Research: partitioned independent-walks 8q priced obstruction (no new kappa)

[VictorLiwentao]

Change and scope

Freestanding #840-style priced obstruction under #1898 at (b,a,x)=(38,2,2). Names one new dirt-legal readout alphabet at Q=8: two restored walks with distinct slot lists, independent dirt, and dual even-parity readout. Answers open question 2 of #2840: does any other priced alphabet undercut tariff 436 at eight queries after a complete dirty bill?

Dual schedule	Covering pairs	Exact min R	Tariff floor (X≥0)	Undercuts 436?
Same-walk even-subset (#2677)	—	≥74	≥452 at X=0	no
Partition (2,6)	3916416	92	≥488	no
Partition (3,5)	10416000	98	≥500	no
Partition (4,4)	14165760	100	≥504	no

Global covering minimum is R=92 on (2,6) only. Abstract tariff 38·8+2·92=488>436. Length-1 components are not restored.

Scoped obstruction / priced alphabet; no new kappa. Leave-alone through #2846 / #2840 / #2779 was not reopened.

Result

Package: research/independent-walks-8q-obstruction/.
Tip: 379aaf8f413d47f3bcbc054e1e4bf3e2daed0ce9.

Exact: partition min R 92 (tariff floor 488); no undercut of 436.

Validation

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

Expected:

PASS_INDEPENDENT_WALKS_8Q_OBSTRUCTION partition_min_R=92 ... tariff_floor=488 ... answers_priced_alphabet_q8_oq no_new_kappa
PASS_INDEPENDENT_PARTITIONED_WALKS_8Q covering_26=3916416 covering_35=10416000 covering_44=14165760 ... tariff_floor=488 ... no_new_kappa
PASS_INDEPENDENT_WALKS_8Q_PACKAGE_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/independent-walks-8q-obstruction outcome=completed

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

Overlap and credit

Closest prior: #2779 (Q=7 partitioned dual), #2840, #2677. Freestanding Q=8 partitioned dual; no competing open PR at refresh.

Credit the mutable-source / #2779 / #2840 / #2677 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.