It Works required the actual words and semantic failure controls; Laziness Protocol kept all changes in one additive package.

Merge Danger

Door: two-way. Only a new research package is added; frozen inputs, production verifiers and the selected frontier are untouched.

Blast radius: research. The package opts into the bounded replay hook. Its theorem must retain the separated-source and fixed-reader hypotheses.

[thakrarsagar]

For reference, #2865 independently re-derives this PR's core facts on PR2696's words with separate code:

• Q on rows 23, 34, 50 and 108 has det −1/16;
• the omitted residual, T invertible and F_P + T Q_P = I_P;
• the forced centres {9, 92, 224, 240} and the invoice 4H7 + 4H1 + 4H8.

It also evaluates your hypotheses, quoted verbatim, as computed booleans on #2751's words:

• changed: h1, the compensation clause of h2, h3 and the line-30 premise;
• kept: the continuation clause of h2, the cut incidences, the zero readers and the rank-8 producers.

So #2751 lies outside the stated family, as your exclusion list says, and constructively answers your first open question: the partner correction moves to rows 21, 37, 47 and 110 (det 1/2), which are never cut-written. No error was found in this PR.