Research: odd-cardinality cheaper readout collapses under dirty-parity repair (no new kappa)

[VictorLiwentao]

Change and scope

Answers open question 1 of #2686 in the five-source common-B mutable-source alphabet of #1898.

Define the natural all-subset (odd-cardinality allowed) connector-state readout score on Q=7 walks. Free of dirty-cancellation, it reaches R=66 (spectrum {66,72} on distinct-6 covers; one-repeat layer R=80) and would tariff 410 < 436 at X=6. But odd live-connector R_m counts leave arbitrary connector dirt on those outputs. The minimal zero-slot parity repair restores even live-connector parity and collapses every covering schedule to even-subset cost R≥82 (tariff 442), matching #2686.

Readout model	Distinct-6 min R	One-repeat R	Tariff at X=6	Undercuts 436?
All-subset (free, illegal dirt)	66	80	410	yes (not legal)
Even-subset (#2686)	82	96	442	no
Parity-repaired odd sets	82	96	442	no

Scoped obstruction / priced alphabet; no new kappa. Leave-alone through #2687 (including #2686, #2677, #2643, #2593) was not reopened.

Result

Package: research/cheaper-readout-7q-obstruction/.
Tip: 5f188dcf6c5043b65a3205cf1f8fdcea7dc98fd6.

Exact: free all-subset min R 66 (hypothetical tariff 410); after dirty-parity repair min R 82 (tariff 442); no legal undercut of 436.

Validation

python3.12 -I -B research/cheaper-readout-7q-obstruction/verify.py
python3.12 -I -O -B research/cheaper-readout-7q-obstruction/verify.py
python3.12 -I -B research/cheaper-readout-7q-obstruction/independent.py
python3.12 -I -B research/cheaper-readout-7q-obstruction/test_package.py
python3.12 -B scripts/research_package.py --package research/cheaper-readout-7q-obstruction

Expected:

PASS_CHEAPER_READOUT_7Q_OBSTRUCTION all_subset_min_R=66 parity_repair_min_R=82 hypothetical_tariff=410 repair_tariff=442 no_undercut_after_dirty_parity_repair answers_7qr_oq1 no_new_kappa
PASS_INDEPENDENT_CHEAPER_READOUT_7Q covering=583296 all_min=66 repair_min=82 tariff_free=410 tariff_repair=442 answers_7qr_oq1 no_new_kappa
PASS_CHEAPER_READOUT_7Q_PACKAGE_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/cheaper-readout-7q-obstruction outcome=completed

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

Overlap and credit

Closest prior: #2686 even-subset R floor (OQ1). Freestanding; no competing open PR on this all-subset/parity-repair obstruction at refresh.

Credit the mutable-source / #2686 / PR1898 lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.