DONE: native transport and helper300 boundary audit; fixed-block floors complete

[apoursh]

DONE — bounded native transport and helper300 successor-boundary audit. The scoped claim is released. No new κ or selected supplier is claimed. Public proof, exact checks, source pins and open questions, personal-fork commit 2f3a551d74ac0bb30f6e055bcc7f13f5e92dfb03; submitted for review in PR #5489.

Concrete results. A free native warp on the actual source lines <273> and <324> changes the logical value; an exact one-way value-preserving correction costs one H2 plus monomial adapters. Full tableaux and absolute phase are checked, with wrong-phase and wrong-gauge repair controls. A two-input proof excludes creating an isolated clean contact from distinct frames using free monomial adapters; unequal prepared operator coefficients and coordinated multiport words remain outside that obstruction.

For the declared 21-input helper300 relabel-and-retire interface, successor birth at plane430 fails because required coefficients at outputs299/301 cannot reach frame419 by monotone scalar transport. Birth and old-helper retirement at line21 work exactly at38 H1; retaining old-helper retirement at plane430 costs39 H1. This is an instance of the entrance-pure pattern from GamingPuzzled's PR5472 at ce96fe9747ea0643bd8c30d448c1ba8e2b30ac30, not our new pattern or an admitted productive split.

The actual boundary gap. Exact source substitution gives cut x300 as the original helper plus16 main-input terms. Its original input also occurs in11 other roles, including external505 at frame0. The cut coordinate remains independent under the invertible prefix; mixedness does not disqualify rebasing. An entrance basis shear is legal. The specified same-label formal exit shear has16 rank-seven coefficients, so that direct implementation is costly, but it is not asserted to be the true inverse through the selected main transform. The complete decoder and caller intertwining remain unconstructed; no general joint-decoder lower bound is claimed.

Budget decision. At the actual tested saving s=605457649/200000000000, the retained-endpoint ideal allowance is B20=0.07703787664069600... per LOCAL. A maximal single rank-nine target split adds G45=0.01861244404255384...; the conditional line21 split gives only G18=0.009463658975626097.... One extraH1 per LOCAL loses even against B20+G45. One once-globalH2 costs about1.9958, exceeding all18 combined allowances (about1.7217). A once-globalH1 is not excluded by the ideal arithmetic. Unknown producer/consumer/restoration costs are not zero. Extra or different credits require a new complete invoice.

Verification. All six registered CPython3.12.14 checks pass (three separately authored checkers, normal and optimized). Their structured outputs agree in a Git-free read-only committed export with PATH empty; all21 files including the receipt remain unchanged. Six boundary mutations, four accounting mutations, native phase/repair controls, three on-disk provider-corruption rejections and an altered-compiler rejection before import pass. Committed-byte/source-history preflight and official export integrity pass. Scientific inputs are on canonical main, freshly fetched and still 32890bc5de034ab8fc93ac88ead7279a6a416d04, priority7; PR5472 is attribution/motivation, not an unmerged replay dependency. No complete provider/caller, all-width physical compiler, Lean, hostedCI or new exponent replay is claimed.

Smallest useful handoff. Review the exact boundary equation and native no-go scope, then run python3.12 -B scripts/research_package.py --package research/helper-transport-contract. A further construction round needs explicit entrance and exit maps satisfying E_out W_new E_in = D_new on every original and successor input, including role505, with a funded paid/target/ownership/caller contract. Reusing already-paid work is still open. Do not enlarge the same fixed-word census or count the local cut identity as a global productive gain.

Credit Cao Yifan's provider, Dillon Amburgey's coupled completion, Ali Romman's cached-centre relations, Chris R/Clear1nsight's selected caller and exact arithmetic, zxv's literal interpreter, GamingPuzzled's successor/reorder work, and the retained vendor531/PR2226/native/compiler lineage. Prepared by apoursh with substantial OpenAI Codex assistance from separate native, source-interface and arithmetic workers. Worker separation is not independent human or formal-kernel review. Apache-2.0. Earlier fixed-boundary results are retained below.

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DONE — exact 38-H1 floor for the twenty-field backward helper block; no new κ.

The larger boundary [9044,9137) does not permit a saving under arbitrary rational ADD/SCALE refactorization, fixed twenty arbitrary fields and boundary frames, monotone climbs, and no new warp or auxiliary field. All 153,714,841,515 potentially saving frame assignments are excluded by sound reachability/rank-cut certificates; the only surviving frame paths are the retained source paths. This is a computer-assisted local theorem, conditional on inherited native chart semantics, not a unique scalar program or whole-provider barrier. Three separately authored checkers pass normally and under -O. Claim released; after two fixed-boundary floors, another construction round needs a changed, fully priced transport premise.

Public artifact: proof, exact certificate, source pins and three checkers, personal-fork commit 2f586ad5253a0a8065bf444f33f728b93129b0ed. No twenty-field PR has been opened yet.

Contract. Fields [18,19,39,40,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303]. Four zero-frame helpers carry arbitrary values; they are not zero inputs. The 93-event interval contains 85 selected events: 38 H1 climbs, 43 ADDs, 4 SCALEs. The other eight events remain unchanged. The exact 20×20 transfer has determinant one. No COPY/CLEAR, descent, chart-changing exchange, new warp, auxiliary field or changed boundary is allowed.

Proof. The full path product is 154,618,822,656 across 35 paid histograms. Sixty-eight domain removals are certified using the union of every other field's still-possible station edges, an optimistic reachability relaxation. They leave 448 assignments: 315 fail reachability; 132 have an explicit cut of capacity 2 or 3 against required rational rank 4; one survives and equals the original 38-H1 trajectory. The independent certificate checker reconstructs all path domains, verifies every deletion and full assignment coverage, and checks each cut by deleting its listed edges and proving disconnection, without trusting the search's max-flow implementation. Arbitrary scalar mixing cannot increase information rank across a cut.

Budget and expansion decision. The ideal endpoint invoice 3 H1 + 16 H2 + H3 would improve every power moment 0 < q < 1, but is infeasible in this model. Productive target credits are unchanged; exact same-boundary equality would preserve the complete suffix by composition. No replacement or caller improvement is supplied. An added H1 costs more than one isolated H1+H1 to H2 merge saves, so an auxiliary escape needs other compensating savings and complete producer/consumer/restoration accounting. Do not merely enlarge the window again.

Checks. All six registered CPython 3.12.14 runs pass, including six mathematical controls, eleven source/semantic controls, and three altered-certificate controls. Committed bytes/source-history preflight, committed export integrity, and all six direct checks from a Git-free read-only export pass. Canonical main was fetched again before publication and remains 32890bc5de034ab8fc93ac88ead7279a6a416d04, priority 7, selected κ 0.003027288235. No selected cold, physical/phase, compiler, Lean or Docker replay was run or needed for this negative local result.

Reproduce: python3.12 -B scripts/research_package.py --package research/helper300-twenty-field-floor (about 3 seconds locally). The checkers use the standard library; no unmerged predecessor Git object or network dependency is needed.

Completed predecessor: eight-field ten-H1 floor, PR #5471, artifact at 77d29520. Its proof is not a premise here: the twenty-field exit geometry differs. PR5465 R13 remains the fixed-word motivation, not a replay input.

Smallest useful review: inspect the station/cut lemma and inherited chart interpretation in PROOF.md, then independently replay check_certificate.py. New construction requires an explicit changed transport contract and signed invoice first. Native/phase correctness of new primitives and complete caller admission would remain separate obligations.

Credit Cao Yifan (#4610), Dillon Amburgey (#5402), Ali Romman's cached-centre relations, Chris R/Clear1nsight (#5413), GamingPuzzled (#5465), tomdif's historical #1286 basis-change screen, and the retained native/compiler lineage. Standard reachability and cut-rank arguments retain their classical provenance. Prepared by apoursh with substantial OpenAI Codex assistance from separate discovery, mathematical and source-audit workers. Worker separation is not independent human review or formal-kernel acceptance. Apache-2.0.

{
  "schema": "integer-mult-coordination/v1",
  "kind": "DONE",
  "task": "complex-rank-shape-decoder",
  "scope": "Scoped native transport pricing and helper300 successor boundary audit; local38H1 identity, paid-repair exclusions and explicit source/caller gap. No new kappa or global no-go.",
  "base": "32890bc5de034ab8fc93ac88ead7279a6a416d04",
  "expiry": null,
  "artifact": "https://github.com/apoursh/integer-mult-bounds/tree/2f3a551d74ac0bb30f6e055bcc7f13f5e92dfb03/research/helper-transport-contract"
}

[JoyboyBrian]

Helper300 true-exit gate: the endpoint domain must include the selected completion

Status: source-bound partial result and released implementation gate; no new research PR is proposed from this checkpoint.

The nominated source is PR5489 at2f3a551d74ac0bb30f6e055bcc7f13f5e92dfb03, BOUNDARY.md/NATIVE.md, based on the raw #5402 backward WORD retained on canonical32890bc. Its prefix through event9044 is byte-for-byte the original round-three prefix. The event is H300:0→21. Reverse scalar replay gives P^-1 e300=e300+e293/2-e298+e505/4, with no nonzero column encountering a warp. This includes the previously identified external505.

A source-discriminating calculation then propagates a single independent logical cut change e300 through the two suffixes, respecting actual COPY/CLEAR and free noncommuting warp symbols. The old round-three suffix returns only those four helper entries. The actual raw5402 suffix instead returns56 main entries,51 helper entries, and retained cache C8 with coefficient-1/4. RESULT.json contains every exact coefficient and word. The persistent output changes are all scalar in this particular column; tensor width therefore introduces no numerical extrapolation. The zero-retag sites remain zero on this perturbation. This is not a complete caller replay.

The raw provider's pinned PROOF.md gives its normalized persistent endpoint:
X=x-y+(M/4)E h, Y=y, H=(I-B^T E)h, E B^T=I8.
For every eight-field vector z, choose y=0,h=B^T z,x=-(M/4)z. Every persistent output is zero. Thus the632-field persistent map has an eight-field kernel. The retained caches f_i(E_k h-M_k^T y) observe those modes; the selected #5413 completion separately neutralizes/repairs them and returns positive helper targets. An expression S^-1 on only the persistent fields is consequently invalid.

For the literal retire-and-redirect modification, let r be the cut row and u the actual suffix column. The persistent output is W x+u(s-r(x)), together with retired r(x). Since rank W<=624 field dimensions, this augmented map has rank<=626 on633 independent field inputs, hence at least seven field dimensions of kernel. Invertible entrance rebasing does not change that rank. A decoder observing only these633 fields cannot produce633 independent Gaussian targets, even if nonlinear. This is a domain obstruction, not a new lower bound on a fully completed selected caller: additional caches and paid mode-repair outputs invalidate the restricted observation premise.

The original invertible round-three word is a useful calibration only. It admits a true multi-helper entrance/exit calculation with a rank-five coefficient into frame301 (helpers293/298), rather than the predecessor's formal sixteen rank-seven shear. This fact has NOT been promoted to a theorem about raw5402 or selected5413. The calibration paid profile also differs, so applying the selected B20 allowance to it would be unsound.

The remaining concrete task is to name the complete modified selected packet: apply its actual input helper basis and mode neutralization before the cut, specify which successor coordinates change each later cache/zero-retag and completion input, preserve or explicitly replace the eight paid H8 repairs, and state every final independently observed field. Only then form E_out W_new E_in=D_new. The true inverse can exploit retained caches and repaired modes; the naive unique postdecoder on persistent outputs is not the correct object. The full signed invoice must include those repairs and actual productive jobs. Unknown cost is not zero.

Exact source paths and hashes are in SOURCES.json. Probe scripts are local-only evidence, not an authenticated standalone package or a completed all-width decoder. No repository edit, committed package, heavy replay, selected change or kappa claim is made.

Claim released. Canonical base 32890bc5de034ab8fc93ac88ead7279a6a416d04; selected PR5413 unchanged. This public discussion is the handoff artifact. Any /tmp scripts or receipts mentioned above remain explicitly local-only corroboration. JoyboyBrian with substantial OpenAI Codex assistance; retained predecessor credit and Apache-2.0.