DONE: joint late helper entrances have rank at most one on PR589

[mtpsl]

DONE — scoped negative result in PR1975, exact commit ec0a05954acdbd8f3047c007b0249160d3c7274b. Claim scope released.

All 4,954 common-first-contact supports on the pinned PR589 word were checked. Exactly {444,470} and {444,470,578} survive individually. At targets 113,118,150,153,192,197,214,219 their joint response is (0,1), but accessible source-free helper values map into span{(1,1)}. The dual (1,1) separates these, proving joint entrance rank at most one under the explicit fixed-A/scatter, helper-only prefix and monotone late-compensation contract. The proof permits restored dirty relays after the scatter; it does not resolve the single-triple construction.

Reproduce: python3 scripts/research_package.py --package research/r439-joint-late-entrance-bound. Registered replay passed: source pins, 661-column raw map, all 4,954 supports, eight separating witnesses, four rejection controls, four positive controls, six basis changes and exact certificate equality. No native/hosted/outer replay or new kappa is claimed. Final overlap inspection covered 542 open PR bodies, 60 recent discussions and the available round1929 comments/replies. PR1932 remained at its pinned head.

Credit Sagar Thakrar (PR1932's unrun joint-test question), Philipp/@mightyOil (PR1253 closure), Adam Gall (PR1179 kernel entrance), Ali Romman (PR1128), DreamingOfClouds and eumemic (PR589/555). Prepared by Matthieu Pascal with substantial OpenAI Codex assistance.

Original claim

CLAIM — bit-supplier track, OS assignment seed 0, refined bit-helper-contract card.

Base ae95f60feec79897b153dba6459bb3f9fd4d7b8e; predecessor Sagar Thakrar's PR1932 at d5e6ac0e442a1acfd0ac933af90a2adfb3417138 (explicit unrun joint test), plus the merged PR1253 closure and PR1179 kernel entrance.

Question: can two independent helper-only entrance directions be jointly late-compensated in PR1932's fixed-A/scatter, monotone post-scatter model? Bounded domain: selected PR589 word, the 4,954 common-frame support columns of the pinned PR1253 closure, all joint sets of those columns via a linear-algebraic rank argument. No source-donor entrances, new COPY or changed pre-scatter routing.

First calculation: the two individually surviving supports c1={444,470} and c2={444,470,578} have joint response (0,1) at eight targets, but each target's accessible dirt space maps only to span{(1,1)}. The difference c1+c2={578} gives a dual obstruction. I will independently reconstruct the required finite data, prove the simultaneous-interface implication and check explicit separating witnesses. This does not settle the single-triple restoration question.

Three candidates: multi-donor pre-first-read star absorption (covered by PR1937); construct the open single triple using restored storage relays (larger unresolved synthesis task); the explicitly unrun simultaneous-entrance condition (chosen). Fresh inspection: 537 open PR bodies, 60 recent discussions/handoff comments and local notes. No other joint late-entrance investigation found.

Deliverable: one source-pinned scoped negative-result package with reproducible exact checker, meaningful mutation controls, boundary assumptions, and favorable cost limits. No new kappa, supplier admission, selected-frontier change or full cold replay claim. Expected finish 2026-10-14 16:29 UTC; claim expires 17:29 UTC. Matthieu Pascal (@mtpsl), with substantial OpenAI Codex assistance.