Research: shared-dirt 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 fourth dirt-legal readout alphabet at Q=8 beyond same-walk / dirty-shadow / partitioned dual / one-repeat / two-repeat: shared-dirt (joint even live-read parity) dual on distinct partitioned walks. Soft-overlap-safe vs deferred shared-XOR (R-side dirt coupling only).

Dual schedule	Covering pairs	Exact min R	Tariff floor (X≥0)	Undercuts 436?	Beats independent floors?
Independent (2,6) (#2851)	3916416	92	≥488	no	—
Shared-dirt (2,6) (this)	3916416	82	≥468	no	yes
Independent (3,5) (#2851)	10416000	98	≥500	no	—
Shared-dirt (3,5) (this)	10416000	82	≥468	no	yes
Independent (4,4) (#2851)	14165760	100	≥504	no	—
Shared-dirt (4,4) (this)	14165760	82	≥468	no	yes

Global shared-dirt min is R=82 (spectra include 82/88/96). Abstract tariff 38·8+2·82=468>436. Undercuts independent-dirt floors but not the six-query endpoint.

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

Result

Package: research/shared-dirt-walks-8q/.
Tip: fc3a2cb3362934b1e34df974e64f9d0acfe07b77.

Exact: partition min R 82 (tariff floor 468); no undercut of 436.

Validation

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

Expected:

PASS_SHARED_DIRT_WALKS_8Q_OBSTRUCTION partition_min_R=82 ... tariff_floor=468 ... soft_overlap_shared_xor_safe no_new_kappa
PASS_SHARED_DIRT_WALKS_8Q covering_26=3916416 ... partition_min_R=82 tariff_floor=468 ... no_new_kappa
PASS_SHARED_DIRT_WALKS_8Q_PACKAGE_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/shared-dirt-walks-8q outcome=completed

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

Overlap and credit

Closest prior: #2851, #2861, #2860, #2858, #2677. Freestanding shared-dirt alphabet; deferred shared-XOR not reopened; no competing open PR at refresh.

Credit the mutable-source / #2851 / #2861 / #2860 / #2858 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.