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Research: partitioned independent-walks 7q readout obstruction (no new kappa) - #2779
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Mister-Meeseeks merged 1 commit intoOct 16, 2026
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…w kappa) Prove every covering dual of two restored walks at total Q=7 (partitions (2,5) and (3,4), independent dirt, dual even-parity) has exact R=112, so the abstract tariff is already >=490>436 at X=0. Answers the partitioned half of the independent-walks OQ after same-walk multi-connector; leave-alones and pending mc7q/dp8q fixtures untouched. Prepared by Wentao Li with substantial AI assistance.
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Full (p,a,b) census at Q=7 closes the remaining-shapes follow-up after the (5,1,1)-only transfer-coupled package 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.
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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.
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Full nine-shape census answers CrocSwap#2779 OQ1 and the remaining-shapes OQ left by the (5,1,1)-only transfer-coupled package: global min R=84 only on (5,1,1) with min fair X=9 (tariff 452>436); every other shape has R>=86. Prepared by Wentao Li with substantial AI assistance. Co-authored-by: Victor Li <VictorLiwentao@users.noreply.github.com>
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Change and scope
Answers the partitioned independent-walks open question on the #2715 / #2761 multi-connector lineage in the five-source common-B mutable-source alphabet of #1898: can two restored walks with distinct slot lists, independent dirt, and dual even-parity readout undercut tariff
436at totalQ=7?(2,5)(3,4)Every covering partitioned dual has exact
R=112. Length-1 components are not restored. Abstract tariff already≥490 > 436atX=0.Scoped obstruction / priced alphabet; no new kappa. Leave-alone through #2764 / #2761 / #2715 was not reopened.
Result
Package:
research/independent-walks-7q-obstruction/.Tip:
1f2a413f9e27ce9609924f7ab196548c4cbe43d8.Exact: partitioned dual min R 112 (tariff floor 490); no undercut of 436.
Validation
Expected:
Default verify is read-only. Admission uses
need();-Oalso passes.Overlap and credit
Closest prior: #2761 (same-walk multi-connector), #2686, #2715. Freestanding partitioned dual-walk fixture; no competing open PR at refresh.
Credit the mutable-source / #2761 / #2715 / #2686 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.