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Conditional κ = 0.001674137810105185: X54 slot on the seven-slot k8 word with the exact T37 owner optimum #1157

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Merged
Mister-Meeseeks merged 2 commits into from
Oct 16, 2026
Merged

Conditional κ = 0.001674137810105185: X54 slot on the seven-slot k8 word with the exact T37 owner optimum #1157

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a007dc2
Prove and attain the fixed R480 all-replica owner optimum
aliromman Oct 13, 2026
c5647ae
Conditional kappa 0.001674137810105185: X54 slot on the seven-slot k8…
Oct 13, 2026
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122 changes: 122 additions & 0 deletions research/k8-x54-t37/CERTIFICATE.json
View file
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Original file line number Diff line number Diff line change
@@ -0,0 +1,122 @@
{
"replicas": 37,
"width_prices": {
"4": -1,
"5": -20,
"7": -8,
"8": -2,
"9": 4
},
"capacity_bonuses": {
"8": 2,
"16": 4,
"32": 8,
"48": -13
},
"packing": [
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"capacity": 8,
"width_counts": [
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],
"bins": 24864
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{
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],
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{
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],
"bins": 9394
},
{
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],
"bins": 3876
},
{
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],
"bins": 298
},
{
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"bins": 10656
},
{
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},
{
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"bins": 11302
},
{
"capacity": 48,
"width_counts": [
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0,
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],
"bins": 5274
}
],
"root_interval": [
"0.001676945247549584231285",
"0.001676945247549584231286"
],
"kappa_grid": "0.001674137810105185"
}
218 changes: 218 additions & 0 deletions research/k8-x54-t37/CODE-DERIVATION.json
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Original file line number Diff line number Diff line change
@@ -0,0 +1,218 @@
{
"emit_allcold.py": {
"source_sha256": "354367e1fd6185a67b04f4268bcae4d502e47b18cb2131e247f5bcab5b3a769e",
"derived_sha256": "3219e0706d497a2e6b595cec0a0d5bdbfbd1d991bf70136762eada44126a9ac1",
"edits": [
{
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"after": "==333",
"count": 3
},
{
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"after": "T=37;",
"count": 1
},
{
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"after": "==11840",
"count": 1
},
{
"before": "deficit=5120",
"after": "deficit=11840",
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}
]
},
"audit_allcold.py": {
"source_sha256": "1467a2acb654e62552c69fb9a7c4c85f70a02120881d222313865058ab71a6cc",
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{
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},
{
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"count": 2
},
{
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"count": 1
},
{
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]
},
"assemble.py": {
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"derived_sha256": "23e6b2301cd3d2f3556e5f0290eeeb2e52a5a8128f4e892b3bd4e98dca910d3a",
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{
"before": "==144*R",
"after": "==333*R",
"count": 1
},
{
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"after": "invoice['bridge_sweeps']==333",
"count": 1
},
{
"before": "data_and_owner_families=14336",
"after": "data_and_owner_families=33152",
"count": 1
},
{
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"after": "len(calls)==333",
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},
{
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},
{
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},
{
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},
{
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"after": "2*112*333,4*112*37",
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},
{
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"after": "4*112*37*9+2*112*37*9+2*333*R",
"count": 1
},
{
"before": "(144*invoice['local_adapters']",
"after": "(333*invoice['local_adapters']",
"count": 1
},
{
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"after": "invoice['charged_prefix_bits']==1024",
"count": 1
},
{
"before": "invoice['row_prefix_extra']==1024",
"after": "invoice['row_prefix_extra']==2048",
"count": 1
},
{
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"after": "+37+333+333+4",
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},
{
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{
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},
{
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"after": "(4+1024)",
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},
{
"before": "two independent bank groups, each with R0=504 helpers; restored private workspace is shared",
"after": "five bank groups with 8,8,8,8,5 active lanes and R0=504 helpers; shared private work is restored",
"count": 1
},
{
"before": "Conditional native exact-complex witness after complete conservative admission, moment and outer checks; PR559 exact-cover recurrence correction only, bit bad-residue surcharge and H1-H5 retained. The new source-branch gauge and retired-basis completion, the gauge44-barch U8 local word and all 72 cold helper ends, and explicit all144 whole-owner dispatch with a two-copy remainder trade are composed with the cited unchanged merged PR589 bit supplier (PR555 punctured R439 word; derived bit deficit T(2Kv-L*cst)), replacing the PR543 supplier of PR635; This is a new T16 composition of the accepted PR799 and PR589 suppliers. All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape and analytic transfer remain assumptions. No unconditional theorem or full Lean certification.",
"after": "Conditional R480 seven-slot k8 construction with 37 replicas. The owner map attains the fixed-inventory bin bound. The full conservative invoice, native moment correction, PR589 bit surcharge and 47 outer inequalities are checked. Local admission and all-size/compiler, mutable-source, whole-call hosting, precision/tape, exact-recovery, analytic-transfer and bit H1-H5 assumptions remain.",
"count": 1
}
]
},
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"derived_sha256": "29ba6742d899d2318a96745c8ec21de06ba3968d4641c3400a15bc714e0d7f9e",
"edits": [
{
"before": "1 + 37 + 144 + 144 + 4",
"after": "1 + 37 + 333 + 333 + 4",
"count": 1
}
]
},
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"derived_sha256": "e9132a9d195c66123f2747a17f7ef404b4d1e3ef6263ab4c28c983a052cf10bd",
"edits": [
{
"before": "{'gauge44':144}",
"after": "{'gauge44':333}",
"count": 1
}
]
},
"invoice_allcold.py": {
"source_sha256": "71eb57514e28ced97251e0507105f654f59885ec4d40486a780bf166098858a8",
"derived_sha256": "e97c74d1ccfb0b0e26260e65bb780fa0103f4c716647e238f943a2e840a1f566",
"edits": [
{
"before": "stages,replicas,blocks_per_stream=9,16,4",
"after": "stages,replicas,blocks_per_stream=9,37,4",
"count": 1
},
{
"before": "==5120",
"after": "==11840",
"count": 1
},
{
"before": "payload=512",
"after": "payload=1024",
"count": 1
},
{
"before": "previous['charged_prefix_bits']==payload",
"after": "previous['charged_prefix_bits']==512",
"count": 1
},
{
"before": "all 144 invocation and 144 bridge sweeps",
"after": "all 333 invocation and 333 bridge sweeps",
"count": 1
},
{
"before": "All three providers use fresh hash-bound independent all-column/frame/phase/normalization admission.",
"after": "The fixed provider uses fresh hash-bound independent all-column/frame/phase/normalization admission.",
"count": 1
},
{
"before": "take maximum local scalar/Horner prefix over all three providers and orientations.",
"after": "take the maximum local scalar/Horner prefix over both orientations of the fixed provider.",
"count": 1
}
]
}
}
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