{"as_of":"2026-08-16T17:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7f75768e9898cd813559500adcc2ba21f4544bc58c8f805bd6ebd5be3527fad7","coverage":[{"denominator":10,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T09:55:39.470243Z","state":"measured"},{"denominator":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.29291/citation-record","integrity":"/paper/2607.29291/integrity","json":"/paper/2607.29291/citation-record.json","paper":"/paper/2607.29291"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T09:55:38.750444Z","title":null,"venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2607.29291","last_updated":"2026-07-31T11:09:22Z","snapshot_observed_at":"2026-08-06T10:03:14.816469Z","submitted_at":"2026-07-31T11:09:22Z","title":"SAT Certificates for the Matrix-Multiplication Challenges over F2: All Ten `Expected-UNSAT` Instances Are Satisfiable, and a Type-3-Free Rank-23 Scheme","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-03T09:55:38.750444Z"},"links":{"citing_paper":"/paper/2607.29291"},"observation_digest":"sha256:3d7dfd6650401caa09037e9b7a3fd6692fd0107d070bfb355a70877d6ebc79d7","observation_id":"7abc8a36-1fca-4e75-b02b-8c89a450d99d","resolution":{"observed_at":"2026-08-03T09:55:38.750444Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1108.2830","last_updated":"2011-08-19T09:02:22Z","snapshot_observed_at":"2026-08-15T04:38:19.274747Z","submitted_at":"2011-08-14T00:23:37Z","title":"A New General-Purpose Method to Multiply 3x3 Matrices Using Only 23 Multiplications","version":3},"cited_work":{"arxiv_id":"1108.2830","doi":"10.48550/arxiv.1108.2830","metadata_source":"pith","pith_arxiv_id":"1108.2830","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"A New General-Purpose Method to Multiply 3x3 Matrices Using Only 23 Multiplications","venue":"cs.SC","work_id":"1c597d0a-c6ba-4135-8b5b-94a68375f7b8","year":2011},"citing_paper":{"arxiv_id":"2607.29291","last_updated":"2026-07-31T11:09:22Z","snapshot_observed_at":"2026-08-06T10:03:14.816469Z","submitted_at":"2026-07-31T11:09:22Z","title":"SAT Certificates for the Matrix-Multiplication Challenges over F2: All Ten `Expected-UNSAT` Instances Are Satisfiable, and a Type-3-Free Rank-23 Scheme","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-03T09:55:38.844999Z"},"links":{"cited_paper":"/paper/1108.2830","citing_paper":"/paper/2607.29291"},"observation_digest":"sha256:b0e850bea768f5d8c5dabd4a805ee617756651b0d5cfce8f68d4ce4a482e04ea","observation_id":"690d021b-47b7-41ef-a151-e8d04d16bbe3","resolution":{"observed_at":"2026-08-03T09:59:02.132948Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T09:55:38.914682Z","title":"de Groote","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2607.29291","last_updated":"2026-07-31T11:09:22Z","snapshot_observed_at":"2026-08-06T10:03:14.816469Z","submitted_at":"2026-07-31T11:09:22Z","title":"SAT Certificates for the Matrix-Multiplication Challenges over F2: All Ten `Expected-UNSAT` Instances Are Satisfiable, and a Type-3-Free Rank-23 Scheme","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-03T09:55:38.914682Z"},"links":{"citing_paper":"/paper/2607.29291"},"observation_digest":"sha256:86fadc504f1fd5b8fdc6a30b46309c998065c276fe8b954ca5ba7dae7641a176","observation_id":"d55e0bc4-6fa0-44e9-83d3-709bff5bdea4","resolution":{"observed_at":"2026-08-03T09:55:38.914682Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-030-24258-9_10","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Lecture notes in computer science","work_id":"1e2b2090-faf9-4431-aab0-6e95c706ecb8","year":2019},"citing_paper":{"arxiv_id":"2607.29291","last_updated":"2026-07-31T11:09:22Z","snapshot_observed_at":"2026-08-06T10:03:14.816469Z","submitted_at":"2026-07-31T11:09:22Z","title":"SAT Certificates for the Matrix-Multiplication Challenges over F2: All Ten `Expected-UNSAT` Instances Are Satisfiable, and a Type-3-Free Rank-23 Scheme","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-03T09:55:38.975594Z"},"links":{"citing_paper":"/paper/2607.29291"},"observation_digest":"sha256:bceda3ba13664dc6f09e0d237864c4be89fbd0dddf080edc22f2f115c1de3f3a","observation_id":"b0a53209-b759-46f2-bcd5-ef25649fcaff","resolution":{"observed_at":"2026-08-03T09:59:01.884938Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T09:55:39.052297Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.29291","last_updated":"2026-07-31T11:09:22Z","snapshot_observed_at":"2026-08-06T10:03:14.816469Z","submitted_at":"2026-07-31T11:09:22Z","title":"SAT Certificates for the Matrix-Multiplication Challenges over F2: All Ten `Expected-UNSAT` Instances Are Satisfiable, and a Type-3-Free Rank-23 Scheme","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-03T09:55:39.052297Z"},"links":{"citing_paper":"/paper/2607.29291"},"observation_digest":"sha256:fa523c769ae2e87607b0201d6397ecac49fbccaa8a71abc50716c9f4723878ec","observation_id":"ec56f278-a4d4-4d52-bd3b-646cc79c7f9d","resolution":{"observed_at":"2026-08-03T09:55:39.052297Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jsc.2020.10.003","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Journal of Symbolic Computation","work_id":"6ef07376-6671-47ff-b9b6-59b4499992a6","year":2021},"citing_paper":{"arxiv_id":"2607.29291","last_updated":"2026-07-31T11:09:22Z","snapshot_observed_at":"2026-08-06T10:03:14.816469Z","submitted_at":"2026-07-31T11:09:22Z","title":"SAT Certificates for the Matrix-Multiplication Challenges over F2: All Ten `Expected-UNSAT` Instances Are Satisfiable, and a Type-3-Free Rank-23 Scheme","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-03T09:55:39.137821Z"},"links":{"citing_paper":"/paper/2607.29291"},"observation_digest":"sha256:5fbc86dffe0ce557a9f951a985719fdf429f357a83c707dbe00c2e58ccb1a0aa","observation_id":"4d1e1ba2-8eb1-496c-af36-fef62fab4b9d","resolution":{"observed_at":"2026-08-03T09:59:01.615837Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T09:55:39.229142Z","title":"Laderman","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.29291","last_updated":"2026-07-31T11:09:22Z","snapshot_observed_at":"2026-08-06T10:03:14.816469Z","submitted_at":"2026-07-31T11:09:22Z","title":"SAT Certificates for the Matrix-Multiplication Challenges over F2: All Ten `Expected-UNSAT` Instances Are Satisfiable, and a Type-3-Free Rank-23 Scheme","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-03T09:55:39.229142Z"},"links":{"citing_paper":"/paper/2607.29291"},"observation_digest":"sha256:def441e28c55770daccf04390269e4798264d0b9ce0d65348c97282fcf2f6f64","observation_id":"315fc1d4-644d-4835-afb9-1c49c33fbb9b","resolution":{"observed_at":"2026-08-03T09:55:39.229142Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T09:55:39.313349Z","title":"A rank 23 algorithm for multiplying \\(3 3\\) matrices with an arithmetic complexity of 59","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.29291","last_updated":"2026-07-31T11:09:22Z","snapshot_observed_at":"2026-08-06T10:03:14.816469Z","submitted_at":"2026-07-31T11:09:22Z","title":"SAT Certificates for the Matrix-Multiplication Challenges over F2: All Ten `Expected-UNSAT` Instances Are Satisfiable, and a Type-3-Free Rank-23 Scheme","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-03T09:55:39.313349Z"},"links":{"citing_paper":"/paper/2607.29291"},"observation_digest":"sha256:3f7fd5ec47a0ffd8302870817d088164e3673b578d9c008e0b61f42aba72c230","observation_id":"522f90e5-3875-4a0c-8fbc-60aca2d7c699","resolution":{"observed_at":"2026-08-03T09:55:39.313349Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T09:55:39.404244Z","title":"SAT certificates for the matrix-multiplication challenges over \\( _2\\): Reproducibility artifact","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.29291","last_updated":"2026-07-31T11:09:22Z","snapshot_observed_at":"2026-08-06T10:03:14.816469Z","submitted_at":"2026-07-31T11:09:22Z","title":"SAT Certificates for the Matrix-Multiplication Challenges over F2: All Ten `Expected-UNSAT` Instances Are Satisfiable, and a Type-3-Free Rank-23 Scheme","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-03T09:55:39.404244Z"},"links":{"citing_paper":"/paper/2607.29291"},"observation_digest":"sha256:07f6d0ce5996643ef03e0d08ae30ed914992c8c724ab2ca7a28363774393af18","observation_id":"d8be3dcc-4531-4833-996c-b4ed69f21d0b","resolution":{"observed_at":"2026-08-03T09:55:39.404244Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T09:55:39.470243Z","title":null,"venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2607.29291","last_updated":"2026-07-31T11:09:22Z","snapshot_observed_at":"2026-08-06T10:03:14.816469Z","submitted_at":"2026-07-31T11:09:22Z","title":"SAT Certificates for the Matrix-Multiplication Challenges over F2: All Ten `Expected-UNSAT` Instances Are Satisfiable, and a Type-3-Free Rank-23 Scheme","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-03T09:55:39.470243Z"},"links":{"citing_paper":"/paper/2607.29291"},"observation_digest":"sha256:b4f9f6e0b4b2e707a6687a5eb8b2495123f888af5e77bbdc58e57baefaa9dcd0","observation_id":"f4f23871-4a12-432b-81bf-e768f0e9c6ec","resolution":{"observed_at":"2026-08-03T09:55:39.470243Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.29291","last_updated":"2026-07-31T11:09:22Z","latest_version":1,"primary_category":"cs.SC","snapshot_observed_at":"2026-08-06T10:03:14.816469Z","submitted_at":"2026-07-31T11:09:22Z","title":"SAT Certificates for the Matrix-Multiplication Challenges over F2: All Ten `Expected-UNSAT` Instances Are Satisfiable, and a Type-3-Free Rank-23 Scheme"},"reference_resolution":{"displayed":10,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":3,"verified_fuzzy":0},"total_outbound_references":10},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2607.29291."}