Research: one-repeat transfer-coupled (5,1,1) obstruction (no new kappa)

[VictorLiwentao]

Change and scope

Answers open question 1 of #2836 in the five-source common-B mutable-source alphabet of #1898: do non-distinct (one-repeat) label layers inside a transfer-coupled (5,1,1) schedule improve on distinct-label R=84?

Layer	Covering pairs	Exact min R	Tariff at X=0,C=1	Undercuts 436?	Beats distinct 84?
Distinct-label (#2836 / #2817)	8749440	84	≥439 (needs X≥2)	no	—
Prefix-internal double	2499840	98	463	no	no
Suffix–prefix collision	1666560	96	459	no	no
Combined one-repeat	4166400	96	459	no	no

Every covering one-repeat dual has R∈{96,98}. Combined minimum is R=96, strictly worse than the distinct-label floor 84. Abstract tariff 38·7+2·96+1=459>436 already at X=0.

Scoped obstruction / priced alphabet; no new kappa. Leave-alone through #2840 / #2836 / #2817 was not reopened.

Result

Package: research/transfer-coupled-onerepeat-7q/.
Tip: 90d879d143f9570c140d105a5cc60f445766d852.

Exact: combined one-repeat min R 96 (tariff floor 459); no undercut of 436; does not beat distinct-label 84.

Validation

python3.12 -I -B research/transfer-coupled-onerepeat-7q/verify.py
python3.12 -I -O -B research/transfer-coupled-onerepeat-7q/verify.py
python3.12 -I -B research/transfer-coupled-onerepeat-7q/independent.py
python3.12 -I -B research/transfer-coupled-onerepeat-7q/test_package.py
python3.12 -B scripts/research_package.py --package research/transfer-coupled-onerepeat-7q

Expected:

PASS_TRANSFER_COUPLED_ONEREPEAT_7Q_OBSTRUCTION combined_min_R=96 ... tariff_floor=459 ... answers_all_shapes_oq1_onerepeat no_new_kappa
PASS_INDEPENDENT_TRANSFER_COUPLED_ONEREPEAT_7Q ... tariff_floor=459 ... no_new_kappa
PASS_TRANSFER_COUPLED_ONEREPEAT_7Q_PACKAGE_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/transfer-coupled-onerepeat-7q outcome=completed

Default verify is read-only. Admission uses need(); -O also passes. Requires gcc for local dual.c (Python fallback available).

Overlap and credit

Closest prior: #2836 (OQ1), #2817. Freestanding one-repeat layer; no competing open PR at refresh.

Credit the mutable-source / #2836 / #2817 / #2779 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.