Research: one-repeat partitioned (3,5)/(4,4) 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-repeat companions of the partitioned (3,5) and (4,4) Hamilton layers at Q=8. Answers the remaining one-repeat companion question after #2851 / pending independent-walks-onerepeat-8q (2,6): do one-repeat layers on (3,5) or (4,4) improve on distinct-label floors R=98 / R=100?

Dual schedule	Covering pairs	Exact min R	Tariff floor (X≥0)	Undercuts 436?	Beats distinct?
Distinct (3,5) (#2851)	10416000	98	≥500	no	—
One-repeat (3,5) (this)	2499840	112	≥528	no	no
Distinct (4,4) (#2851)	14165760	100	≥504	no	—
One-repeat×distinct (4,4) (this)	1666560	112	≥528	no	no
One-repeat×one-repeat (4,4)	0	—	—	—	—

Length-3 cannot host a one-repeat (closed zero edge). Abstract tariff 38·8+2·112=528>436.

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

Result

Package: research/independent-walks-onerepeat-35-44/.
Tip: 8bd3d2985cfaef59d800409a283b2fbca15a4b73.

Exact: one-repeat min R 112 on both shapes (tariff floor 528); no undercut of 436; does not beat distinct 98/100.

Validation

python3.12 -I -B research/independent-walks-onerepeat-35-44/verify.py
python3.12 -I -O -B research/independent-walks-onerepeat-35-44/verify.py
python3.12 -I -B research/independent-walks-onerepeat-35-44/independent.py
python3.12 -I -B research/independent-walks-onerepeat-35-44/test_package.py
python3.12 -B scripts/research_package.py --package research/independent-walks-onerepeat-35-44

Expected:

PASS_INDEPENDENT_WALKS_ONEREPEAT_35_44_OBSTRUCTION one_repeat_35_min_R=112 one_repeat_44_min_R=112 ... tariff_floor=528 ... no_new_kappa
PASS_INDEPENDENT_WALKS_ONEREPEAT_35_44 covering_35=2499840 covering_44=1666560 ... tariff_floor=528 ... no_new_kappa
PASS_INDEPENDENT_WALKS_ONEREPEAT_35_44_PACKAGE_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/independent-walks-onerepeat-35-44 outcome=completed

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

Overlap and credit

Closest prior: #2851 (distinct partitioned Q=8), pending independent-walks-onerepeat-8q (one-repeat (2,6)), #2846, #2779. Freestanding (3,5)/(4,4) one-repeat layer; no competing open PR at refresh.

Credit the mutable-source / #2851 / onerepeat-8q / #2779 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.