Research: two-repeat partitioned 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 a third dirt-legal readout alphabet at Q=8 beyond same-walk / dirty-shadow / partitioned dual / one-repeat: two-repeat (excess-2) layers on partitioned independent duals. Answers the remaining priced-alphabet handoff after #2851 / #2858: does any further alphabet undercut tariff 436 at eight queries?

Dual schedule	Valid	Covering pairs	Undercuts 436?
Two-repeat (2,6)	26970	0	no
Two-repeat (3,5)	465	0	no
Two-repeat (4,4)	0	0	no

Exact covering census is empty on every shape (structural span/sumset bounds), so there is no covering R and no undercut of the six-query endpoint. Length-4 {d:3} never restores.

Scoped obstruction / priced alphabet; no new kappa. Leave-alone through #2858 / #2851 / #2846 was not reopened.

Result

Package: research/independent-walks-tworepeat-8q/.
Tip: c4581aaf852dc0ec49f41d6404e484c7a43dcd9f.

Exact: covering 0 on (2,6)/(3,5)/(4,4); no undercut of 436.

Validation

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

Expected:

PASS_INDEPENDENT_WALKS_TWOREPEAT_8Q_OBSTRUCTION covering_26=0 covering_35=0 covering_44=0 ... no_undercut_436 no_new_kappa
PASS_INDEPENDENT_WALKS_TWOREPEAT_8Q covering_26=0 covering_35=0 ... no_undercut_436 no_new_kappa
PASS_INDEPENDENT_WALKS_TWOREPEAT_8Q_PACKAGE_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/independent-walks-tworepeat-8q outcome=completed

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

Overlap and credit

Closest prior: #2858 (one-repeat (3,5)/(4,4)), #2851, #2840, #2677. Freestanding two-repeat alphabet; no competing open PR at refresh.

Credit the mutable-source / #2858 / #2851 / #2840 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.