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Merged
Mister-Meeseeks merged 1 commit into from
Oct 13, 2026
Merged

Scoped negative result: five-port quadratic decoder cost ceiling (no new kappa) #958

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211 changes: 211 additions & 0 deletions research/five-port-quadratic-decoder/CERTIFICATE.json
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{
"schema": "five-port-quadratic-certificate-v1",
"base_commit": "47481c89fd30a43f8f882eb4b391e89c29273fd0",
"witness_sha256": "d646efe099b20098fe02f9249cb8318ba2cdf4f50ef26dc54a8b2577567d2f28",
"source_sha256": {
"sources/pr231-README.md": "2dc89289d1d979aec6709b8c55a2af7cd39d97297bc20fb94adc7d4cdf867cd1",
"sources/format-axioms-README.md": "0fa0d6b2df96ddc06b876c41c5fa8d2335b97f36bc8f17d1371296d23199c263",
"sources/selected-result-base.json": "41fb066ff0f43ce472323195e9088d6d888715c13c54eae7b42e357ed5bfc726",
"sources/pr446-PROOF.md": "7a8c3bab633c08e7d96297dec9f9e7ed68d6bd0e076b73310c7d6b08a16df017"
},
"prime": 65521,
"ranks": [
{
"p": 5,
"kind": "corrector",
"rank_lower": 15,
"determinant_mod_prime": 64590
},
{
"p": 5,
"kind": "star",
"rank_lower": 11,
"determinant_mod_prime": 7200
},
{
"p": 6,
"kind": "corrector",
"rank_lower": 50,
"determinant_mod_prime": 39381
},
{
"p": 6,
"kind": "star",
"rank_lower": 35,
"determinant_mod_prime": 16722
},
{
"p": 7,
"kind": "corrector",
"rank_lower": 83,
"determinant_mod_prime": 45089
},
{
"p": 7,
"kind": "star",
"rank_lower": 60,
"determinant_mod_prime": 48334
},
{
"p": 8,
"kind": "corrector",
"rank_lower": 111,
"determinant_mod_prime": 47175
},
{
"p": 8,
"kind": "star",
"rank_lower": 84,
"determinant_mod_prime": 40322
},
{
"p": 9,
"kind": "corrector",
"rank_lower": 143,
"determinant_mod_prime": 15656
},
{
"p": 9,
"kind": "star",
"rank_lower": 112,
"determinant_mod_prime": 42257
},
{
"p": 10,
"kind": "corrector",
"rank_lower": 179,
"determinant_mod_prime": 14223
},
{
"p": 10,
"kind": "star",
"rank_lower": 144,
"determinant_mod_prime": 38013
},
{
"p": 11,
"kind": "corrector",
"rank_lower": 219,
"determinant_mod_prime": 57920
},
{
"p": 11,
"kind": "star",
"rank_lower": 170,
"determinant_mod_prime": 40517
},
{
"p": 12,
"kind": "corrector",
"rank_lower": 263,
"determinant_mod_prime": 31288
},
{
"p": 12,
"kind": "star",
"rank_lower": 210,
"determinant_mod_prime": 37917
},
{
"p": 13,
"kind": "corrector",
"rank_lower": 311,
"determinant_mod_prime": 2988
}
],
"algebra": {
"literal_decoder_pairs": 37888,
"parity_clique_size": 16,
"affine_label_span_upper": 6,
"logarithm_partial_sum": "3897967/3548160",
"logarithm_lower": "549/500"
},
"finite_bounds": [
{
"p": 5,
"ports": 32,
"active_rank_lower": 15,
"star_rank_lower": 11,
"copy_charge_lower": 110,
"positive_deficit_possible": false
},
{
"p": 6,
"ports": 192,
"active_rank_lower": 50,
"star_rank_lower": 35,
"copy_charge_lower": 420,
"positive_deficit_possible": false
},
{
"p": 7,
"ports": 672,
"active_rank_lower": 83,
"star_rank_lower": 60,
"copy_charge_lower": 840,
"positive_deficit_possible": false
},
{
"p": 8,
"ports": 1792,
"active_rank_lower": 111,
"star_rank_lower": 84,
"copy_charge_lower": 1344,
"positive_deficit_possible": true,
"saving_upper": "125/121878"
},
{
"p": 9,
"ports": 4032,
"active_rank_lower": 143,
"star_rank_lower": 112,
"copy_charge_lower": 2016,
"positive_deficit_possible": true,
"saving_upper": "125/78507"
},
{
"p": 10,
"ports": 8064,
"active_rank_lower": 179,
"star_rank_lower": 144,
"copy_charge_lower": 2880,
"positive_deficit_possible": true,
"saving_upper": "125/76433"
},
{
"p": 11,
"ports": 14784,
"active_rank_lower": 219,
"star_rank_lower": 170,
"copy_charge_lower": 3740,
"positive_deficit_possible": true,
"saving_upper": "31375/20198808"
},
{
"p": 12,
"ports": 25344,
"active_rank_lower": 263,
"star_rank_lower": 210,
"copy_charge_lower": 5040,
"positive_deficit_possible": true,
"saving_upper": "5875/4235352"
}
],
"all_p_ge_13_tail_upper": "250/170739",
"supplier_saving_strict_upper": "125/76433",
"selected_kappa_at_base": "1661957774647029/1000000000000000000",
"strict_gap": "2028418589596367557/76433000000000000000000",
"stage_scope": "every integer s >= 3 under PROOF.md accounting premises",
"negative_controls": [
"duplicate minor row",
"self substituted for corrector",
"false determinant residue",
"invalid paired-port label",
"reader outside copied star",
"invoice rank differs from witness",
"unproved logarithm bound",
"linear kernel rejected at overlap three",
"singular matrix detected by elimination"
],
"new_kappa_claim": false
}
47 changes: 47 additions & 0 deletions research/five-port-quadratic-decoder/CLAIM.json
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{
"track": "structural decoder research",
"assignment_seed": 40,
"randomness": "secrets.randbelow(100), operating-system CSPRNG; drawn once at 2026-10-13T14:01:22Z",
"base_commit": "47481c89fd30a43f8f882eb4b391e89c29273fd0",
"started_utc": "2026-10-13T14:01:22Z",
"claim_utc": "2026-10-13T14:10:44.190873+00:00",
"expected_finish_utc": "2026-10-13T14:51:22Z",
"time_budget_minutes": 50,
"verification_reserve_minutes": 12.5,
"coordination": "No pinned issue exists; local claim per sprint instructions. No reservation issue opened.",
"candidates": [
{
"task": "Five-port level-one star decoder: minimum polynomial degree, natural quadratic pairing and complete optimistic copy/frame budget",
"chosen": true,
"reason": "PR231 explicitly leaves k=5 geometry and complete pricing open; distinct from higher proper-star information thresholds."
},
{
"task": "Power-of-two proper-star decoder through asymmetric punctures",
"chosen": false,
"reason": "PR669 already gives uniform higher-target results; PR725/732/747/772 overlap."
},
{
"task": "Stronger Gaussian decoder floor using weighted clique certificates",
"chosen": false,
"reason": "PR868 closes all nonempty cliques at 40; extending this finite search would duplicate a closed class."
}
],
"object": "Unpunctured signed five-ports on p coordinate pairs, scalar level-one stars and odd-overlap correction; natural symmetric quadratic kernel G(S,T)=2(|S intersect T|-1)(|S intersect T|-3).",
"hypothesis": "The degree-two lift repairs the linear-label obstruction, but its exact star-copy ranks and mandatory active climbs alone cannot beat the selected saving, even if every other expense is zero.",
"method": "Character decomposition over sign flips and exact rational subset-incidence eigenspaces; literal Gram/rank controls at small p; rational optimistic budget with all-p tail.",
"seed_diversification": "The two next odd-port candidates are k=5 and k=7; 40 mod 2 chooses k=5. The seed also fixes finite witness order. This is a new quadratic geometry class, not a re-run of E8 puncture search.",
"expected_deliverable": "Scoped negative-result research note, written rank proof, exact certificate and standalone verifier with adverse controls; no new kappa, supplier or selected-frontier edit.",
"scope_exclusions": [
"Other asymmetric/non-polynomial decoder geometries",
"Different copy supports or readers",
"Physical all-size implementation",
"Formal proof of multiplication"
],
"result": {
"status": "completed research note / scoped negative result; ready for external review",
"statement": "Natural five-port quadratic Gram with separate stars and fixed-window accounting has supplier saving < 125/76433 for all p>=5 and s>=3; no new kappa.",
"link": "https://github.com/RossRichardson/integer-mult-bounds/blob/research/structural-decoder-seed40/research/five-port-quadratic-decoder/README.md",
"verification": "17 minors in two implementations, nine primary controls, six package tests, canonical Git-blob export with identical receipts, selected-record integrity",
"completed_utc": "2026-10-13T14:36:20.963267+00:00"
}
}
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