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Mister-Meeseeks merged 1 commit into from
Oct 16, 2026
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Research: dirty-shadow sym-diff collapse at eight queries (no new kappa) #2840

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340 changes: 340 additions & 0 deletions research/dirty-shadow-8q-obstruction/CERTIFICATE.json
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{
"schema_version": 1,
"status": "PASS_DIRTY_SHADOW_8Q_OBSTRUCTION",
"scope": "Five-source common-B mutable-source Q/R/X alphabet (PR1898). Priced dirty-shadow snapshot readout at Q=8: sym-diff collapse to even-subset, plus illegal clean-shadow counterfactual. Answers #2761 OQ2 / #2764 OQ2 (dirty-shadow at eight queries).",
"claim": {
"Q": 8,
"dirty_shadow_min_R": 74,
"even_subset_min_R": 74,
"clean_shadow_counterfactual_min_R": 67,
"one_dup_dirty_min_R": 82,
"one_dup_clean_counterfactual_min_R": 71,
"undercuts_436_if_clean_shadow_free": false,
"undercuts_436_after_complete_dirty_bill": false,
"legal_tariff_at_X0": 452,
"hypothetical_clean_tariff_at_X0": 438,
"endpoint_Q6_tariff": 436,
"matches_2677_even_floor": true,
"answers_mc7q_oq2": true,
"oq2_answer": "The dirty-shadow sym-diff collapse extends verbatim to eight queries: on all 2430400 covering distinct-7 length-8 slot lists, priced dirty-shadow totals match even-subset exactly (spectrum {74,80,84}; matches_even=2430400), so legal R>=74 and tariff >=452>436 at X=0, matching #2677. One-duplicate multisets likewise collapse (spectrum {82,88} on 4083072 covering lists). A dirt-free shadow would reach R=67 (tariff 438) on distinct-7 and R=71 (tariff 446) on one-dup, but both still fail to undercut 436 at X=0 and remain illegal under PR1898 inherited dirt; shadow-only reads leave odd dirt. After a complete dirty bill, legal dirty-shadow alphabets stay at tariff >=452 and do not undercut the six-query endpoint 436.",
"no_new_kappa": true
},
"champion": {
"slots": [
0,
1,
2,
3,
4,
8,
16,
29
],
"even_R": 74,
"dirty_shadow_R_by_k": [
74,
74,
74,
74,
74,
74,
74,
74
],
"dirty_shadow_min_R": 74,
"clean_shadow_R_by_k": [
74,
73,
67,
67,
67,
67,
67,
67
],
"clean_shadow_min_R": 67,
"clean_best_k": 2,
"legal_tariff_X0": 452,
"hypothetical_clean_tariff_X0": 438,
"endpoint_Q6": 436,
"symdiff_checked_at_k2": 128
},
"clean_shadow_dirt_examples": [
{
"note": "champion_shadow_only_sigma",
"slots": [
0,
1,
2,
3,
4,
8,
16,
29
],
"snapshot_index": 2,
"sigma": 2,
"mask": 2,
"primary_reads": 0,
"shadow_reads": 1,
"inherited_dirt_parity": 1,
"legal_under_correlated_dirt": false,
"clean_R": 67,
"dirty_R": 74
},
{
"note": "first_clean_70_witness_shadow_dirt",
"slots": [
0,
1,
2,
3,
4,
8,
12,
16
],
"snapshot_index": 7,
"sigma": 16,
"mask": 16,
"primary_reads": 0,
"shadow_reads": 1,
"inherited_dirt_parity": 1,
"legal_under_correlated_dirt": false,
"clean_R": 70,
"dirty_R": 80
}
],
"distinct7": {
"covering_sets": 2430400,
"dirty_matches_even_on_covering": 2430400,
"even_subset": {
"attainable_R": [
74,
80,
84
],
"histogram": {
"74": 416640,
"80": 1180480,
"84": 833280
},
"min_R": 74,
"first_witnesses": {
"74": [
0,
1,
2,
3,
4,
8,
16,
29
],
"80": [
0,
1,
2,
3,
4,
8,
12,
16
],
"84": [
0,
1,
2,
3,
4,
5,
8,
16
]
}
},
"dirty_shadow": {
"attainable_R": [
74,
80,
84
],
"histogram": {
"74": 416640,
"80": 1180480,
"84": 833280
},
"min_R": 74,
"matches_even_on_covering": 2430400,
"first_witnesses": {
"74": [
0,
1,
2,
3,
4,
8,
16,
29
],
"80": [
0,
1,
2,
3,
4,
8,
12,
16
],
"84": [
0,
1,
2,
3,
4,
5,
8,
16
]
}
},
"clean_shadow_counterfactual": {
"attainable_R": [
67,
70,
76
],
"histogram": {
"67": 416640,
"70": 1180480,
"76": 833280
},
"min_R": 67,
"first_witnesses": {
"67": [
0,
1,
2,
3,
4,
8,
16,
29
],
"70": [
0,
1,
2,
3,
4,
8,
12,
16
],
"76": [
0,
1,
2,
3,
4,
5,
8,
16
]
},
"legal_under_dirty_contract": false
}
},
"one_duplicate": {
"covering_multisets": 4083072,
"dirty_matches_even_on_covering": 4083072,
"even_subset": {
"attainable_R": [
82,
88
],
"histogram": {
"82": 680512,
"88": 3402560
},
"min_R": 82,
"first_witness": [
0,
0,
1,
2,
4,
8,
15,
16
]
},
"dirty_shadow": {
"attainable_R": [
82,
88
],
"histogram": {
"82": 680512,
"88": 3402560
},
"min_R": 82,
"matches_even_on_covering": 4083072,
"first_witness": [
0,
0,
1,
2,
4,
8,
15,
16
]
},
"clean_shadow_counterfactual": {
"attainable_R": [
71,
80
],
"histogram": {
"71": 680512,
"80": 3402560
},
"min_R": 71,
"first_witness": [
0,
0,
1,
2,
4,
8,
15,
16
],
"legal_under_dirty_contract": false
}
},
"leave_alone": {
"through": 2817,
"includes": [
2487,
2593,
2643,
2677,
2686,
2687,
2715,
2761,
2764,
2779,
2817
],
"deferred": [
"transfer-coupled-dual-7q soft-overlap",
"shared-xor soft-overlap #2643",
"host screens"
],
"do_not_touch_package": "research/transfer-coupled-7q-obstruction/"
}
}
30 changes: 30 additions & 0 deletions research/dirty-shadow-8q-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`; not edited.
- Open #2715 `research/cheaper-readout-7q-obstruction` — all-subset /
dirty-parity repair; not edited.
- Open #2761 `research/multi-connector-7q-obstruction` — dirty-shadow at Q=7;
OQ2 answered here; not edited.
- Open #2764 `research/dirty-parity-8q-obstruction` — dirty-parity at Q=8;
matching OQ2 handoff; not edited.
- Open #2817 `research/transfer-coupled-7q-obstruction/` — leave-alone; not
touched.
- Live pin: `research/mutable-source-shear-cost/CERTIFICATE.json`.

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