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223 lines (223 loc) · 9.88 KB
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{
"schema_version": 1,
"problem_id": "apsp/word-ram",
"model": {
"id": "word-ram",
"version": "1",
"description": "Deterministic directed APSP with polynomially bounded integer weights and no negative cycles. Same fixed-width word RAM and quantifiers as EndStatement. Input edge-presence and weight matrices; output reachability flags and distances for every ordered pair.",
"definition_url": "https://github.com/anthropics/formal-math/blob/e1a4e6508154ea59f030480661590a9fe3018011/3sum-apsp/EndStatement.lean"
},
"score": {
"id": "time-exponent",
"version": "1",
"symbol": "alpha",
"definition": "Worst-case O(n^alpha).",
"direction": "lower-is-better",
"encoding": "rational-string",
"minimum": "0",
"maximum": "3"
},
"checked_at": "2026-10-10",
"sources": [
{
"url": "https://github.com/anthropics/formal-math/blob/e1a4e6508154ea59f030480661590a9fe3018011/3sum-apsp/EndStatement.lean",
"checked_at": "2026-10-08"
},
{
"url": "https://algol60.org/acm/097.pdf",
"checked_at": "2026-10-08"
},
{
"url": "https://github.com/anthropics/formal-math/blob/e1a4e6508154ea59f030480661590a9fe3018011/3sum-apsp/README.md",
"checked_at": "2026-10-08"
},
{
"url": "https://arxiv.org/abs/2610.06783v1",
"checked_at": "2026-10-08"
},
{
"url": "https://github.com/Swapnil-jain/threesum-derand/blob/087ece61dd9ef6108441927785b16dfda0e95284/proofs/stacked.md",
"checked_at": "2026-10-10"
}
],
"records": [
{
"id": "classical-baseline",
"kind": "baseline",
"score": "3",
"tier": "claimed",
"submitted_at": null,
"upstream_status": "not-applicable",
"upstream_status_at": "2026-10-08T21:34:39.207006Z",
"site_observed_at": "2026-10-08T21:34:39.207006Z",
"source": {
"kind": "paper",
"url": "https://doi.org/10.1145/367766.368168"
},
"spec_version": "1",
"title": "Robert W. Floyd (1962), Algorithm 97: Shortest path",
"authors": [
{
"name": "Robert W. Floyd (1962), Algorithm 97: Shortest path",
"url": "https://doi.org/10.1145/367766.368168"
}
],
"predecessors": [],
"submission_url": "https://doi.org/10.1145/367766.368168",
"artifact": {
"path": "sources/apsp-baseline.json",
"sha256": "e471e3f98e7c9a4077c837f3d764114845c4d3d63ec7adbbe0d37b97ba24463b"
},
"evidence": {
"paper_url": "https://doi.org/10.1145/367766.368168",
"theorem": null,
"certificate_path": null
},
"dependencies": []
},
{
"id": "anthropic-2026",
"kind": "improvement",
"score": "149971/50000",
"tier": "verified",
"submitted_at": "2026-10-05T17:44:29Z",
"upstream_status": "not-applicable",
"upstream_status_at": "2026-10-08T21:34:39.207006Z",
"site_observed_at": "2026-10-08T21:34:39.207006Z",
"source": {
"kind": "repo-artifact",
"url": "https://github.com/anthropics/formal-math/blob/e1a4e6508154ea59f030480661590a9fe3018011/3sum-apsp/EndStatement.lean"
},
"spec_version": "1",
"title": "Anthropic formalization; Alman and Vassilevska Williams result",
"authors": [
{
"name": "Josh Alman and Virginia Vassilevska Williams",
"url": "https://arxiv.org/abs/2610.06783"
},
{
"name": "Anthropic",
"url": "https://github.com/anthropics/formal-math"
}
],
"predecessors": [],
"submission_url": "https://github.com/anthropics/formal-math/blob/e1a4e6508154ea59f030480661590a9fe3018011/3sum-apsp/EndStatement.lean",
"artifact": {
"path": "sources/anthropic-EndStatement.lean",
"sha256": "4291e3f05781cea42f9d672ff73ceac1f6d1a0c3021038e94372fa8f7e1ad987"
},
"evidence": {
"paper_url": "https://arxiv.org/abs/2610.06783v1",
"theorem": "endStatement_theorem_22_APSP",
"certificate_path": null
},
"dependencies": [],
"source_commit": "e1a4e6508154ea59f030480661590a9fe3018011",
"rerun_status": {
"state": "passed",
"checked_at": "2026-10-08T22:12:13.857231Z",
"receipt_path": "sources/anthropic-comparator-receipt.json"
}
},
{
"id": "swapnil-jain-apsp-2026",
"kind": "improvement",
"score": "2995943/1000000",
"tier": "claimed",
"submitted_at": "2026-10-10T06:05:39Z",
"upstream_status": "not-applicable",
"upstream_status_at": "2026-10-10T09:04:13Z",
"site_observed_at": "2026-10-10T09:04:13Z",
"source": {
"kind": "repo-artifact",
"url": "https://github.com/Swapnil-jain/threesum-derand/blob/087ece61dd9ef6108441927785b16dfda0e95284/proofs/stacked.md"
},
"spec_version": "1",
"title": "Swapnil Jain deterministic APSP claim",
"authors": [
{
"name": "Swapnil Jain",
"url": "https://github.com/Swapnil-jain"
}
],
"predecessors": [
"https://arxiv.org/abs/2610.06783",
"https://github.com/qawbecrdtey/ImprovedExponents"
],
"submission_url": "https://github.com/Swapnil-jain/threesum-derand/blob/087ece61dd9ef6108441927785b16dfda0e95284/proofs/stacked.md",
"source_commit": "087ece61dd9ef6108441927785b16dfda0e95284",
"artifact": {
"path": "sources/Swapnil-jain-threesum-model-check.json",
"sha256": "6e01ec709b57163860535f9cc7c60b867102c643734ba67778ef3f2bd66d620d"
},
"evidence": {
"paper_url": "https://github.com/Swapnil-jain/threesum-derand/blob/087ece61dd9ef6108441927785b16dfda0e95284/proofs/stacked.md",
"theorem": "Theorem 1'; stacked.md Theorem A' and Corollary B'",
"certificate_path": null
},
"dependencies": [
{
"id": "written-reductions-and-cost-accounting",
"statement": "Lean checks certificate arithmetic and finite lemmas only. Reductions, cost accounting and Theorem 3 combinatorics remain written proof dependencies; no site rerun.",
"source_url": "https://github.com/Swapnil-jain/threesum-derand/blob/087ece61dd9ef6108441927785b16dfda0e95284/proofs/stacked.md",
"status": "unverified"
}
]
}
],
"record_metadata": {
"classical-baseline": {
"checked_at": "2026-10-08",
"eligible_for_record": true,
"proof_status": "Classical paper baseline; no site proof check.",
"date_precision": "Publication year only; exact submission time unknown. site_observed_at is separate.",
"source_access": "opened paper scan; DOI full text unchecked",
"publication_year": 1962,
"publication_date_precision": "year",
"publication_source_url": "https://doi.org/10.1145/367766.368168",
"upstream_tier": "claimed",
"site_tier": "claimed",
"comparison_key": "apsp/word-ram/v1"
},
"anthropic-2026": {
"checked_at": "2026-10-08",
"eligible_for_record": true,
"proof_status": "proved upstream; independent rerun passed; see rerun_status receipt",
"site_badge": false,
"source_url": "https://github.com/anthropics/formal-math/blob/e1a4e6508154ea59f030480661590a9fe3018011/3sum-apsp/EndStatement.lean",
"upstream_tier": "verified",
"site_tier": "verified",
"comparison_key": "apsp/word-ram/v1",
"publication_date_precision": "date-time",
"publication_year": 2026,
"publication_date": "2026-10-05T17:44:29Z",
"publication_source_url": "https://arxiv.org/abs/2610.06783v1",
"publication_date_role": "arXiv v1 paper submission, not formalization publication",
"date_precision": "Exact arXiv v1 submission timestamp in UTC; observation time separate."
},
"swapnil-jain-apsp-2026": {
"checked_at": "2026-10-10",
"source_url": "https://github.com/Swapnil-jain/threesum-derand/blob/087ece61dd9ef6108441927785b16dfda0e95284/proofs/stacked.md",
"repo": "Swapnil-jain/threesum-derand",
"site_badge": false,
"eligible_for_record": true,
"proof_status": "Lean checks certificate arithmetic and finite lemmas only. Reductions, cost accounting and Theorem 3 combinatorics remain written proof dependencies; no site rerun.",
"upstream_tier": "claimed",
"site_tier": "claimed",
"comparison_key": "apsp/word-ram/v1",
"comparison_status": "Deterministic worst-case algorithms for each fixed polynomial input-magnitude bound on logarithmic-word RAM. Not a randomized claim. Unlike EndStatement, the paper does not supply a fixed-width program or quantify all sufficiently large word widths in Lean. Model compatibility is an algorithmic interpretation, not a checked formal statement equivalence: polynomial-sized words can be simulated by the signed arithmetic/load/store/branch model with polylogarithmic overhead, absorbed by the explicit strict exponent margin.",
"scope": "Directed integer weights, no negative cycles, all-pairs distances. Lemmas 4.3-4.4 handle missing edges with a polynomial infinity sentinel and repeated squaring; reachability is recovered from infinity.",
"publication_date_precision": "date-time",
"publication_date": "2026-10-10T06:05:39Z",
"publication_date_role": "First README commit stating this exponent, not scientific priority",
"publication_source_url": "https://github.com/Swapnil-jain/threesum-derand/blob/584026f4e64e214a67ef0f5a5a11835dc96b8e34/README.md",
"claim_date_commit": "584026f4e64e214a67ef0f5a5a11835dc96b8e34",
"listing_status": "research-draft",
"open_race": false,
"credits": "Swapnil Jain; builds on Alman and Vassilevska Williams, ImprovedExponents, and the reductions credited in the source README.",
"license_status": "Apache-2.0; LICENSE and NOTICE retained",
"notes_url": "https://github.com/Swapnil-jain/threesum-derand/blob/087ece61dd9ef6108441927785b16dfda0e95284/proofs/stacked.md"
}
},
"updated_at": "2026-10-10T09:04:13Z"
}