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Merged
Mister-Meeseeks merged 1 commit into from
Oct 16, 2026
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Research: odd-cardinality cheaper readout collapses under dirty-parity repair (no new kappa) #2715

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279 changes: 279 additions & 0 deletions research/cheaper-readout-7q-obstruction/CERTIFICATE.json
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{
"schema_version": 1,
"status": "PASS_CHEAPER_READOUT_7Q_OBSTRUCTION",
"scope": "Five-source common-B mutable-source Q/R/X alphabet (PR1898). Priced odd-cardinality (all-subset) connector-state readout at Q=7 versus dirty-parity repair back to even live-connector schedules. Answers #2686 OQ1 for this alphabet.",
"claim": {
"Q": 7,
"all_subset_min_R": 66,
"even_subset_min_R": 82,
"parity_repair_min_R": 82,
"one_repeat_all_subset_min_R": 80,
"one_repeat_parity_repair_min_R": 96,
"undercuts_436_if_all_subset_free": true,
"undercuts_436_after_parity_repair": false,
"hypothetical_all_subset_tariff_at_X6": 410,
"parity_repair_tariff_at_X6": 442,
"endpoint_Q6_tariff": 436,
"answers_7qr_oq1": true,
"oq1_answer": "Free all-subset (odd-cardinality) readout reaches R=66 and would tariff 410<436 at X=6, but odd live-connector R_m parity leaves arbitrary connector dirt on those outputs. Minimal zero-slot parity repair collapses every covering schedule to even-subset cost R>=82 (tariff 442), so this cheaper alphabet does not undercut the six-query endpoint under the PR1898 dirty-connector contract.",
"no_new_kappa": true
},
"champion": {
"slots": [
0,
1,
2,
6,
12,
24,
16
],
"path_X": 6,
"all_subset_R": 66,
"even_subset_R": 82,
"parity_repair_R": 82,
"all_subset_odd_dirt_masks": [
1,
2,
5,
6,
9,
11,
12,
15,
16,
19,
21,
23,
24,
27,
29,
31
],
"all_subset_odd_dirt_count": 16,
"hypothetical_tariff_all_X6": 410,
"tariff_repair_X6": 442,
"endpoint_Q6": 436
},
"dirt_obstruction_examples": [
{
"note": "champion_all_subset",
"slots": [
0,
1,
2,
6,
12,
24,
16
],
"odd_dirt_masks": [
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2,
5,
6,
9,
11,
12,
15,
16,
19,
21,
23,
24,
27,
29,
31
],
"odd_dirt_count": 16,
"legal_under_dirty_cancellation": false,
"all_R": 66,
"repair_R": 82
},
{
"note": "first_all_subset_66_witness",
"slots": [
0,
1,
2,
4,
8,
15,
16
],
"odd_dirt_masks": [
1,
2,
4,
8,
15,
16,
19,
21,
22,
23,
25,
26,
27,
28,
29,
30
],
"odd_dirt_count": 16,
"legal_under_dirty_cancellation": false,
"all_R": 66,
"repair_R": 82
}
],
"distinct6": {
"covering_sets": 583296,
"all_subset": {
"attainable_R": [
66,
72
],
"histogram": {
"66": 97216,
"72": 486080
},
"min_R": 66,
"first_witnesses": {
"72": [
0,
1,
2,
3,
4,
8,
16
],
"66": [
0,
1,
2,
4,
8,
15,
16
]
}
},
"even_subset": {
"attainable_R": [
82,
88
],
"histogram": {
"82": 97216,
"88": 486080
},
"min_R": 82,
"first_witnesses": {
"88": [
0,
1,
2,
3,
4,
8,
16
],
"82": [
0,
1,
2,
4,
8,
15,
16
]
}
},
"parity_repair": {
"attainable_R": [
82,
88
],
"histogram": {
"82": 97216,
"88": 486080
},
"min_R": 82,
"first_witnesses": {
"88": [
0,
1,
2,
3,
4,
8,
16
],
"82": [
0,
1,
2,
4,
8,
15,
16
]
},
"matches_even_on_covering": 583296
}
},
"one_repeat_all_subset": {
"kind": "one_repeat_on_standard_basis",
"covering_walks": 1680,
"attainable_R": [
80
],
"histogram": {
"80": 1680
},
"min_R": 80,
"first_witness": [
0,
1,
0,
2,
4,
8,
16
]
},
"one_repeat_parity_repair": {
"kind": "one_repeat_on_standard_basis",
"covering_walks": 1680,
"attainable_R": [
96
],
"histogram": {
"96": 1680
},
"min_R": 96,
"first_witness": [
0,
1,
0,
2,
4,
8,
16
]
},
"leave_alone": {
"through": 2686,
"includes": [
2593,
2643,
2677,
2686
],
"pending_skeptical_not_edited": "cursor/odd-kernel-query-pair-60b9@c319093b",
"deferred": [
"mutable-source-7q-shared-xor soft-overlap #2643",
"host screens"
]
}
}
23 changes: 23 additions & 0 deletions research/cheaper-readout-7q-obstruction/NOTICE.md
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# Notice

New material in this directory is Apache-2.0.

Predecessor credit (do not alter historical notices elsewhere):

- Arham Tahir / PR1898 `research/mutable-source-minimum-queries` — five-source
alphabet, minimum-query endpoint, abstract complete-call tariff.
- ywz65 / open PR2455 `research/mutable-source-six-query-xor` — component lemma
and restored interaction-graph census at six queries.
- Arham Tahir / PR1370 — path-local shear lowering.
- TennisBowling / PR1524 — equal-price theorem and unequal-price handoff.
- Ross Richardson / PR943/934 — prefix framework.
- Fork path-lowered `research/mutable-source-789q-invoice` / open #2677 —
distinct-slot spectrum and champion path; not edited.
- Open #2643 `research/seven-query-xor-floor` — restored `X ≥ 6` at `Q = 7`;
not edited.
- Open #2686 `research/seven-query-r-floor` — even-subset `R ≥ 82` and OQ1
answered here; not edited.
- Live pin: `research/mutable-source-shear-cost/CERTIFICATE.json`.

Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI
assistance.
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