Research: three-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 fifth dirt-legal readout alphabet at Q=8 beyond same-walk / dirty-shadow / partitioned dual / one-repeat / two-repeat / shared-dirt: three-repeat (excess-3) layers on partitioned independent duals.

Dual schedule	Valid	Covering pairs	Undercuts 436?
Three-repeat (2,6)	930	0	no
Three-repeat (3,5)	0	0	no
Three-repeat (4,4)	0	0	no

Exact covering census is empty on every shape (span/coset bounds; {d:4} never restores; excess 3 impossible on L4), so there is no covering R and no undercut of the six-query endpoint.

Scoped obstruction / priced alphabet; no new kappa. Leave-alone through #2867 / #2861 / #2860 / #2858 / #2851 was not reopened.

Result

Package: research/independent-walks-threerepeat-8q/.
Tip: 0aa5cf439fdf210a455b78b46b16b3c92ca38f87.

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

Validation

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

Expected:

PASS_INDEPENDENT_WALKS_THREEREPEAT_8Q_OBSTRUCTION covering_26=0 covering_35=0 covering_44=0 ... no_undercut_436 no_new_kappa
PASS_INDEPENDENT_WALKS_THREEREPEAT_8Q covering_26=0 covering_35=0 ... no_undercut_436 no_new_kappa
PASS_INDEPENDENT_WALKS_THREEREPEAT_8Q_PACKAGE_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/independent-walks-threerepeat-8q outcome=completed

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

Overlap and credit

Closest prior: #2867 (shared-dirt), #2860 (two-repeat), #2861, #2851. Freestanding three-repeat alphabet; no competing open PR at refresh.

Credit the mutable-source / #2867 / #2860 / #2861 / #2851 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.