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Mister-Meeseeks merged 1 commit into from
Oct 16, 2026
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Research: partitioned independent-walks 8q priced obstruction (no new kappa) #2851

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286 changes: 286 additions & 0 deletions research/independent-walks-8q-obstruction/CERTIFICATE.json
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{
"schema_version": 1,
"status": "PASS_INDEPENDENT_WALKS_8Q_OBSTRUCTION",
"scope": "Five-source common-B mutable-source Q/R/X alphabet (PR1898) at (b,a,x)=(38,2,2). Freestanding partitioned independent dual walks at total Q=8 (valid restored lengths (2,6), (3,5), (4,4)): covering dual even-parity readout has global min R=92 at (2,6); tariff floor at X=0 is 488>436. Answers dirty-shadow/#2840 OQ2 / onerepeat OQ2 by naming one new priced alphabet at eight queries.",
"claim": {
"Q": 8,
"partition_covering_min_R": 92,
"partition_26_covering": 3916416,
"partition_35_covering": 10416000,
"partition_44_covering": 14165760,
"partition_26_min_R": 92,
"partition_35_min_R": 98,
"partition_44_min_R": 100,
"tariff_floor_at_X0": 488,
"endpoint_Q6_tariff": 436,
"undercuts_436_after_complete_bill": false,
"length1_walks_invalid": true,
"answers_priced_alphabet_q8_oq": true,
"oq_answer": "Every covering partitioned dual-walk schedule with total query count Q=n0+n1=8 (valid restored walks of lengths (2,6), (3,5), or (4,4), distinct nonzero labels within each walk, independent dirt, dual even-parity readout) has R\u226592, attained only on (2,6) (spectrum {92,96,104}; covering 3916416). Partitions (3,5) and (4,4) have min R 98 and 100. At X=0 the abstract tariff is already 488>436 under (b,a,x)=(38,2,2); positive path X only increases the bill. Length-1 components are not restored. Transfer-coupled / onerepeat / dirty-shadow leave-alones are not reopened.",
"no_new_kappa": true
},
"partition_2_plus_6": {
"kind": "partition_2_plus_6",
"Q": 8,
"covering_pairs": 3916416,
"attainable_R": [
92,
96,
104
],
"histogram": {
"92": 1416576,
"96": 1249920,
"104": 1249920
},
"min_R": 92,
"first_witnesses": {
"92": [
[
0,
16
],
[
0,
1,
2,
4,
8,
15
]
],
"96": [
[
0,
1
],
[
0,
1,
2,
4,
8,
16
]
],
"104": [
[
0,
16
],
[
0,
1,
2,
3,
4,
8
]
]
},
"champion_structural_rank4_outside": {
"applies": true,
"rank": 4,
"sigma_in_span": false,
"R": 92,
"sum_even": 30
}
},
"partition_3_plus_5": {
"kind": "partition_3_plus_5",
"Q": 8,
"covering_pairs": 10416000,
"attainable_R": [
98,
104
],
"histogram": {
"98": 3124800,
"104": 7291200
},
"min_R": 98,
"first_witnesses": {
"98": [
[
0,
1,
2
],
[
0,
4,
8,
13,
16
]
],
"104": [
[
0,
1,
2
],
[
0,
1,
4,
8,
16
]
]
}
},
"partition_4_plus_4": {
"kind": "partition_4_plus_4",
"Q": 8,
"covering_pairs": 14165760,
"attainable_R": [
100,
104,
112
],
"histogram": {
"100": 3610880,
"104": 9999360,
"112": 555520
},
"min_R": 100,
"first_witnesses": {
"100": [
[
0,
1,
2,
4
],
[
0,
7,
8,
16
]
],
"104": [
[
0,
1,
2,
4
],
[
0,
1,
8,
16
]
],
"112": [
[
0,
1,
2,
3
],
[
0,
4,
8,
16
]
]
}
},
"champion": {
"champion_26": {
"walks": [
[
0,
16
],
[
0,
1,
2,
4,
8,
15
]
],
"R": 92,
"path_X": 16,
"tariff": 520,
"structural_rank4_outside": {
"applies": true,
"rank": 4,
"sigma_in_span": false,
"R": 92,
"sum_even": 30
}
},
"champion_35": {
"walks": [
[
0,
1,
2
],
[
0,
4,
8,
13,
16
]
],
"R": 98,
"path_X": 12,
"tariff": 524
},
"champion_44": {
"walks": [
[
0,
1,
2,
4
],
[
0,
7,
8,
16
]
],
"R": 100,
"path_X": 16,
"tariff": 536
},
"tariff_floor_at_X0": 488,
"endpoint_Q6": 436,
"single_walk_even_min_R_Q8": 74,
"partition_min_R": 92
},
"length1_invalid_examples": [
{
"slots": [
0
],
"valid_restored_walk": false,
"path_X": null,
"note": "closed_(0,0)_zero_edge"
}
],
"unit_tariff": {
"b": 38,
"a": 2,
"x": 2
},
"tariff_check": {
"formula": "38*Q + 2*R + 2*X",
"at_R92_X0": 488,
"champion_26": 520,
"champion_35": 524,
"champion_44": 536,
"endpoint_Q6": 436
}
}
26 changes: 26 additions & 0 deletions research/independent-walks-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 `(b,a,x)=(38,2,2)`.
- 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 at Q=8; not edited.
- Open #2779 `research/independent-walks-7q-obstruction` — partitioned dual at
Q=7; not edited; this package is the freestanding Q=8 companion.
- Open #2840 `research/dirty-shadow-8q-obstruction` — dirty-shadow at Q=8; OQ2
answered here for partitioned independent walks; not edited.
- Open #2836 / #2817 transfer-coupled packages — leave-alone; not edited.
- Pending `cursor/transfer-coupled-onerepeat-7q-60b9@90d879d1` — not edited or
competed.
- Live pin: `research/mutable-source-shear-cost/CERTIFICATE.json`.

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