Research: transfer-coupled all-shapes 7q obstruction (no new kappa)

[VictorLiwentao]

Change and scope

Completes the transfer-coupled census across every unordered shape (p,a,b) with p+a+b=7, answering open question 1 of #2779 and the remaining-shapes follow-up left by #2817 ((5,1,1)-only) in the five-source common-B mutable-source alphabet of #1898.

Shape (p,a,b)	Covering pairs	Exact min R	Tariff floor (C=1)	Undercuts 436?
Same-walk even-subset (#2686)	—	≥82	≥442 at X=6	no
Partitioned dual (#2779)	—	≥112	≥490 at X=0	no
(5,1,1) transfer-coupled	8749440	84	≥439 (X≥2)	no
(4,1,2)	34997760	86	≥439 at X=0	no
All other unordered shapes	—	≥88	≥443 at X=0	no

Global covering minimum is R=84 at (5,1,1) only. Gray X=0 covering on that shape is empty, and fair path X is always even, so covering forces X≥2 and tariff ≥439>436. Every other unordered shape already has R≥86.

Scoped obstruction / priced alphabet; no new kappa. Leave-alone through #2817 was not reopened (freestanding package path).

Result

Package: research/transfer-coupled-all-shapes-7q/.
Tip: b4e312f952aea55a0b9f013a1d152423f6cf0f56.

Exact: global min R 84 (only at (5,1,1) with X≥2); companions R≥86; tariff floor 439; no undercut of 436.

Validation

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

Expected:

PASS_TRANSFER_COUPLED_7Q_OBSTRUCTION global_min_R=84 ... tariff_floor=439 ... no_new_kappa
PASS_INDEPENDENT_TRANSFER_COUPLED_7Q companions=7 ... tariff_floor=439 ... no_new_kappa
PASS_TRANSFER_COUPLED_7Q_PACKAGE_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/transfer-coupled-all-shapes-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: #2817 ((5,1,1)-only fair-X floor 452), #2779. Freestanding full-shape census; no competing open PR on this package path at refresh.

Credit the mutable-source / #2817 / #2779 / #2761 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.