{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:3HPEFGYZJTWVYDAK745PE3FOXX","short_pith_number":"pith:3HPEFGYZ","schema_version":"1.0","canonical_sha256":"d9de429b194ced5c0c0aff3af26caebdf753b4be51306aae9759cb48c261334d","source":{"kind":"arxiv","id":"2204.10881","version":2},"attestation_state":"computed","paper":{"title":"A Ihara-Bass Formula for Non-Boolean Matrices and Strong Refutations of Random CSPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LO","stat.ML"],"primary_cat":"cs.CC","authors_text":"Luca Trevisan, Tommaso d'Orsi","submitted_at":"2022-04-20T16:21:21Z","abstract_excerpt":"We define a novel notion of ``non-backtracking'' matrix associated to any symmetric matrix, and we prove a ``Ihara-Bass'' type formula for it.\n  We use this theory to prove new results on polynomial-time strong refutations of random constraint satisfaction problems with $k$ variables per constraints (k-CSPs). For a random k-CSP instance constructed out of a constraint that is satisfied by a $p$ fraction of assignments, if the instance contains $n$ variables and $n^{k/2} / \\epsilon^2$ constraints, we can efficiently compute a certificate that the optimum satisfies at most a $p+O_k(\\epsilon)$ fr"},"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":"2204.10881","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2022-04-20T16:21:21Z","cross_cats_sorted":["cs.AI","cs.LO","stat.ML"],"title_canon_sha256":"cea06480a80218201e5d24e36bfe3592b7c562d31f4f57ad1665f004b4fc99fc","abstract_canon_sha256":"10e48b76cae7de4df643f4c9c65506b885430c58c26de5e864d4b540bef33ab7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:09:42.826299Z","signature_b64":"E4sAJHzpmk+QCdepujFDt7ujmeZV31LAWjumXky9L9qP6Td4fd+yqLOzhdAOUizMII8ugOFzxSFdYrbUjOu4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9de429b194ced5c0c0aff3af26caebdf753b4be51306aae9759cb48c261334d","last_reissued_at":"2026-07-05T06:09:42.825904Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:09:42.825904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Ihara-Bass Formula for Non-Boolean Matrices and Strong Refutations of Random CSPs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LO","stat.ML"],"primary_cat":"cs.CC","authors_text":"Luca Trevisan, Tommaso d'Orsi","submitted_at":"2022-04-20T16:21:21Z","abstract_excerpt":"We define a novel notion of ``non-backtracking'' matrix associated to any symmetric matrix, and we prove a ``Ihara-Bass'' type formula for it.\n  We use this theory to prove new results on polynomial-time strong refutations of random constraint satisfaction problems with $k$ variables per constraints (k-CSPs). For a random k-CSP instance constructed out of a constraint that is satisfied by a $p$ fraction of assignments, if the instance contains $n$ variables and $n^{k/2} / \\epsilon^2$ constraints, we can efficiently compute a certificate that the optimum satisfies at most a $p+O_k(\\epsilon)$ fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.10881","kind":"arxiv","version":2},"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/2204.10881/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":"2204.10881","created_at":"2026-07-05T06:09:42.825964+00:00"},{"alias_kind":"arxiv_version","alias_value":"2204.10881v2","created_at":"2026-07-05T06:09:42.825964+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.10881","created_at":"2026-07-05T06:09:42.825964+00:00"},{"alias_kind":"pith_short_12","alias_value":"3HPEFGYZJTWV","created_at":"2026-07-05T06:09:42.825964+00:00"},{"alias_kind":"pith_short_16","alias_value":"3HPEFGYZJTWVYDAK","created_at":"2026-07-05T06:09:42.825964+00:00"},{"alias_kind":"pith_short_8","alias_value":"3HPEFGYZ","created_at":"2026-07-05T06:09:42.825964+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/3HPEFGYZJTWVYDAK745PE3FOXX","json":"https://pith.science/pith/3HPEFGYZJTWVYDAK745PE3FOXX.json","graph_json":"https://pith.science/api/pith-number/3HPEFGYZJTWVYDAK745PE3FOXX/graph.json","events_json":"https://pith.science/api/pith-number/3HPEFGYZJTWVYDAK745PE3FOXX/events.json","paper":"https://pith.science/paper/3HPEFGYZ"},"agent_actions":{"view_html":"https://pith.science/pith/3HPEFGYZJTWVYDAK745PE3FOXX","download_json":"https://pith.science/pith/3HPEFGYZJTWVYDAK745PE3FOXX.json","view_paper":"https://pith.science/paper/3HPEFGYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2204.10881&json=true","fetch_graph":"https://pith.science/api/pith-number/3HPEFGYZJTWVYDAK745PE3FOXX/graph.json","fetch_events":"https://pith.science/api/pith-number/3HPEFGYZJTWVYDAK745PE3FOXX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3HPEFGYZJTWVYDAK745PE3FOXX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3HPEFGYZJTWVYDAK745PE3FOXX/action/storage_attestation","attest_author":"https://pith.science/pith/3HPEFGYZJTWVYDAK745PE3FOXX/action/author_attestation","sign_citation":"https://pith.science/pith/3HPEFGYZJTWVYDAK745PE3FOXX/action/citation_signature","submit_replication":"https://pith.science/pith/3HPEFGYZJTWVYDAK745PE3FOXX/action/replication_record"}},"created_at":"2026-07-05T06:09:42.825964+00:00","updated_at":"2026-07-05T06:09:42.825964+00:00"}