{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:SZXZYZ3LHIZALJMPCNG3H4IRMM","short_pith_number":"pith:SZXZYZ3L","schema_version":"1.0","canonical_sha256":"966f9c676b3a3205a58f134db3f1116316bf7f3f9059cc6f267b0a32b750a591","source":{"kind":"arxiv","id":"2607.29291","version":1},"attestation_state":"computed","paper":{"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","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.SC","authors_text":"Nick Palladinos","submitted_at":"2026-07-31T11:09:22Z","abstract_excerpt":"The matrix-multiplication SAT benchmark of Heule, Kauers, and Seidl asks, among other tasks, for solutions of ten known-satisfiable rank-23 formulas, proofs of unsatisfiability for ten formulas expected to be unsatisfiable, and a rank-23 scheme over $\\mathbb{F}_2$ having a summand with no type-3 monomial. We give complete satisfying assignments for the 21 CNFs in the repository's top-level challenge1/, challenge2/, and challenge3/ directories at commit 150b2e2f. The principal finding is that all ten top-level Challenge-2 formulas are satisfiable. A direct audit shows that their hardcoded type-"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.29291","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.SC","submitted_at":"2026-07-31T11:09:22Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"cff47bef5131aadb7736f081c8dab0ad069cdd837a64116bf3c63e3d87a7615d","abstract_canon_sha256":"b890b79f3bf74c0f23999f164ea626c86c09ecb9db1fa913ae69716acc190779"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-03T01:23:53.500574Z","signature_b64":"71OSnTG9EP1bIY7RdQPTTgoTq+QfA+yhC39/d8NXJg/LDLsh08zbAvlnPqY0HHEUzB1WivSdBJurY/MkKx0uBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"966f9c676b3a3205a58f134db3f1116316bf7f3f9059cc6f267b0a32b750a591","last_reissued_at":"2026-08-03T01:23:53.498902Z","signature_status":"signed_v1","first_computed_at":"2026-08-03T01:23:53.498902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"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","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.SC","authors_text":"Nick Palladinos","submitted_at":"2026-07-31T11:09:22Z","abstract_excerpt":"The matrix-multiplication SAT benchmark of Heule, Kauers, and Seidl asks, among other tasks, for solutions of ten known-satisfiable rank-23 formulas, proofs of unsatisfiability for ten formulas expected to be unsatisfiable, and a rank-23 scheme over $\\mathbb{F}_2$ having a summand with no type-3 monomial. We give complete satisfying assignments for the 21 CNFs in the repository's top-level challenge1/, challenge2/, and challenge3/ directories at commit 150b2e2f. The principal finding is that all ten top-level Challenge-2 formulas are satisfiable. A direct audit shows that their hardcoded type-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.29291","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.29291/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.29291","created_at":"2026-08-03T01:23:53.499852+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.29291v1","created_at":"2026-08-03T01:23:53.499852+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.29291","created_at":"2026-08-03T01:23:53.499852+00:00"},{"alias_kind":"pith_short_12","alias_value":"SZXZYZ3LHIZA","created_at":"2026-08-03T01:23:53.499852+00:00"},{"alias_kind":"pith_short_16","alias_value":"SZXZYZ3LHIZALJMP","created_at":"2026-08-03T01:23:53.499852+00:00"},{"alias_kind":"pith_short_8","alias_value":"SZXZYZ3L","created_at":"2026-08-03T01:23:53.499852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SZXZYZ3LHIZALJMPCNG3H4IRMM","json":"https://pith.science/pith/SZXZYZ3LHIZALJMPCNG3H4IRMM.json","graph_json":"https://pith.science/api/pith-number/SZXZYZ3LHIZALJMPCNG3H4IRMM/graph.json","events_json":"https://pith.science/api/pith-number/SZXZYZ3LHIZALJMPCNG3H4IRMM/events.json","paper":"https://pith.science/paper/SZXZYZ3L"},"agent_actions":{"view_html":"https://pith.science/pith/SZXZYZ3LHIZALJMPCNG3H4IRMM","download_json":"https://pith.science/pith/SZXZYZ3LHIZALJMPCNG3H4IRMM.json","view_paper":"https://pith.science/paper/SZXZYZ3L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.29291&json=true","fetch_graph":"https://pith.science/api/pith-number/SZXZYZ3LHIZALJMPCNG3H4IRMM/graph.json","fetch_events":"https://pith.science/api/pith-number/SZXZYZ3LHIZALJMPCNG3H4IRMM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SZXZYZ3LHIZALJMPCNG3H4IRMM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SZXZYZ3LHIZALJMPCNG3H4IRMM/action/storage_attestation","attest_author":"https://pith.science/pith/SZXZYZ3LHIZALJMPCNG3H4IRMM/action/author_attestation","sign_citation":"https://pith.science/pith/SZXZYZ3LHIZALJMPCNG3H4IRMM/action/citation_signature","submit_replication":"https://pith.science/pith/SZXZYZ3LHIZALJMPCNG3H4IRMM/action/replication_record"}},"created_at":"2026-08-03T01:23:53.499852+00:00","updated_at":"2026-08-03T01:23:53.499852+00:00"}