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F-star family gap: the v = 7..11 census, the first gap-2 instance below v = 12, and the box-completeness attack (no kappa) #2936

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F-star family gap: the v = 7..11 census, the first gap-2 instance below v = 12, and the box-completeness attack (no kappa) #2936

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81 changes: 81 additions & 0 deletions research/fstar-family-gap-v711-seed3e3478d8/CERTIFICATE.json
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Original file line number Diff line number Diff line change
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{
"box_attack": {
"box_violations": 0,
"demo_box": 1,
"demo_cert": 2,
"sweep_replayed": 100,
"sweep_total": 126,
"tau0_pattern": 115,
"tau0_total": 115,
"tau_ge1": 11
},
"calibration": "PASS_FG_CALIBRATION tied_min=11/12 cex_min_1=18/19 mp=9/16 chain=22 reach=0/12,8/19",
"cheap": {
"below_threshold": 0,
"falsifiers": 0,
"gap1_witnessed": 452,
"gap2_potential": 70,
"gap2_witnessed": 38,
"min_named_lo_ratio": 0.7143,
"mp_below_threshold": 0,
"records": 1638,
"trivial_gap0": 946,
"witnesses_replayed": 1384
},
"deep": {
"gap2_open_labels": [
"tied_min|0,1,2,3,4,5,6,7,8,9,10",
"tied_min|0,1,2,3,4,5,6,7,8,9,11",
"tied_min|0,1,2,3,4,5,6,7,8,10,11",
"tied_min|0,1,2,3,4,5,6,7,9,10,11",
"tied_min|0,1,2,3,4,5,6,8,9,10,11",
"tied_min|0,1,2,3,4,5,7,8,9,10,11",
"tied_min|0,1,2,3,4,6,7,8,9,10,11",
"tied_min|0,1,2,3,5,6,7,8,9,10,11",
"tied_min|0,1,2,4,5,6,7,8,9,10,11",
"tied_min|0,1,3,4,5,6,7,8,9,10,11",
"tied_min|0,2,3,4,5,6,7,8,9,10,11",
"tied_min|1,2,3,4,5,6,7,8,9,10,11"
],
"gap2_open_scan_only": 12,
"gap2_stored": 5,
"gap_named_proven": 17,
"gap_named_proven_max": 1,
"records": 113,
"reproduced": 24
},
"digest": "a4525ee97862ba34",
"package": "research/fstar-family-gap-v711-seed3e3478d8",
"predecessor_pin_digest": "9b78dfe85f2cd5a08aa2ebb31d814a3416ca55266e5f109121a5a00324136364",
"predecessor_pins": "predecessor/PREDECESSOR-PINS.json",
"receipts": {
"deep-priorities.json": "48ff78484369de0b657f4196581b3cf2c74aa24aab51d38dd3315db7e7d74c7b",
"receipt-cex_min_1-s10-cheap.json": "f9c9fea9edbdd5aa2041e28efe8f23d309f4b0e1108a3dfb977d197a1aeef7b7",
"receipt-cex_min_1-s10-deep.json": "e8ab3a48245e6359981cec546fc58d77c6d475233c1c2e884a79917063bf5ce3",
"receipt-cex_min_1-s11-cheap.json": "8bad12896a00bb4ac6bc9c720d0af41c24e4e5d64d14e9a997aed426a1447557",
"receipt-cex_min_1-s11-deep.json": "90300ac849aad2fc63a279ac4ce5785346fdb869e39f532f1a58b5cff0efc7ce",
"receipt-cex_min_1-s7-cheap.json": "bc0aaa57b285245790e7671bea6dd84d1c3cbb78e98995de79737539d63cd542",
"receipt-cex_min_1-s7-deep.json": "f51b58c4accbcada384d87b1beaef24bfcd7269d55b6ee0497c68c89cddd0d8d",
"receipt-cex_min_1-s8-cheap.json": "b9aa1d86d48597f48ec88dd87fea59080b47bbd85132d48609d1ad1e3937adf5",
"receipt-cex_min_1-s8-deep.json": "a44de741e60f646590ac9d61f895e4f886d94f9656715f6b5713c6cb25aed037",
"receipt-cex_min_1-s9-cheap.json": "e389b1b7d2061b8a72ca7a9c1fcd647207ff1204f67008a1820020c82ea12505",
"receipt-cex_min_1-s9-deep.json": "acab3e324c33cab21af8968cb90f17431b4a1eb391659e6e6784813c6748422d",
"receipt-supplement-settle-named.json": "4168af7a78828d69e628e4b61f6715225f237749ffc3c801c7b58a9714043c1d",
"receipt-tied_min-s10-cheap.json": "b53069652719dbe71c296444c21e9c3cdfc052ed86bc364483b1a4365c118a00",
"receipt-tied_min-s10-deep.json": "acad91c6a7eeac76fb000a4b3b79a112c817f450fbda47caa777fb6f840790c4",
"receipt-tied_min-s11-cheap.json": "e85c76cf6a41c9a6a05cf6f43c965b83f9ea233f61581d950c420cb65550ef59",
"receipt-tied_min-s11-deep.json": "78376e6c86d9571bd834173561e5e8f7e8163572d8fe578e852bed12cec51ddf",
"receipt-tied_min-s7-cheap.json": "7ec3314209628b38e5c09d31da0b7c367b007e4bea561020e8bfff4fcbfa82b9",
"receipt-tied_min-s7-deep.json": "4490c68864ccace776b15a5dcd376488f1596ef8751fb871a4c5adeeac79690f",
"receipt-tied_min-s8-cheap.json": "83590f5cd6c57d92c4ba7e7b71608b0376ba9b772135dddd48fa455101d6bedd",
"receipt-tied_min-s8-deep.json": "077aa377b42ed5ce5b440bbf482b9efed6d608703f1b266535b6802671895d55",
"receipt-tied_min-s9-cheap.json": "042269e7716b9a9f6d5b6fbd29aac608042fa4c5e52484ca7b99eb521cc35149",
"receipt-tied_min-s9-deep.json": "6781995b3c23c9167f72d7a370b39cbc74e2df220294ccfadac45710075c8bd8"
},
"task": "KB5h: the remaining search space of F-star's family gap - v = 7..11 census and the box-completeness attack",
"verdict": {
"box_completeness": "NOT PROVEN at general v; NOT REFUTED. box = cert on all 113 deep records (exact or ceiling/in-box), both fixtures (PR 2914: 11/11, 18/18), all 21 PR 2914 exact records, and all 11 tau >= 1 synthetic instances; every recorded attaining witness is box-valued. tau >= 1 hypothesis PROVEN necessary: explicit v = 2 exact 3-total decoder P = [[1,0,1],[2,1,0]], Q = [[1,0,0],[1,0,1]] (M = [[1,2],[2,2]], tau = (1,0)) has cert = 2 > box = 1; on the 115 tau = 0-line synthetic instances box = #{t : tau(t) >= 1} exactly (CHECKED pattern). Lemma BPP (PROVEN) pins the projection parity obstruction.",
"enumeration": "CHECKED (receipts + independent witness replay): 1638 sub-decoder records at v = 7..11 (tied_min complete at v = 9..11, strided at v = 7..8; cex_min_1 strided), 113 deep records, 126 synthetic instances. Falsifier criterion armed everywhere and PROVEN inoperative on the domain: named_lo = max(MP, reach) >= floor(2v/3) on all 1638 records (min 5/7), and each named_lo is a replayed certificate value, so the chain cost >= cert >= named_lo >= threshold rules out any admissible B below threshold. FIRST gap-2-or-more instance below v = 12 FOUND at v = 7: cex_min_1|0,1,2,5,6,8,15 (cert = 7 = v exact, MP = 5 exact, gap vs named_lo = 2 PROVEN); 22 such records. Family gap: first nonzero below v = 12 is gap_named = 1 PROVEN exact at v = 7 (tied_min|0,1,2,5,6,8,10 and tied_min|2,3,4,7,9,10,11: named = 6 exact, cert = 7 exact). gap_named = 2 below v = 12 EXCLUDED on every enumerated record except the 12 tied_min v = 11 sub-decoders (scan-only named, Lemma MX product 1977326743 - the exact obstruction; gap there is in {0,1,2}). The minimal PROVEN gap_named = 2 instance remains tied_min at v = 12 (PR 2914 record). Scan pitfall quantified: on 3 of 10 settled records the seeded 20k-iteration MX scan under-reported named by 1..2 (8 -> 10 exact on the v = 10 candidate).",
"matched_pivot": "DEMOTED (retained, no new evidence): MP strictly weaker than cert on the fixtures (9 < 11, 16 < 18); MP >= floor(2v/3) witnessed but not proved; MP alone does not meet the threshold on every record (mp_below_threshold counts them - the reach rung carries the threshold there)."
}
}
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