[mihir-s-05]

The fixed three-field, monotone-frame contract already forces the incumbent paid cost in all 128 eligible forward PR4470 receiver windows. This package proves that statement for every finite scalar-shear word, without a length or coefficient bound, and for every nonnegative concave integer-rank price with f(0)=0, including r^t for 0<t<=1. The original path attains each floor. No new kappa is claimed.

The proof uses two necessary conditions: a contact that carries the original source must contain its entrance subspace, and every bridge of the admissible-contact graph must be used. Coarsening each field's path at those contacts gives a finite list of necessary rank partitions. Exact capped-sum inequalities establish the concave-price comparison. There is no word or state-graph truncation in the proof.

Scope and coordination

Adds only research/receiver-contact-floor/: the written proof, source-bound checker, complete 128-window certificate and registered metadata.

Canonical investigation: Discussion #4574. The submission refresh found concurrent #4572, #4573 and #4577, with public finite-state certificates now in #4581 and #4582. This is a parallel static-contact proof/checker, with no priority claim and no claim to have reviewed those packages. It supplies a different, small structural argument for the same conclusion.

Base and refreshed canonical main: f626db5c3a3d781d8f7695038776c621651f75e1, priority revision 7. Scientific predecessor pins are retained in TASK.json. #4567's later 5ac594d1bc1e6d91f20ef8157f38bb9b29768bfd adds nonadjacent/single-contact checks; this package stays with the original 128 adjacent forward windows. Remote overlap pagination was complete; sparse local-note coverage was not.

Evidence

• All 128 boundaries reconstructed from seven authenticated PR4470 constructor/data inputs: 96 triangle contact graphs and 32 two-edge trees.
• Every coarsened partition passes exact integer concave-price inequalities; every incumbent is attained.
• 2,989 actual geometric paths across three tiny contracts, drawn from all 84 exact-endpoint unit-shear words through length four, satisfy the information invariant and relaxation containment.
• Removing the information or bridge condition admits a false (2,1) bill in a (1,1,1) case. A changed-boundary fixture genuinely improves to (2,2,2), showing the checker does not assert a universal ceiling.
• Decreasing contacts and rank-mass mismatches rejected. Private exported-copy controls reject altered rank, boolean type, missing certificate field, and modified/missing constructor.
• Registered replay, isolated optimized replay, committed-byte check and final-commit Git-free export replay passed on Windows / CPython 3.12.0, standard library only. Direct replay takes about two seconds.

python -B scripts/research_package.py --package research/receiver-contact-floor
python -I -O -B research/receiver-contact-floor/verify.py
python -B scripts/check_research_commit.py --package research/receiver-contact-floor

Exact publication head: 025f37fe346203cfe18d47367ce239e420961d36. Local passing checks are not a claim of upstream CI success.

Hosted CI outcome: run 39746239704 failed in the repository-wide onboarding step, before package selection/replay. All four failures are in unchanged tests/test_research_current_status.py: the selected decimal's bold formatting, the historical heading/banner, and the old CI replay documentation. The test file and its three inputs are byte-identical to base f626db5c3a3d781d8f7695038776c621651f75e1. A private extraction of those four base files reproduces exactly the same four failures (and two passing tests) with python -I -B tests/test_research_current_status.py. The research-package CI job was skipped; the package's registered local and Git-free checks passed. This PR keeps the shared documentation repair outside its isolated research scope.

Limits and credit

Fixed three persistent fields and fixed monotone boundaries only. No extra/owned fields, decreasing frames, internal warps, backward-window claim, joint/nonadjacent rewrite theorem or summation of overlapping gains. Reusing the source constructor does not independently validate the full native/phase/stock/precision/compiler/outer construction. The default selected baseline was attempted but unavailable in this sparse checkout; selected cold replay was not run. The selected kappa=0.0023 record is unchanged.

Credit Chris R / Clear1nsight (#4546), Ryanson Jonathan / pinterbanget (#4567), Cinna Davis / 1337isnot1337 (#4470), zxv, Jacob Alan Sussman and the retained native/Clifford/geometry/outer contributors. Concurrent investigations are linked above. Prepared for Mihir Srivastava with substantial OpenAI Codex assistance; author-checked, not formal or independent human review. Apache-2.0.

Open next questions specify fully paid additional-field or joint-boundary contracts and independent review of the source-information/coarsening lemma.