Research: dirty-shadow sym-diff collapse at eight queries (no new kappa)

[VictorLiwentao]

Change and scope

Answers open question 2 of #2761 and the matching handoff in #2764 in the five-source common-B mutable-source alphabet of #1898: does the dirty-shadow sym-diff collapse extend verbatim to eight queries?

Alphabet	Distinct-7 min R	One-dup min R	Tariff at X=0	Undercuts 436?
Even-subset (#2677)	74	82	452	no
Dirty shadow (legal)	74	82	452	no
Clean shadow (illegal)	67	71	438	no (still ≥436)

Dirty shadow collapses to even-subset by sym-diff with the snapshot index on every covering distinct-7 list and every covering one-duplicate multiset. A dirt-free shadow would reach R=67 (tariff 438) but still fails to undercut 436 at X=0 and remains illegal under PR1898 inherited dirt.

Scoped obstruction / priced alphabet; no new kappa. Leave-alone through #2836 / #2817 / #2764 / #2761 was not reopened.

Result

Package: research/dirty-shadow-8q-obstruction/.
Tip: ad644b1eff88e7ee2ca0ee6d5561fafb439bb369.

Exact: legal dirty-shadow min R 74 (tariff 452); illegal clean-shadow min R 67 (tariff 438); no undercut of 436.

Validation

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

Expected:

PASS_DIRTY_SHADOW_8Q_OBSTRUCTION dirty_shadow_min_R=74 ... answers_mc7q_oq2 matches_2677_even_floor no_new_kappa
PASS_INDEPENDENT_DIRTY_SHADOW_8Q covering=2430400 one_dup=4083072 dirty_min=74 ... answers_mc7q_oq2 no_new_kappa
PASS_DIRTY_SHADOW_8Q_PACKAGE_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/dirty-shadow-8q-obstruction outcome=completed

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

Overlap and credit

Closest prior: #2761 (dirty-shadow at Q=7; OQ2), #2764, #2677. Freestanding Q=8 dirty-shadow fixture; no competing open PR at refresh.

Credit the mutable-source / #2761 / #2764 / #2677 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.