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Research: multi-connector / priced-shadow 7q readout obstruction (no new kappa) - #2761
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…w kappa) Answers CrocSwap#2715 OQ1 (cr7q): legal dirty-shadow and dual same-walk collapse to even-subset R>=82 (tariff 442); illegal clean-shadow would hit R=71 (tariff 420). Prepared by Wentao Li with substantial AI assistance.
Compute dual R as sum_m min_a (e[a]+e[a xor m]) and verify triangle on every covering set instead of incrementing dual_matches/triangle_ok unconditionally. Align TASK.json illegal clean-shadow tariff from 432 to 420 (38*7+2*71+2*6). Prepared by Wentao Li with substantial AI assistance.
This was referenced Oct 15, 2026
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Answers #2761/#2764 OQ2 in the PR1898 alphabet: priced dirty-shadow at Q=8 matches even-subset R>=74 (tariff 452) on all covering distinct-7 and one-dup lists; illegal clean-shadow reaches R=67 (tariff 438) but still fails to undercut 436 at X=0. Prepared by Wentao Li with substantial AI assistance.
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Change and scope
Answers open question 1 of #2715 in the five-source common-B mutable-source alphabet of #1898: can a multi-connector readout alphabet reach
R≤78atQ=7withX=6after a complete dirty bill?Dirty shadow collapses to even-subset by sym-diff with the snapshot index. Independent dual same-walk equals even-subset by triangle inequality (
Σ_m min_a (e[a]+e[a⊕m])machine-checked on all covering sets; not a Σe copy). A dirt-free shadow would undercut, but inherits dirt under PR1898 and fails the dirty bill.Scoped obstruction / priced alphabet; no new kappa. Leave-alone through #2715 (including #2687, #2686, #2677, #2643, #2593) was not reopened.
Result
Package:
research/multi-connector-7q-obstruction/.Tip:
cd4ff9427c3e35efb4de09bbf1137e7b68732ecf.Exact: legal dirty-shadow / dual-indep min R 82 (tariff 442); illegal clean-shadow min R 71 (tariff 420); no legal undercut of 436.
Validation
Expected:
Default verify is read-only. Admission uses
need();-Oalso passes.Overlap and credit
Closest prior: #2715 (cr7q OQ1), #2686. Freestanding; no competing open PR on this multi-connector/shadow obstruction at refresh.
Credit the mutable-source / #2715 / #2686 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.