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research: consume P104 residuals in actual cleanup and price source return - #11

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@Clear1nsight Clear1nsight commented Oct 19, 2026 •

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Publication status and upstream submission

This fork PR contains 11 research files in research/p104-residual-consumer/, plus the existing P112 workflow compatibility repair carried from fork PR #8 by a parallel workflow-fix activity. The repair changes only .github/workflows/p112-common-slice.yml; it does not change any scientific file.

The scientific head is 2cba526a4ebe0ef6c3c0143498adcf67dca97941, tree 7c99dccf508a722feb74ccd2d4692d0d9143f35f. The fork PR head is 38c0ec0089bd3c9723de9b8db2154fec0b3148a1, which adds that one CI repair. The initial PR description predated detection of this concurrent commit; this paragraph corrects its head and file-count wording.

For a research-only upstream PR, use Clear1nsight:publication/p104-residual-consumer-science-only against CrocSwap:main. That branch is pinned to the exact scientific head and contains three commits, 11 added files, and no workflow changes. The contribution branch and its concurrent repair are preserved. The dedicated validation workflow lives on a third, isolated branch and is not part of either scientific submission.

Change and mathematical scope

This follows CrocSwap PR #3882. It supplies an actual source-bound consumer of the encoded q fields, an exact source-return adapter with a sharp scoped transport floor, and a conditional complete-coverage stopping decision. No new kappa, admitted physical supplier, or selected-frontier change is claimed.

The actual consumer is the frozen native word's final query cleanup, zero-based events 3642 through 4057. Its 416 weighted updates are Q += D x, with 52 signed-double coefficients in each of eight rows. The actual prefix has X=x, Y=v=y+A x, and Q=h_Q-Dx at that cut; all other 64 dirty helpers are restored, every original transport is finished, and all private lifetimes are closed.

For PR3882's pivots J=[0,1,3,6,22,31,93,103], complement N, and B=A[J,N], the literal suffix satisfies

D = T [I B],     q = x_J+B x_N,     Dx = Tq.

The complete 8-by-8 T has 32 nonzero coefficients, all signed doubles. Moving the unchanged PR3882 tail to that cut and replacing the old cleanup by Q += Tq preserves all 280 output rows and prescribed endpoint frames. The tail does not touch Q, and q/Q remain FULL for the replacement. All 72 original arbitrary dirty helpers are restored.

This replaces 416 weighted ADDs with 32. Under the same explicit read-only-donor lowering, 832 unit Gaussian array ADDs become 64, saving 768 array ADDs, or 786,432 real component ADDs at 512 complex words per array. The replacement adds no banks, source mutations, halves, doubles, frame conversions, or native children. This is not scalar-circuit optimality or measured runtime.

Source return and complete cost

An explicit adapter supplies the legacy boundary X_i=x_i in FULL and Y_i=x_i+y_i in each target hyperplane. It lifts X_N, computes Y_N -= B^t q, performs X_N -= Y_N; Y_N += X_N, subtracts B X_N from X_J, and descends Y_N. Its exact bill is 192 formal rank-one transports, 960 unit array ADDs, 104 halves, and 104 restoring doubles, without new banks or clean-input assumptions.

The 192 transport-rank cost is sharp under the stated equal-chart, nested-transport, fixed-occupancy contract. Each of 96 distinct hyperplanes must export an admissible independent w_n input to supply the required FULL-frame x_n, and preserved occupancy requires an arrival. Incomparable hyperplanes cannot share an endpoint-counted nested transport. The proof adapts the retained terminal-floor occupancy method. Different input, output, allocation, or cross-chart contracts are outside its conclusion.

The scalar cleanup saving leaves the encoded native profile (1282,58,86,104,48,24,8,8) and mass 2576 unchanged. Including source return gives (1474,58,86,104,48,24,8,8) and mass 2768.

For the explicitly hypothetical equal-profile paired-chain template, use s=2p+1, m=8s+1, and W=104(s-1). Grant every stage the same profile, all 2312 net endpoint-progress units, zero other costs, and child ranks at most m. For every p >= 1, finite number b >= 0 of fully paid auxiliary banks, and 0 <= a < 1,

M(a)        >= 1 + (160s+104)/(m(W+b)) > 1,
M_return(a) >= 1 + (352s+104)/(m(W+b)) > 1.

At nine stages the lower paid masses are 62,280 and 64,008, versus capacity 60,736, with deficits 1,544 and 3,272. Return excursions are not donated additional persistent-progress credit. The all-stage result is a written coverage proof, not an inference from sampling.

This does not construct an opposite orientation or physical owner embedding, and does not cover arbitrary different profiles or changed coverage laws. PR3620/PR3782's 358-bank dual thresholds are not transplanted here. Decision is NARROW. Retain the scalar consumer and source-return module, but stop supplier expansion under the named failed complete-cost model.

Sources, task, and overlap

Canonical scientific base is 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. PR3882 is pinned at 9d56eeedbed5e3e9bbbc8c189d66f14cf15b6067. Its two original input blobs are retained in ancestor dfc903ed50be38d7299413deadd5855cc44d4a3f, so declared source history is self-contained. Frozen research sources, shared mathematical tools, upstream/, and the selected record are unchanged.

The user assigned the actual-consumer and full-cost continuation. TASK.json records changed scope under p104-side-correction, the exact catalogue card, stopping rule, credit, and open obligations. AGENTS.md, autoresearch.md, CONTRIBUTING.md, current priorities, and the family gate were read. A canonical fetch at 04:17:22 UTC on 19 October 2026 found main and the relevant guidance/selected-record bindings unchanged.

Targeted live PR and visible Discussion checks were supplemented by find_overlap.py --task p104-side-correction --offline in a sparse checkout. The latter explicitly reports no cached remote snapshot. The latest P104 creation query since session entry at 03:34 UTC found no new matching PR. Coverage excludes exhaustive Discussion pagination, historical diffs, and unpublished work. Nearby PR3894 is a direct source-preserving correction, PR3907 a different lifetime audit, and PR3915 a flag-coefficient check. No novelty guarantee is claimed.

Verification and reproduction

Use Python 3.12 and the standard library.

GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/research_package.py --package research/p104-residual-consumer
GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/check_research_commit.py --package research/p104-residual-consumer --check-source-history

The exact scientific head passed actual source-bound hosted verification on Ubuntu 24.04.5 and CPython 3.12.15 in run 39198705385, job 117886956529. The isolated workflow explicitly checked out and asserted 2cba526a4ebe0ef6c3c0143498adcf67dca97941.

Passed checks include metadata/source pins, normal and optimised primary replay, a separate integer-matrix implementation importing no primary or predecessor executable, all 16 semantic/control groups, committed-byte/source-history checks for 13 package/input files, and unchanged hashes for every package file. Both implementations execute the actual 3642-event prefix, bind the cleanup matrix, and verify the full new endpoint and legacy return. The primary also checks underlying binary nesting, actual cut frames, and all 96 information-export witnesses.

Controls cover missing, early, sign-flipped, or duplicated cleanup; wrong donors and output locations; missing doubles or return transports; scope and coverage errors; and actual isolated CLI failures for malformed typed results, changed geometry bytes, and missing main sources. They remain active under -O.

The canonical result digest is cdf6210cb348566f7647722f05c695d268b220909fb12997d12255817985f43f. The cut digest is 3a9ca839f995e137be6796522a655b7a9d502ce68a3fd35d2aeeaeb500d3357b. The encoded endpoint remains 6c0b0574f2eaa6b91d260206958eb87136e5c722f26b5f4d7627ed9d65983bcd.

The first hosted attempt failed on literal basis-spelling comparison at a private copy. Commit 2cba526 fixes both interpreters to match the archived binary-subspace semantics using separate span and reduced-basis algorithms. Frozen inputs, the new circuit, and RESULT.json did not change. The subsequent exact-head run passes. A final Git-free algebra-only local replay also passed, with all 11 files matched to the hosted scientific head and file bytes/modes unchanged; it is not a substitute for source-bound verification. The automatic fork-PR run is recorded separately in the publication handoff when its actual result is available.

Remaining obligations and credit

New-role native recipe and phase replay, literal signed-floor admission, actual physical producer domains, finite widths, routing/control/tape, affordable opposite orientation, physical owners, and all-size transfer remain unproved or unrun. The original prefix retains its inherited owned live-copy discard semantics. No full selected cold replay, independent human acceptance, proof-kernel verification, or complete supplier is claimed.

Credit Rohan Arun / PR1972, Chafik Boukhalfa / PR1991, Adam Gall / PR1940, PR3882's tail and residual encoding, the retained terminal-floor occupancy argument, Dominik Scholz's larger-gain model, Sagar Thakrar / PR1012, Douglas Colkitt, and the retained geometry/native/compiler lineage. PR3609, PR3620, PR3782, and PR3810 retain their separate results. The concurrent P112 workflow repair retains its fork PR #8 provenance and is not new research in this package.

Prepared by Clear1nsight with substantial OpenAI assistance. The two implementations share the same assisted session and frozen sources, and are not independent human review or formal proof-kernel acceptance. New work is Apache-2.0, with predecessor attribution and exact source bytes preserved.

Open next questions

A useful next consumer must remove actual native work or change a proved coverage obligation, including a compatible opposite orientation. Derive the fully charged inequality before further synthesis and stop if the favourable bill still fails. Source recovery and residual disposal are not free.

A bounded native audit may bind one changed-role hyperplane/FULL map, phase, and physically supplied entrance without claiming supplier expansion. A larger implementation requires an affordable complete consumer first. These obligations are released, not reserved.

Carry the focused change from 89031d2 (PR #8) onto this active branch. Initialise TMPDIR after runner setup, preserving workflow triggers, repository guard, permissions, pinned actions, timeouts, replay commands and all research inputs.

Validated YAML, exact semantic delta, shell syntax and TMPDIR assignment including spaces. Substantial OpenAI assistance.

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Completed verification and upstream-ready handoff

The automatic fork-PR workflow has now passed at PR head 38c0ec0089bd3c9723de9b8db2154fec0b3148a1. Both its planning/onboarding job and the registered P104 package replay succeeded, including the unchanged-input step.

https://github.com/Clear1nsight/integer-mult-bounds/actions/runs/39199181285

The separate exact-scientific-head workflow also passed on 2cba526a4ebe0ef6c3c0143498adcf67dca97941, with CPython 3.12.15 on Ubuntu 24.04.5. It observed normal and optimised source-bound PASS markers, the independent implementation PASS, all 16 control groups, committed-byte and source-history validation for 13 package/input files, and unchanged hashes for all 11 research files.

https://github.com/Clear1nsight/integer-mult-bounds/actions/runs/39198705385

The difference between those two heads is only the separately authored P112 workflow compatibility repair from fork PR #8. I preserved that concurrent work. The new branch publication/p104-residual-consumer-science-only points directly to the verified scientific head for a research-only upstream submission. Its fresh comparison against canonical main shows three commits, exactly 11 added files, 1,356 additions, and no deletions, entirely under research/p104-residual-consumer/.

Upstream compare settings are CrocSwap/integer-mult-bounds main against Clear1nsight/integer-mult-bounds publication/p104-residual-consumer-science-only.

https://github.com/CrocSwap/integer-mult-bounds/compare/main...Clear1nsight:publication/p104-residual-consumer-science-only?expand=1

A final local Git-free algebra-only replay matched all 11 published scientific file hashes, passed both implementations and the 16 tests under optimised Python 3.13.5, and preserved file bytes and modes. That portable mode omits the original main witness and full fixture; it is not presented as a complete source-bound export. The actual original-prefix checks are the hosted source-bound runs above.

Canonical main remains 20ecf2891d80b5acf18d980b2164fb44ea7faa90 at the final check. The science result and canonical digest cdf6210cb348566f7647722f05c695d268b220909fb12997d12255817985f43f are unchanged. The initial basis-spelling failure and its canonical-subspace fix remain in history; no failed run is represented as a pass.

The established result is an actual logical cleanup consumer, replacing 416 weighted additions by 32, or 832 by 64 under the specified strict unit lowering. This preserves the full encoded endpoint and all 72 arbitrary dirty helpers. The legacy source return attains the scoped 192-rank transport floor. Neither result improves the native profile enough to pass the named equal-profile paired-chain bill. Its nine-stage deficits remain 1,544 for encoded return and 3,272 with source restoration.

Decision remains NARROW. New-role native/global-phase and signed-floor admission, physical producer domains, widths, routing/control/tape, opposite orientation, ownership, and all-size transfer remain open. No supplier, improved kappa, independent human review, or proof-kernel acceptance is claimed. Next obligations are released, not reserved. Predecessor attribution remains in the package and PR description. This PR is intentionally left in the fork for the user to submit upstream.

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Closing this fork-local review in favour of upstream CrocSwap#3943. That research-only submission preserves the three scientific commits through 2cba526 and all 11 package files. Its description explicitly compares the cleanup consumer and overlapping return analysis with upstream CrocSwap#3940, including the limits of comparing 960 versus 1152 ADD schedules. The extra P112 workflow repair at this fork head is separately represented by upstream CrocSwap#3885. Discussion, evidence and branches remain available. Closure is duplicate-review housekeeping, not upstream merge or scientific acceptance.

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