Repository navigation
Research: 7–9Q mutable-source invoices cannot beat six-query tariff 436 - #2677
Merged
Mister-Meeseeks merged 3 commits intoOct 16, 2026
Conversation
Answer PR2455/PR1898 unequal-price handoff with exact path-lowered even-subset invoices: Q=7 minimum is 442 (R=82,X=6); Q=8/Q=9 floors are 452/466 under the PR1898 (b,a,x)=(38,2,2) fixture. No new kappa. Prepared by Wentao Li with substantial AI assistance.
Machine-check even-subset R over all C(31,6) covering sets so exact min
tariff 442 / no beat of six-query 436 does not rely on prose excluding
intermediate R in {83..87}. Independent rechecks the spectrum; align
controls=2 receipt. No new kappa.
Prepared by Wentao Li with substantial AI assistance.
Independent R-spectrum census fits the prior 120s slot; raising it broke the generic replay total-timeout gate. Prepared by Wentao Li with substantial AI assistance.
This was referenced Oct 15, 2026
Merged
Merged
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Change and scope
Answers the unequal-price handoff in #1898 / open question tracked via #2455: under path-lowered even-subset schedules and the PR1898 tariff
(b,a,x)=(38,2,2), can a 7–9 query mutable-source word beat the sharp six-query endpoint tariff 436?No. Exact invoices show:
Package is freestanding (
research/mutable-source-789q-invoice/). Leave-alone through #2643 (including #2593 and #2487) was not reopened. Path-lowered schedule class only; non-path XOR floor at Q=7 is settled separately by #2643.Priced finite invoice / obstruction; no new kappa.
Result
Q=7 has exact minimum tariff 442 at
(R,X)=(82,6), with certified attainable R spectrum{82,88}(intermediate R∈{83..87} excluded by exhaustive census). Q=8 and Q=9 admit only floors 452 and 466 under the same fixture. None beats the Q=6 endpoint 436.Package:
research/mutable-source-789q-invoice/.Tip:
e703687cc7a3cb4dd3834aa12d8816ddb134a4ae.Validation
Expected:
Default verify is read-only. Full
make verify, selected cold replay, Lean, and multiplication-theorem obligations were not rerun for this isolated invoice package.Overlap and credit
Closest priors: #1898 (tariff fixture / unequal-price handoff), #2455 OQ1, #1370, #2643 (Q=7 XOR floor for the full restored alphabet). Leave-alone through #2643. No competing open PR on this freestanding path-lowered 7–9Q invoice package at refresh.
Credit the mutable-source / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.