[ToikY]

Change and mathematical scope

For the exact published unpooled PR #4067 OQ4 invoice, even a zero-surcharge favorable relaxation fails the retained moment-certification budget at the current admitted BIT slot. This is a fixed-invoice/certification-method result, not a runtime lower bound, physical theorem extension or universal R437 exclusion.

The source price fixes dimension64, productive W28416 and the authenticated nine-bin profile with903456 paid children/rank mass1808352. Set M0(c)=sum n_r*r/(64W)*exp(c log(64/r)). Classical log(x)>=2(x-1)/(x+1) and exp(y)>=1+y give M0(c)>=L(c)=A+Bc, where:

A = 18837/18944
B = 227656981418642299/126181391898481920 > 0
L(17/5000)-1 = 18039021780054799/37112174087788800000 > 0

Hence every c>=17/5000 and every nonnegative added normalized charge D(c) fails the fixed gate M0(c)+D(c)<=1. No numerical log, exponential or root search runs. The independent oracle derives the same sign through integer common-denominator arithmetic, with positive cross-product gap78505822786798485248.

The current selected ordinary BIT saving8590884599/2500000000000 is distinct from admitted17/5000 and whole multiplication kappa62009/20000000. This uses the weaker admitted target. Under the separately declared ordinary bridge a<=c, reaching a>=17/5000 would require a rejected c. The source #3690 argument fixes c=1/576 and physical range c<1/512; relaxing that range here does not extend its physical theorem or establish refinement of changed #4067.

A failed upper-bound moment test does not lower-bound actual runtime or exclude a different analysis. Different paid/target invoices, productive normalization, transfer law and pooled callers remain outside. All nonnegative extra costs are omitted optimistically, not asserted zero in reality. The local-only pooled allocation already exists with a different profile; its complete price/physical catalogue binding is separate.

Task and overlap

Fresh canonical main de5ec2e, priority8. Source #4067 exact head a95f11c; #4147 head72e7bb797adf82aeb525a399f56ab8adbab8e93c. Raw inputs are exact unchanged main blobs, not normalized orientation copies.

TASK.json and the canonical claim explicitly change r437-carrier-integration to this narrow current-budget implication. #3668/#3700 already cover historical profile/root/outer comparisons; #4067 already constructs/prices its carrier; #4147 already derives its reverse coefficient. None is repeated as new. This result supplies the compact revision8 destination-budget decision with all surcharges favorably removed. Completing stock or reducing nonnegative overhead alone cannot repair this same moment gate.

Live intake covered360 open PRs at round start and361 before submission, actual #4682/#1166 handoffs, focused R437 Discussion search, the distinct expired #4927 directory scope and relevant merged PR heads/bodies. Sparse local/history/search coverage remains partial; no-match is not novelty proof. Exactly15 files are added in research/r437-unpooled-budget-obstruction. No source archive, selected record or frontier is edited.

Validation

Python3.12.14, standard library:

python3.12 -B scripts/research_package.py --package research/r437-unpooled-budget-obstruction

Registered normal/optimized primary and separate oracle pass, with exact agreement on A,B,lower bound,slack,profile and target stages. Six primary controls and independent source/model/target guards pass. A synthetic profile change retains total paid calls but makes this lower screen inconclusive; the frozen-contract guard rejects it, without claiming physical feasibility. The wrong whole-kappa target likewise loses this lower-bound rejection. WrongW, source drift, negativec and numeric receipt aliases reject. Complete canonical receipts distinguish bool/int/float.

Raw SHA256/Git blob authentication covers allfive source inputs. The primary statically checks selected price AST sites without executing source code; the full formula/model is read and stated in PROOF.md. Committed bytes/modes/main history and official export pass. Read-only Git-free isolated optimized replay with empty PATH passes both checkers in about0.18seconds, preserving every exported byte/mode. Export SHA256: 1af66e1fd4044bd0f0764779a332aecd6cc6e474a65398a1ebf5eb8666930505. Selected baseline passed bindings/metadata only.

Publication head7207b930f8362bf1cf95d8a3ee9c3596948e2dd8; tree4edff8db675b7438266791889fb1530cbbd50dda. Hosted checks not yet observed; no hosted scientific success is claimed. No native/source-word/pooled compiler/full selected or Lean replay ran.

Credit and open next questions

Chris R/Clear1nsight supplied #4067's carrier/host/price; unpaidmoon supplied #4147's reverse-envelope distinction. Retain ai-nanachi/#3647, Ali Romman/#1043, Sagar Thakrar/#3700/#2423, zxv/#3690, mightyOil/#1281, Rohan Arun/#3959 and all actual word/native/hosting/physical/compiler/analytic lineage. NOTICE retains attribution. New compact current-budget implication, checker, independent integer oracle and proof: ToikY with substantial OpenAI Codex assistance in separate primary/oracle/proof-review contexts. Classical inequalities are not claimed as new general discoveries. Apache-2.0.

Next: freeze a complete changed pooled invoice and receiver/ordinary-transfer contract, then derive its own budget before importing any fixed-model exclusion. Native/compiler/stock/precision/tape/analytic obligations and the five inherited assumptions remain. Independent acceptance remains open. No new kappa/frontier claim; maintainer edits disabled; no merge or closure requested.

[ToikY]

Hosted status for publication head7207b930f8362bf1cf95d8a3ee9c3596948e2dd8: planning failed with8failures and2errors only in unchanged CurrentResearchAssignmentTests (511tests,22platformskips). Scientific replay was SKIPPED. The existing shared fixture repair remains PR #5761, outside this focused package. Registered normal/optimized and read-only Git-free empty-PATH cold replay pass locally; no hosted scientific success is claimed. The result is a fixed moment-contract obstruction, not a runtime lower bound or exclusion of changed pooled models. Maintainer edits remain disabled.