[petalas]

Result and claim type

An explicit finite certificate in the fixed immutable-channel scalar quotient realizes the complete eight-mode response with delivery profile H0 + 14 H7 + 7 H8. At the positive nondecreasing tariff H0=0, H1=...=H7=1, H8=H9=15, its 22 channels cost 119 versus 120 for 8 H8. Thus an arbitrary-finite-channel 8 H8 floor for every monotone tariff is false in this response model. This is a new source-specific positive witness, not an audit of the predecessor exclusions.

Fourteen grade-seven frames and one ground-frame channel jointly produce mode (0,0,0,0,1,1,1,1). Seven cited clean grade-eight directions from Ali Romman's #5745 complete the correction using immutable original-mode payloads. The written linear identity and all 69 exact cut/field/coefficient contacts are included in research/monotone-noisy-delivery-counterexample.

The CLAIM proposed a three-frame search. That minimum remains unsettled. The progress update records the larger 22-channel scope delivered here.

This contribution was produced by Nick Petalas. Credit Nicholas Stone #5845 for the explicit monotone-tariff continuation, Ali Romman #5745 for the canonical model, clean directions and temporal discovery routine, #5808/#5823 for the cited distinct exclusions, flyingviper #5720/#5755, Cao Yifan, Cinna Davis, Dugongue and the unchanged archive's mode/native/controller/caller contributors. The new forward verifier imports no predecessor executable. Independent human and formal proof-kernel review are unclaimed.

Evidence and reproduction

Publication commit: 33ac3431cd610e013d0666304ab82eb64f75565a. Baseline: canonical main de5ec2e7a6074068452f45b1a191b5c72832df4a, priority revision 8. The only live input is the existing source archive on main, authenticated by Git blob and SHA256; no pending predecessor commit is required for replay.

From the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B research/monotone-noisy-delivery-counterexample/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -O -B research/monotone-noisy-delivery-counterexample/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/monotone-noisy-delivery-counterexample
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/monotone-noisy-delivery-counterexample --check-source-history

Use an equivalent CPython 3.12 path on another machine. Sparse checkouts first need git sparse-checkout add research/filtered-native-kappa004/inputs.

Local CPython 3.12.15 / macOS arm64 results:

• Warning-strict normal and optimized checks pass. Each registered command took 0.33 seconds wall in a local timeout-budget observation.
• Exact replay covers all 22,585 events, 22 independent channel symbols, 69 contacts, all 2,192 retained field/mode equalities and zero return response on all nine C slots, including the eight owned slots.
• Eight controls reject changed coefficients, premature contacts, wrong frames, understated grades, incorrect payloads, missing ground delivery, equality instead of strict gain, and a nonmonotone tariff.
• Registered replay, source metadata, exact committed bytes and declared source ancestry pass. The generated receipt binds the source archive, witness and verifier hashes.
• Official committed export and declared-input integrity pass. An isolated optimized replay from a read-only Git-free export with empty PATH passes; all ten exported files, including the export manifest, retain their hashes and sealed modes.

Limitations and unrun obligations

This is a certificate in the retained common-fixed-vector scalar quotient, not a full native operator identity or a physical supplier. All 112 Y responses and 50 non-ground-helper responses restore, but 113 exempt ground helpers have nonzero residuals after payload substitution. Their physical compensation is absent. Canonical delivery alone does not pay for payload preparation, scatter arithmetic, ownership/return, native phase correctness, precision, stock, tape movement or the full caller. No new kappa, selected-frontier change or discharge of the five framework assumptions is claimed. No exhaustive triple search, minimum-channel proof, native lift, Lean build or full multiplication replay was run.

Related open work

• Prove nine-channel delivery floor for monotone tariffs #5845 proves the monotone floor for at most nine channels; this positive quotient witness uses 22 and leaves the ten-channel boundary open.

• Prove the sharp all-rank floor for immutable mode delivery #5823 proves the all-channel floor for concave power tariffs; the displayed step tariff lies outside that class, and this witness is more expensive than 8 H8 under those powers.

• Exclude arbitrary mixed-rank active repair below rank eight #5808 excludes a favorable all-eight-mode completion using only grades one through seven under concave power pricing; this witness also uses seven grade-eight channels and a different tariff.

• Rule out fixed rank-one active repair with a 101-channel bound #5755 studies rank-one-only immutable delivery; this witness uses grades seven and eight. No predecessor numerical census was replayed for comparison.

• Prove exact tariffs for consecutive queries sharing a detour #5884 proves shared-detour tariffs for consecutive queries under a concave metric-chart contract. This witness combines fixed-frame immutable channels under a general monotone tariff; no common numerical invoice is compared.

Completion refresh inspected this account's nine other open PRs created since the CLAIM at 2026-10-27T10:37:37Z: #5876, #5877, #5878, #5879, #5880, #5882, #5883, #5884 and #5885. None supplies the same fixed-word 22-channel quantity or a conflicting same-instance number. No additional mathematical computation was run to check another contribution.

Open next questions

1. Can three, or fewer than fifteen, low-grade frames produce a nonzero clean response in this exact quotient? Start with a triple-span search retaining literal contacts; no such exclusion or channel optimum is established here.
2. Can the fourteen named grade-seven responses lift to a full native identity while physically compensating the 113 residual helpers? Start with their full operator action and a complete cleanup invoice. Scalar fixed-vector equality is insufficient.

CI notes

At commit 33ac3431cd610e013d0666304ab82eb64f75565a, run 40491507234 finished with plan failed; replay skipped. The sole failed step was Onboarding helper tests.

All ten failure/error headers name test_research_current_assignment, and their source traces point to unchanged tests/test_research_current_assignment.py. The exact summary is FAILED (failures=8, errors=2, skipped=22). The two errors are KeyError: 'follow_up_steps' and KeyError: 'catalog_first_step'. The eight assertion failures are 0 != 16, five missing-helper/reference cases reporting ValueError not raised, and two empty-versus-expected sparse-reference lists. The complete ten failure/error headers match PR #5876's failed run exactly; both logs were read. This is the reported shared onboarding failure on canonical main de5ec2e7a6074068452f45b1a191b5c72832df4a. Maintainers will repair it; no shared file or onboarding test was changed.

The package replay job was skipped. Hosted replay has not certified this package; only local scientific checks have run. Local warning-strict normal/optimized replay, both registered commands, source metadata, committed-byte/source-history validation and the read-only Git-free optimized export replay passed as recorded above. The published mathematical package and head are unchanged.