Research: dirty-parity collapse extends to eight queries (no new kappa)

[VictorLiwentao]

Change and scope

Answers open question 2 of #2715 in the five-source common-B mutable-source alphabet of #1898: does the dirty-parity collapse that blocked free all-subset readout at Q=7 also apply at eight queries?

Readout model	Distinct-7 min R	One-dup min R	Tariff at X=0	Undercuts 436?
All-subset (free, illegal dirt)	61	66	426	yes (not legal)
Even-subset (#2677)	74	—	452	no
Parity-repaired odd sets	74	82	452	no

Free all-subset reaches R=61 (hypothetical tariff 426 < 436 even at X=0). Odd live-connector counts leave dirt. Minimal zero-slot parity repair restores even live-connector parity and collapses every covering distinct-7 schedule to even-subset R≥74 (tariff ≥452), matching #2677.

Scoped obstruction / priced alphabet; no new kappa. Leave-alone through #2715 was not reopened.

Result

Package: research/dirty-parity-8q-obstruction/.
Tip: d4d5f0f37929df97ea1e0f8d2bf0859f92407e55.

Exact: free all-subset min R 61 (tariff 426); parity-repair min R 74 (tariff 452); no legal undercut of 436 after dirty-parity repair.

Validation

python3.12 -I -B research/dirty-parity-8q-obstruction/verify.py
python3.12 -I -O -B research/dirty-parity-8q-obstruction/verify.py
python3.12 -I -B research/dirty-parity-8q-obstruction/independent.py
python3.12 -I -B research/dirty-parity-8q-obstruction/test_package.py
python3.12 -B scripts/research_package.py --package research/dirty-parity-8q-obstruction

Expected:

PASS_DIRTY_PARITY_8Q_OBSTRUCTION all_subset_min_R=61 parity_repair_min_R=74 ... answers_cr7q_oq2 matches_2677_even_floor no_new_kappa
PASS_INDEPENDENT_DIRTY_PARITY_8Q covering=2430400 all_min=61 repair_min=74 ... answers_cr7q_oq2 no_new_kappa
PASS_DIRTY_PARITY_8Q_PACKAGE_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/dirty-parity-8q-obstruction outcome=completed

Default verify is read-only. Admission uses need(); -O also passes.

Overlap and credit

Closest prior: #2715 (OQ2), #2677. Freestanding Q=8 dirty-parity fixture; no competing open PR at refresh.

Credit the mutable-source / #2715 / #2677 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.