Repository navigation
Research: transfer-coupled (5,1,1) 7q readout obstruction (no new kappa) - #2817
Open
VictorLiwentao wants to merge 1 commit into
Open
VictorLiwentao wants to merge 1 commit into
VictorLiwentao wants to merge 1 commit into
Conversation
Prove every covering distinct-label transfer-coupled dual of shape (5,1,1) at Q=7 (shared prefix length 5, priced transfer C>=1, divergent tips, independent dirt, dual even-parity, fair shared-prefix XOR billing) has R>=84 and fair X>=9 on the R=84 layer, so the abstract tariff is already >=452>436. Answers the transfer-coupled OQ after partitioned independent-walks; leave-alones and pending fixtures untouched. Prepared by Wentao Li with substantial AI assistance.
cursor Bot
pushed a commit
to VictorLiwentao/integer-mult-bounds
that referenced
this pull request
Oct 16, 2026
Full (p,a,b) census at Q=7 closes the remaining-shapes follow-up after CrocSwap#2817 (5,1,1)-only and CrocSwap#2779 OQ1. Global min R=84 only at (5,1,1) with X>=2; all other shapes R>=86; tariff floor 439>436. Prepared by Wentao Li with substantial AI assistance.
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
1 participant
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Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be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 transfer-coupled open question left by #2779 on the #2715 / #2761 lineage in the five-source common-B mutable-source alphabet of #1898: can a shared prefix, priced transfer
C≥1, and divergent suffixes undercut tariff436at totalQ=7after a complete dirty bill?Scoped to maximal-sharing shape
(p,a,b)=(5,1,1)(two length-6 walks, prefix counted once).(5,1,1)Every covering distinct-label
(5,1,1)dual hasR∈{84,88,90}. On theR=84layer, fair shared-prefix XOR billing withC=1is at least9. Abstract tariff38·7+2·84+2·9=452>436.Scoped obstruction / priced alphabet; no new kappa. Leave-alone through #2779 was not reopened.
Result
Package:
research/transfer-coupled-7q-obstruction/.Tip:
adb647eba5842812b36e67fe1aa2be5ecdff6b37.Exact: min R 84, min fair X 9, tariff floor 452; no undercut of 436.
Validation
Expected:
Default verify is read-only. Admission uses
need();-Oalso passes.Overlap and credit
Closest prior: #2779 (partitioned dual), #2761, #2686. Freestanding transfer-coupled
(5,1,1)fixture; no competing open PR at refresh.Credit the mutable-source / #2779 / #2761 / #2715 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.