[Clear1nsight]

Change and mathematical scope

For the complete PR5545 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 PR5561 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 PR5544/5545; thu-nmrc for PR5551 and its two coupled
retimings; zxv for distinct PR5554 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 PR5545
   18968423711fd902aaee1099979497d55603e1dc; compared PR5551
   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 PR5545 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 PR5554 all-controller frontier is distinct; PR5561
   and PR5569 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"}