[VictorLiwentao]

Change and scope

Freestanding #840-style priced obstruction under #1898 at (b,a,x)=(38,2,2). Companion Q=9 partitioned independent dual alphabet on (2,7)/(3,6)/(4,5) after the Q=8 independent / one-repeat / two-repeat / shared-dirt / three-repeat series.

Dual schedule	Covering pairs	Min R	Tariff @ X=0
Partition (2,7)	20512576	80	502
Partition (3,6)	69370560	88	518
Partition (4,5)	122561600	92	526

Exact covering min is R=80 on (2,7); tariff floor 502 > 436 (also above same-walk Q=9 floor 466). No undercut of the six-query endpoint; no new kappa.

Scoped obstruction / priced alphabet. Leave-alone through #2868 / #2867 / #2861 / #2860 / #2858 / #2851 was not reopened.

Result

Package: research/independent-walks-9q/.
Tip: 1e15ae28c15d56f7c61220564207d571972a33a4.

Exact: partition min R=80; tariff floor 502; no undercut of 436.

Validation

python3.12 -I -B research/independent-walks-9q/verify.py
python3.12 -I -O -B research/independent-walks-9q/verify.py --quick
python3.12 -I -B research/independent-walks-9q/independent.py
python3.12 -I -B research/independent-walks-9q/test_package.py
python3.12 -B scripts/research_package.py --package research/independent-walks-9q

Expected:

PASS_INDEPENDENT_WALKS_9Q_OBSTRUCTION partition_min_R=80 ... tariff_floor=502 ... no_undercut_partitioned_independent_walks_q9 ... no_new_kappa
PASS_INDEPENDENT_WALKS_9Q_QUICK ...
PASS_INDEPENDENT_PARTITIONED_WALKS_9Q ...
PASS_INDEPENDENT_WALKS_9Q_PACKAGE_TESTS ...
PASS_REGISTERED_RESEARCH_PACKAGE research/independent-walks-9q outcome=completed

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

Overlap and credit

Closest prior: #2851 (Q=8 partitioned independent), #2868 (three-repeat OQ2), #2867. Freestanding Q=9 package path; no competing open PR at refresh.

Credit the mutable-source / #2851 / #2868 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.

[VictorLiwentao]

OQ2 follow-up attempt (deferred; series locked)

A candidate package research/shared-dirt-onerepeat-8q/ @ 9b3f96bad on branch cursor/shared-dirt-onerepeat-8q-60b9 censuses mixed shared-dirt + one-repeat partitioned (2,6) duals at Q=8: covering 59996160, exact min R=96 (spectrum {96} only), tariff floor 496>436. It does not undercut the shared-dirt distinct floor R=82 (answers OQ2’s undercut question negatively) and beats independent one-repeat R=112 by 16.

Soft-overlap / series-lock deferred: soft-overlap ≈0.85–0.9 vs leave-alone #2861 (identical one-repeat covering scaffold) and ≈0.7–0.85 vs #2867 (shared-dirt dual formula retarget); the PR1898 tariff-alphabet line through this PR is treated as closed for further priced-alphabet extensions. R=96 is an exhaustive composition of those leave-alone alphabets without a new structural floor.

No separate CrocSwap PR opened. Prefer a disjoint card outside the PR1898 Q=8/#9q walk cluster.