[aliromman]

The proposed 31-leaf caller with five rank-two connectors is impossible under the requested two-port full star contract. Paired rank-two full queries need total thin rank at least 28, rather than ten. Even arbitrarily fine nonzero full-stage splits at this dimension need rank at least 20. No kappa increase is claimed.

Proof, complete tariff and obligation ledger, exact evidence, source pins.

The new theorem applies over every characteristic-two field and every finite dimension. If the core dimension is d, every nonzero full query has rank at least r, and b is the extra thin row dimension, then g <= (floor(d/r)+1)b+2. The image-space version is the same. For paired stages this gives R >= 4q+2 ceil((g-2)/3). A prefix determinant contradiction forces a dimension drop on untouched leaves; iteration proves the bound. This uses chronology, beyond the static cut in PR5673 and its sharp witnesses in PR5681. Those static witnesses remain valid. The old 127-leaf ten-rank-one target now needs rank at least 88.

An exact concave tangent proves that every paired-star profile with one or two coupled ports loses at saving .00256, for every positive leaf count. All larger savings lose too. The calculation retains the entire pinned PR5599 paid and helper inventory and charges the new thin-rank lower bound. It is a scoped recursive-tariff ceiling, not a general native lower bound.

A second proof gives a sharp map-count bound: commuting full projectors need at least ceil(g/2) thin maps of any rank. WORD31.json is a complete binary endpoint at that bound: 62 full calls and 16 thin maps of rank eight per two-port block. Every Laurent coefficient is checked without expanding 2^31 stage terms. At 104 ports its 6656 thin rank-one queries give linear margin -3472 and loss at every concave moment. This is a positive operator control with a negative complete recursive price; it is not a native supplier.

Five-map construction targets now need larger coupling and noncommuting full projectors. The 31-leaf, 26-port profile and 13-leaf, eight-port profile pass the new necessary bound and optimistic prices .0035 and .0034. Neither has a supplied word. Two all-order small coupled-seed searches timed out and remain unknown. Native frame maps, physical reads, owned/borrowed state, COPY/CLEAR, dirty compensation, restoration, routes, precision, compiler and outer transfer remain explicit obligations. The characteristic-zero qualifications in PR5701 are retained.

git fetch https://github.com/CrocSwap/integer-mult-bounds.git c10f75f09e41803ae8efe478331a7509b7379b2f
git fetch https://github.com/CrocSwap/integer-mult-bounds.git 67f07448eec5ad8d84bdf96b46981ac0b893592f
python3.12 -B scripts/research_package.py --package research/coupled31-chronology

Expected: PASS_CHRONOLOGICAL_CONNECTOR_RANK_BOUND and PASS_REGISTERED_RESEARCH_PACKAGE. Normal and optimized replay, five corrupted-package controls, all 25 committed files, export integrity and sealed Git-free replay pass. Checks include 216 exact polynomial prefix updates, 2700 local systems with 104 strict dimension drops, the 128-field endpoint, and 66 complete F4 grid assignments including the retained noncommuting escape word. Finite controls support the written proofs; they are not human or proof-assistant acceptance. Full source-history preflight was not run because the two open predecessor commits are explicit provenance outside the fresh-main ancestry. Original-source and retained-copy bytes are separately pinned. Hosted CI and independent scientific review are pending.

Base: df0137efd35e11b4445734bf612bdd4c7ebc330c. Canonical main refreshed before submission to 553d26d796fde9871ff2661a49ac7732e945410f; the changed commits do not alter the entry guidance, priority seven, selected kappa .00310045, or consumed P104 tariff. Final head: f9a3bc99b186b2e08a855e260f2f904ef33821c9. The complete tariff source is PR5599 at 09dd0965711ca7eeb169057a420abab1c9052137. Live overlap was checked; no frontier change, merge or closure occurs. Coordination: Discussion5593.

Credit Cinna Davis's controller/simplex work, PR5617/5631/5649/5673/5681, Pierre-Loic Doulcet, Joel Pulikkan, DreamingOfClouds, thu-nmrc, Gareth Davidson, David Arias, Jacob Alan Sussman, zxv, Cao Yifan, Chris R / Clear1nsight and the retained P104/helper/native/compiler source notices. Prepared by Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0.

[aliromman]

Verification update for f9a3bc99b186b2e08a855e260f2f904ef33821c9: CI run 40349357577 passed the planner, registered package replay and unchanged-input check. Normal, optimized and committed read-only Git-free local checks also passed. These checks support the written proofs; independent scientific review remains pending. No kappa improvement is claimed.