[Clear1nsight]

Change and mathematical scope

For the complete PR #5545 invoice with 18 local calls and unchanged productive targets/nonlocal costs, even free pooling and arbitrary signed combinations of A:H1+H5→H6, B:2H2→H1+H3 and C:H2+H4→H1+H5 cannot reach C=.0033. The unique pooled relaxed optimum uses global exchanges (3942,4005,2016). A conservative rational upper bound for its necessary raw margin is -72275567/5000000 = -14.4551134. The normalized derivative proof extends the exclusion to every .0033 <= C < 1 in this family.

This is a scoped analytic accounting obstruction plus a finite exact coefficient certificate. All physical constraints, contact availability and restoration costs are relaxed favorably. No physically realizable optimum, new funded κ, selected promotion, or general P104 ceiling is claimed. The inherited baseline interval is authenticated; its engine is not rerun. Analytic concavity and derivative implications are paper arguments, not proof-kernel verification. Parent native/precision/tape/compiler/outer and independent human/formal obligations remain separate.

Task and overlap

Publication head 27f6fe375ce947dde9206d8b5adcc6d68752a02f, tree e4fdc3ef60cd4aaecf88e645d8c62f1de8716a85, parent 32890bc5de034ab8fc93ac88ead7279a6a416d04. Current upstream main and guidance were refreshed separately at the 20:07–20:08 UTC checkpoint; main remains 5e0052ca0aa3036a3afa8b0438927377c8d97d53. No claim is made that the contribution parent is current main. The current template and exact repository-input-path policy were checked.

Task scalar-to-moment, priority revision 7, changed scope: the useful negative result prevents recombination of the currently demonstrated paid edits from being mistaken for a route to .0033. It does not meet the original construction-gain gate. Exact source baseline is Ali Romman's PR5545, head 18968423711fd902aaee1099979497d55603e1dc; B/C come from thu-nmrc's PR5551, head 79072da5404a01056df2af2e4132324b01c72366. The qualified baseline interval was published with PR5548.

zxv's PR5554, head 18c1770246340e9f4aaac5a9ebd712e23498d0a3, studies an all-controller architecture frontier. This package adds the distinct exact joint inventory/recycling/pooling ceiling for the fixed 18-call complete invoice; it does not claim an all-controller result. DreamingOfClouds's PR #5561 at 452d27dde67ee9f772dbbd3be129db97a8ecb9c1 and GamingPuzzled's PR5569, head af9f091ac6f30c6eaacb9c27777bfbe2d0e5ffdf, change productive helper targets and lie outside this ceiling. No exhaustive novelty claim is made.

Validation

Package: research/pooled-abc-exchange-ceiling.

python3 -B scripts/research_package.py --package research/pooled-abc-exchange-ceiling --check-only
python3 -B scripts/research_package.py --package research/pooled-abc-exchange-ceiling
python3 -B scripts/check_research_commit.py --package research/pooled-abc-exchange-ceiling --check-source-history

Expected marker: PASS_POOLED_ABC_EXCHANGE_CEILING. The original root-only normal/optimized Fraction qualification passed in 0.403383 seconds with 33,923,072 bytes sampled descendant RSS, under 150 seconds/512 MiB. All twelve mathematical/accounting mutations rejected and every scientific output byte matched, SHA256 882369dbec747ac4fe4c324501dddca7e67240e773bb6782e29bd91dde25b5a7. The portable registered normal/-O pair also passed, in 1.108 seconds with sampled 66.87 MiB, under 150 seconds / 512 MiB. A separate Git-free read-only optimized export with spaces in its path and empty PATH passed in .403 seconds, sampled 41.14 MiB. All 29 exported files remained unchanged. Two custody mutations reject before science in both modes; all 12 scientific controls reject. Metadata, committed-source history and exact remote-commit byte checks passed for 28 package files. Hosted CI remains pending at submission.

The portable wrapper preserves the independently written checker byte for byte, authenticates every package payload and original request input, runs isolated private children with 60 seconds/512 MiB limits, compares complete expected output, and reauthenticates the package. It needs no external live source input, Git or network. Finite checks reconstruct both complete histograms, verify inventory/conservation, rational log bounds, tangent coefficients and normalized derivative coefficients. The actual analytic implications and inherited baseline moment premise remain explicit.

Credit

Ali Romman for PR #5544/PR #5545; thu-nmrc for PR #5551 and its two coupled retimings; zxv for distinct PR #5554 frontier work; DreamingOfClouds and GamingPuzzled for later target-changing results; all retained P104/native/controller/compiler/precision/analytic predecessors. The shared-chart/dual-ADD retiming lineage, Gareth Davidson, David Arias, Cinna Davis, Jacob Alan Sussman, zxv and Cao Yifan retain predecessor credit. Joint inventory analysis, conservative certificate and independent finite qualification for Chris R/Clear1nsight with substantial OpenAI Codex assistance. Apache-2.0. Agent review is not independent human acceptance.

Open next questions

See research/pooled-abc-exchange-ceiling/NEXT.md. Identify a literal paid mechanism outside A/B/C, or explicitly change target/controller hypotheses, then reconstruct its full invoice before construction. Current successor target changes cannot inherit this bound automatically. Independent human or formal review of the analytic proof remains useful. No new search is launched by this publication.

[Clear1nsight]

Seven-field research handoff

1. Research discussion / PR / artifact: PR5577, package research/pooled-abc-exchange-ceiling; canonical proof, source bindings, complete histograms and portable finite qualification.
2. Exact commit: actual base 32890bc5de034ab8fc93ac88ead7279a6a416d04; frozen baseline PR #5545 18968423711fd902aaee1099979497d55603e1dc; compared PR #5551 79072da5404a01056df2af2e4132324b01c72366. Publication head is 27f6fe375ce947dde9206d8b5adcc6d68752a02f, tree e4fdc3ef60cd4aaecf88e645d8c62f1de8716a85; current PR base is 5e0052ca0aa3036a3afa8b0438927377c8d97d53. Observed newer main 5e0052c guidance is reviewed separately, without claiming it as the contribution base.
3. Established: paper proof plus original exact finite qualification excludes C≥.0033 below 1 for the fixed 18-call complete PR #5545 invoice under signed A/B/C exchanges, recycling, free pooling and real averaged counts. Optimal global exchanges (3942,4005,2016); strict conservative raw-margin upper bound -72275567/5000000. Original result SHA256 882369dbec747ac4fe4c324501dddca7e67240e773bb6782e29bd91dde25b5a7; all twelve controls reject and normal/optimized scientific bytes match.
4. Uncertain / excluded: physical realizability, complete native, precision/tape/compiler/outer funding, and independent human/formal acceptance. The proof does not exclude other controllers or paid generators. zxv's PR #5554 all-controller frontier is distinct; PR #5561 and PR #5569 productive-target changes fall outside this fixed-target ceiling. No new κ or selected result is supplied.
5. Smallest useful next task: identify a literal source-bound mechanism outside A/B/C, or explicitly change target/controller hypotheses, then reconstruct its full invoice before construction. Coordinate with the current source authors. Human/formal analytic review is also useful.
6. Reproduction / runtime: Python 3.12 standard library; python3 -B scripts/research_package.py --package research/pooled-abc-exchange-ceiling. Original exact pair 0.403383 seconds / sampled 33923072 bytes. Portable registered normal/-O pair 1.108 seconds / sampled 70115328 bytes; separate read-only Git-free optimized export with spaces and empty PATH .403 seconds / sampled 43139072 bytes. All under unchanged 150 seconds / 512 MiB guard. Two custody mutations reject before science in both modes; all 12 scientific controls reject. Metadata, 28-file exact remote-byte/source-history checks and 29-file exported-byte preservation pass. Hosted CI is pending at publication.
7. Credit: Ali Romman, thu-nmrc, zxv, DreamingOfClouds, GamingPuzzled and retained P104/native/controller/compiler/precision/analytic predecessors, including shared-chart/dual-ADD retiming lineage. New joint inventory analysis, conservative certificate and independent finite qualification for Chris R/Clear1nsight with substantial OpenAI Codex assistance. Apache-2.0. No independent human/formal acceptance.

{"schema":"integer-mult-coordination/v1","kind":"FINDING","task":"scalar-to-moment","scope":"Fixed PR5545 complete 18 call invoice; pooled signed ABC exchange ceiling below .0033; not all controllers or target changes; no kappa","base":"32890bc5de034ab8fc93ac88ead7279a6a416d04","expiry":null,"artifact":"https://github.com/CrocSwap/integer-mult-bounds/pull/5577"}