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Mister-Meeseeks merged 1 commit into from
Oct 14, 2026
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Research theorem: sharp scratch-dependent call bound for dirty echoes #784

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158 changes: 158 additions & 0 deletions research/dirty-echo-space-budget/CLAIM.json
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{
"track": "recursive interfaces",
"assignment_seed": 50,
"seed_source": "Python secrets.randbelow(100), operating-system randomness",
"started_at": "2026-10-13T00:53:05.729600-04:00",
"claimed_at": "2026-10-13T00:55:30.836858-04:00",
"base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
"object": "Ordered all-dirty product-shear trees formed from the PR673 multiway echo, under a caller-specified bound on simultaneously borrowed arrays.",
"method": "Exact dynamic programming over arbitrary positive contiguous child partitions and node fanouts, with the complete 2/4/2 child-call multiplicities and k-1 local arrays. Independent small-domain enumeration and symbolic noncommutative restoration checks.",
"seed_diversification": "The main generic instance has 50 ordered factors. The method changes the search class, rather than repeating balanced ternary placement.",
"domain": "Factor counts 1 through 64, scratch budgets 0 through 8; independent exhaustive tree enumeration in a smaller declared domain.",
"stopping_rule": "One deterministic optimum table for this grammar and budget domain, an executable schedule, complete cost recurrence, and negative controls; no search for a new kappa.",
"expected_deliverable": "Scoped interface construction and exact space/call tradeoff certificate; no multiplication bound claim.",
"expected_finish": "2026-10-13T01:53:05-04:00",
"time_allocation": "60-minute target; orientation at most 12 minutes, final 15 minutes reserved for verification and handoff.",
"coordination": {
"pinned_issues": [],
"open_issue_numbers": [
650
],
"claim_location": "local, because no pinned sprint coordination issue exists",
"open_prs_inspected": 544,
"checked_through_pr": 725
},
"candidate_tasks": [
{
"task": "Optimal all-dirty echo trees under a fixed simultaneous scratch budget",
"decision": "selected; arbitrary partitions and mixed fanouts are outside the balanced family covered by PR689"
},
{
"task": "Clean root checkpoint with dirty descendants",
"decision": "not selected; PR714 already supplies this construction and root optimum"
},
{
"task": "Spectral split with a phase-restored dirty complement",
"decision": "not selected; PR665 already gives the complete unfavorable boundary bill"
}
],
"overlap_heads": {
"628": "0768f97d06c623b8211e651543c66135796b62bf",
"673": "156f259b99723468cfdd2b5d47d0ba894f09bea7",
"689": "0dedef12f05f9a06faf9d4e1c8b1462c0e3bff3a",
"714": "efad8a40094ab453c0525efef0b0eff2a5d8b850"
},
"predecessor_scope": {
"628": "binary dirty inverse and rounded leaf",
"673": "multiway echo identity, exact restoration and general error bound",
"689": "minimum among recursively balanced ternary splits, uniform leaf costs",
"714": "one clean root checkpoint with balanced binary dirty children"
},
"status": "completed",
"completed_at": "2026-10-13T01:24:15.671435-04:00",
"final_overlap": {
"checked_at": "2026-10-13T01:22:02.586894-04:00",
"open_prs": 586,
"highest_pr": 767,
"related": [
{
"number": 673,
"title": "Research: dirty echo, alias repair, and fully priced bit-sharing gates",
"headRefOid": "b3917936aafbd0d680a954a86e25c4ce7e28a9f9",
"updatedAt": "2026-10-13T05:17:11Z"
},
{
"number": 758,
"title": "Research: higher-arity dirty echoes use 152 calls at five-array cap (no new kappa)",
"headRefOid": "a164f06263e438ead570b169e5b7103aa45bf228",
"updatedAt": "2026-10-13T05:10:54Z"
},
{
"number": 744,
"title": "Independent verification: fixed-space ternary echo minima and rounded leaves",
"headRefOid": "302383e0c1ec71c50860362d3f394f85664c2445",
"updatedAt": "2026-10-13T05:10:23Z"
},
{
"number": 730,
"title": "Research: optimize ordered dirty echoes at fixed scratch (no new kappa)",
"headRefOid": "d222e348179cc02a54d6d26dbd2838944f62c6e5",
"updatedAt": "2026-10-13T04:57:06Z"
},
{
"number": 714,
"title": "Research: optimal clean root checkpoint saves 25\u201340% of binary product-shear calls",
"headRefOid": "efad8a40094ab453c0525efef0b0eff2a5d8b850",
"updatedAt": "2026-10-13T04:40:45Z"
},
{
"number": 689,
"title": "Research: minimize balanced ternary dirty echo calls at fixed scratch",
"headRefOid": "0dedef12f05f9a06faf9d4e1c8b1462c0e3bff3a",
"updatedAt": "2026-10-13T04:14:38Z"
},
{
"number": 525,
"title": "Kernel102 checkpoint: full cold reconstruction and exact fixed-word ceiling",
"headRefOid": "71acd0c35ee81de848316b3f2b4c3bd15b219c51",
"updatedAt": "2026-10-12T00:49:30Z"
},
{
"number": 277,
"title": "Verified construction checkpoint: conditional \u03ba = 7.110455476244e-4",
"headRefOid": "c2f07d311bfdad0d89bf961e4da133ee97bb78de",
"updatedAt": "2026-10-10T04:22:16Z"
},
{
"number": 135,
"title": "Paired physical scratch reuse: candidate conditional \u03ba = 3.62108222954e-4 (+4.02% vs #134)",
"headRefOid": "2bb675bba25771ae1cafd4ff7804b9bc094dd415",
"updatedAt": "2026-10-09T03:15:24Z"
},
{
"number": 131,
"title": "Physical frames and scratch reuse on Cayley covers: conditional \u03ba = 3.32205398986e-4",
"headRefOid": "3acf2f944abd069301600ce468f16f1dd8f1f9e4",
"updatedAt": "2026-10-09T02:52:20Z"
},
{
"number": 129,
"title": "Shared bit cores and gauged scratch reuse: conditional \u03ba = 1.29186205798e-4",
"headRefOid": "59fade1f7790db61a56b69e0d3974c0a97b41f4d",
"updatedAt": "2026-10-09T02:50:37Z"
},
{
"number": 90,
"title": "Clarify current review checkpoint and published release",
"headRefOid": "8e0442641696b4c284bf7fbb4f2c97dccf24ea6c",
"updatedAt": "2026-10-08T21:24:49Z"
}
],
"pinned_coordination_issues": [],
"main_head": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
"pr673_consumed_files_unchanged_at_latest_head": "b3917936aafbd0d680a954a86e25c4ce7e28a9f9"
},
"concurrent_contributions": {
"730": {
"head": "d222e348179cc02a54d6d26dbd2838944f62c6e5",
"credit": "unbalanced mixed binary/ternary weighted optimization"
},
"744": {
"head": "302383e0c1ec71c50860362d3f394f85664c2445",
"credit": "independent strict-ternary census and rounded-leaf verification"
},
"758": {
"head": "a164f06263e438ead570b169e5b7103aa45bf228",
"credit": "all-arity weighted optimization; actual planner and words independently compared at nine unit-price instances"
}
},
"result": {
"status": "research note and independent verification; no new kappa",
"theorem": "Every ordered echo tree using at most s dirty arrays has N >= 2^(s+1)*n - 4^s; equality is attained for s>=2 and 3*2^(s-2)<=n<=2^s.",
"example": "F(50,6)=2304, versus 2752 in the pinned balanced binary schedule, with no additional array.",
"distinctness": "Concurrent PR758 already supplies all-arity optimization. The distinct result is the analytic scratch-dependent bound and explicit attaining family; optimizer minima are independent corroboration.",
"complete_search_domain": "All 576 cells n=1..64, s=0..8; 255 feasible witnesses; exact recurrence, no stochastic cutoff.",
"verification": "Python 3.11.15 and 3.14.7; all final certificate fields, relocation and seven artifact controls pass. make verify completed seven historical groups then stopped at inherited missing SymPy.",
"link": "https://github.com/AlexS-scale/integer-mult-bounds/tree/research/dirty-echo-space-budget-seed50/research/dirty-echo-space-budget"
}
}
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