research: source-consuming P104 correction with exactly eight residual replacements

[Clear1nsight]

Change and mathematical scope

Submit the isolated ten-file package research/p104-role-exchange-residue/ from fork PR Clear1nsight#5. It constructs a source-consuming P104 correction tail with an explicit dyadic inverse and proves that exactly eight residual outputs must be replaced in the stated reversible Gaussian-dyadic linear model.

The tail consumes X, reads/modifies channel Y, produces all 104 sums w=x+y on X_N and Y_J, and retains (q,v_N). The 72 arbitrary dirty helpers are untouched. For J=[0,1,3,6,22,31,93,103], B=A[J,N], the source geometry has A[J,J]=I and A[N,N]=B^t B. The construction uses q=x_J+B x_N, w_J=v_J-B x_N, w_N=x_N-B^t q+v_N. Keeping both every corrected sum and every old residual has rank 200 rather than 208 modulo three, giving the sharp eight-replacement obstruction.

Decision: NARROW. The combined profile (1282,58,86,104,48,24,8,8) has mass 2576 and still fails the unchanged width-nine, 280-role bare screen: 2576/(9*280)=46/45>1. This is a scoped local module and interface theorem, with no new kappa, admitted supplier, native recipe replay, physical consumer, or selected-frontier update.

Task and overlap

Task: p104-side-correction; scope changed to the explicit source-consuming/residual-replacing contract. Canonical base: 20ecf28; priority revision 6. Scientific head: 9d56eee. The browser comparison contains one commit and ten files. Current AGENTS.md, autoresearch.md and CONTRIBUTING.md were read for this submission.

Nearest work: #1972/#1991 provide the forward channel/native lineage; p104-side-correction-rank-obstruction supplies the retained root factorisation and terminal tariff; #2383 supplies the root-code relaxation; #3427 and #3810 address source preconditioning/channel-Y access; #3609 uses a different dual entrance. This does not contradict #3810's rank-23 preconditioner bound; #3620 and later consumer audits retain separate budget contributions. Existing source pins, TASK.json and frozen predecessor evidence are retained. No exhaustive novelty or completed find_overlap.py run is claimed; the bounded overlap coverage is recorded in the fork handoff.

Validation

Reproduce:

python3.12 -I -B scripts/research_package.py --package research/p104-role-exchange-residue

The recorded source-bound checks authenticate three sources and original exit frames, execute all 280 input columns, reconstruct the 280-by-280 endpoint independently, check 16 signed fixtures, normal/optimised Python, and 15 failure controls including isolated CLI corruption/missing-source controls. Local algebra-only runs use CPython 3.13.5 and do not authenticate the full repository inputs.

The subsequent verified handoff supersedes the fork body's earlier pending-hosted wording: registered package replay passed on CPython 3.12.15 / Ubuntu 24.04.5 at https://github.com/Clear1nsight/integer-mult-bounds/actions/runs/39189183948 (fork merge ref eede20e). A separate run explicitly pinned the scientific head, ran all four commands and checked all ten file hashes/unchanged bytes: https://github.com/Clear1nsight/integer-mult-bounds/actions/runs/39189389182. That validation workflow is not included in this contribution. These are prior recorded executions, not new executions in this browser submission session; new upstream CI remains separate.

Canonical result SHA256: 0b869d0e68b8e21468a15977a31432d8b17f5a528558edec7eaf6c5461d63b78. The original 4058-event channel identity is inherited. Native rounding, physical ownership/routing/tape/precision, all-size return, complete supplier admission and formal-kernel acceptance are unrun/unproved here.

Credit

Credit Rohan Arun (#1972), Chafik Boukhalfa (#1991), the retained rank-obstruction package, #2383, #3427, Sagar Thakrar (#3810), and the predecessor chain recorded in README. Prepared by Clear1nsight with substantial OpenAI assistance. The two implementations share that assisted context and are not independent human review. Apache-2.0 and source notices are retained.

Open next questions

See research/p104-role-exchange-residue/README.md and TASK.json. First name a consumer of (w,q,v_N), prove its endpoint/return equations and physical owners, and produce a favourable complete coverage and cost bill. Only then rebind/replay the 208 hyperplane/FULL recipes. Source recovery, residual disposal, bank-role conversions and all-size precision/routing remain blockers. Obligations are released, not reserved.

Workflow feedback

The earlier connected integration returned HTTP 403 when creating the upstream PR. This browser submission transfers the original focused contribution; the fork PR remains its historical review/verification record.