[petalas]

Summary

A dirty-output sharing replacement on the PR5907 P104 word saves two ordinary events and twenty scalar allowance units. Claim type: scoped exact circuit construction with a finite certificate for the complete modified word. No new κ.

f = field133 + 2 field721 + field21 - 2 field711

before: a += f; b += f             # eight source ADDs
 after: b -= a; a += f; b += a      # six ADDs; both inputs arbitrary

The actual interleaved window has no observation of either destination and no write to the four shared sources. The patch retains every other event in order. Full events: 25,998 → 25,996. Complete local scalar allowance under PR5827's retained tariff: 228,664 → 228,644. Every non-ADD event, frame, boundary, owned lifetime and productive inventory is preserved, so the paid profile and signed recursive moment are unchanged.

This takes Matarener's PR #5975 ordinary-resynthesis question. Its predecessor compression is cited, not audited. This changes the dependency graph rather than combining repeated ADD pairs or applying sign normalization. Search stopped at the first positive candidate.

Proof, source pins and constructor. Produced by Nick Petalas. Credit DreamingOfClouds #5907, Ali Romman #5827, Mason Hale #5811, Matarener #5975, Cinna Davis #4692 and their retained P104/native/caller/compiler lineage. Dirty-output sharing is a standard technique; this literal window and bill are the new application.

Evidence

• Exact rational matrix equality on the 100 arbitrary fields touched by the 163-event window; the replacement has 161 events.
• Complete modified-word symbolic replay on all 799 independent input columns, specifying all 638,401 endpoint matrix entries. No predecessor scientific replay is used as the deliverable.
• Every new ADD has available equal frames. All 31 owned lifetimes return; peak occupancy remains 13. Context and non-ADD events are exactly preserved.
• Four broken matrix identities and five invalid window premises are rejected. Local prefix row l1 maximum is 17 in both versions relative to independent cut inputs; this is not a rounded-error guarantee.
• Warning-strict normal and optimized CPython 3.12.15 checks pass locally. Each registered command took 0.26 seconds locally, below its 120-second timeout. Registered package checks, syntax/function-length/indentation checks, exact committed bytes and declared source-history checks pass.
• The verifier emits its generated SHA256-bound receipt on stdout. Canonical candidate payload SHA256: 5c2ed3597871bcbfa5a00194671e75aab95345ba6a91b1c7c7bd1c78eb1ef495.

From the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B research/p104-dirty-anchor-window/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B -O research/p104-dirty-anchor-window/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/p104-dirty-anchor-window
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/p104-dirty-anchor-window --check-source-history

Any CPython 3.12 installation can replace the interpreter path. The standard library suffices. Expected markers: PASS_P104_DIRTY_ANCHOR_WINDOW, PASS_REGISTERED_RESEARCH_PACKAGE, PASS_RESEARCH_COMMIT_BYTES. Normal replay writes no files. --emit-word /absolute/external/path/WORD.json exclusively creates the reconstructed candidate outside the checkout.

Limitations

This is an exact local circuit improvement, not supplier admission or a complete multiplication theorem. Exact endpoint equality does not prove rounded equivalence of intermediate states. Native maps, physical caller, compiler, outer inequalities, precision/tape and the selected cold replay are not rerun. The five framework assumptions remain; selected-frontier files are unchanged. Composition with PR5975 compression is not claimed. No Lean, Docker, independent human or formal proof-kernel acceptance is claimed. A standalone linter was unavailable locally; warning-strict execution, AST checks, tabnanny and registered repository checks were run.

Open next questions

Can this literal sharing window compose with PR5975 compression and enable a paid-profile improvement within the event cap? Start with its four shared-form contacts, preserve every observer, then charge one new productive or paid change. Composition and a newly funded construction remain open; the current scalar saving does not improve κ.

Related open work

• Compress the ordinary events of the PR5907 P104 word: 25,998 to 25,861, same invoice #5975 compresses ordinary events of the same PR5907 word. Its reported starting event count, 25,998, agrees with this input; it does not introduce this dirty-anchor dependency. Composition is untested.

• Exhaustion census: no PR5599-type helper split remains on the PR5907 word (no new kappa) #5994 excludes zero-cost helper splits on PR5907. This changes scalar dependencies and preserves the productive inventory; it supplies no new split.

• Independent replay, invoice, native and funding audit of #5827 and #5907 (no new κ) #5960 audits the PR5827/PR5907 construction chain. This supplies a new literal local replacement and does not duplicate that audit or transfer its conclusions.

• Save six more scalar units after P104 sign normalization (no new κ) #5969 combines repeated ADDs after sign normalization on older P104 words. This shares a four-source form through a dirty destination on PR5907; no cumulative saving is claimed.

• Bound rounded error on the two #5833 P104 words: 20-bit guard, envelope below 97B (no new κ) #5964 bounds rounded error on PR5833 gauge words. This proves exact linear equality only and does not import those precision guards.

• Add all-width native certificate for the selected #5599 word (native_all_columns; no new kappa) #5974 studies all-column native implementation for selected PR5599. This preserves the later word's native MOVE sequence and does not establish that assumption.

• Classify P104 lattices invariant under local Clifford gates (no κ) #5971 classifies invariant P104 lattices. This leaves the grid and operation alphabet fixed and makes no new lattice or rounding claim.

• Conditional κ 0.00309871 from a prepared P104 split helper #5606 changes a P104 helper to owned storage and changes its paid/target invoice. This preserves all storage, targets and paid moves.

• Two successor hand-offs on the P104 word: conditional κ 0.0030428242 #5553 constructs successor handoffs on an older P104 word. This preserves boundary helper identities and introduces no handoff.

• Follow-up to #5350: register scalar package for CI replay, document allowance accounting #5386 registers an older scalar-retiming package and explains its allowance accounting. This has a distinct literal word and uses the pinned PR5827 tariff.

• Add P104 flag 0 coefficient transport audit #3915 studies a coefficient in the older 208-flag channel. This operates on the later complete PR5907 ordinary word, without changing channel coefficients.

• Research P104 singular-mixing lifetime floor #3907 studies a singular-mixing lifetime floor. This adds no helper lifetime and makes no lower-bound claim.

• research: price full P104 end-cut correction #3894 prices an end-cut correction on the older flag channel. This preserves the later complete word's existing correction and all native calls.

• Draft construction: P104 dirty-restored gather and low-rank channel with COPY56 (no new kappa) #1972 constructs a dirty-restored P104 gather/channel. Its retained construction lineage is not revalidated here; this is a small ordinary-window rewrite on its successor line.

• Prove one local rank-5 deletion per FULL lifts the selected complex invoice to the BIT saving (no new κ) #6010 studies changes to the selected Raise conditional kappa to 0.00310045 with independent helper splits #5599 paid/target invoice. This changes a later word's ordinary scalar window and preserves its recursive invoice; no common relaxed threshold is computed here.

• Raise the partial-cache observer error floor to sqrt(7/92), exact over scalar witnesses (no new κ) #6006 optimizes scalar witnesses for the older P104 partial-cache observer. This preserves the complete word's exact outputs and claims no observer-error value.

• Prove optimal four-addition, one-halving Pauli pairing normalization (no κ) #6003 gives a Pauli-weighted three-bank pairing normalizer in a changed operation model. This uses ordinary common-frame ADDs on the existing PR5907 word; its four-addition optimum is not an allowance bound for this window.

• Prove exact joint Gaussian transition cost with dirty workspace (no new κ) #6001 proves joint Gaussian-dyadic transition tariffs with dirty workspace. This changes an ordinary same-frame window and preserves every Gaussian transition; no joint-transition optimum is computed here.

• Bound dense cross-port thin-query capacity at 528 requests (no new κ) #5997 studies dense cross-port thin-query capacity. This leaves all thin queries and paid native occurrences unchanged and computes no request-capacity threshold.

The completion refresh inspected all fourteen other account PRs opened since the advance CLAIM (#5997, #5998, #6000 through #6011). None reports the same literal dirty-anchor window or its two-event/twenty-unit saving. No additional predecessor computations were run.

CI notes

At exact head 6dd2ecbe34847270559316d7f1e3590f9fe11be0, both hosted checks passed: plan and replay (research/p104-dirty-anchor-window), in run 40584421368. The checks were read once after completion, and the run head matches the PR head. Hosted replay certifies the registered normal and optimized package commands; the mathematical and admission limits above remain.

Merge Danger

Door: two-way. Blast radius: package. Six new files under research/p104-dirty-anchor-window/; no shared code, predecessor package or selected-frontier file changes.