{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VCSYVYHJHXKJCVF5MLGEHJ4YBD","short_pith_number":"pith:VCSYVYHJ","schema_version":"1.0","canonical_sha256":"a8a58ae0e93dd49154bd62cc43a79808c6bfc2d2f77640f577b758214a159ac5","source":{"kind":"arxiv","id":"1810.00065","version":1},"attestation_state":"computed","paper":{"title":"Proof of the Kalai-Meshulam conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Maria Chudnovsky, Paul Seymour, Sophie Spirkl","submitted_at":"2018-09-28T19:53:18Z","abstract_excerpt":"Let $G$ be a graph, and let $f_G$ be the sum of $(-1)^{|A|}$, over all stable sets $A$. If $G$ is a cycle with length divisible by three, then $f_G= \\pm 2$. Motivated by topological considerations, G. Kalai and R. Meshulam made the conjecture that,if no induced cycle of a graph $G$ has length divisible by three, then $|f_G|\\le 1$. We prove this conjecture."},"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":"1810.00065","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-28T19:53:18Z","cross_cats_sorted":[],"title_canon_sha256":"cf03b546f57b854ec92f41c237fd3fb05bda3154939c126178aacf65212d2c7f","abstract_canon_sha256":"739337c673130f2f2e20894d8c10181be564504becc19499e16f455a68dc7d44"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:28.949518Z","signature_b64":"xiEEDw8MY1iIV+xceDEJzUbkbAWugE7daEet1MD9W1Vqksmr0BuFuKw99qHk0ZfQdp73d/TVg0nNu3TM07myDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8a58ae0e93dd49154bd62cc43a79808c6bfc2d2f77640f577b758214a159ac5","last_reissued_at":"2026-05-18T00:04:28.948852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:28.948852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of the Kalai-Meshulam conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alex Scott, Maria Chudnovsky, Paul Seymour, Sophie Spirkl","submitted_at":"2018-09-28T19:53:18Z","abstract_excerpt":"Let $G$ be a graph, and let $f_G$ be the sum of $(-1)^{|A|}$, over all stable sets $A$. If $G$ is a cycle with length divisible by three, then $f_G= \\pm 2$. Motivated by topological considerations, G. Kalai and R. Meshulam made the conjecture that,if no induced cycle of a graph $G$ has length divisible by three, then $|f_G|\\le 1$. We prove this conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00065","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":""},"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":"1810.00065","created_at":"2026-05-18T00:04:28.948963+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.00065v1","created_at":"2026-05-18T00:04:28.948963+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00065","created_at":"2026-05-18T00:04:28.948963+00:00"},{"alias_kind":"pith_short_12","alias_value":"VCSYVYHJHXKJ","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VCSYVYHJHXKJCVF5","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VCSYVYHJ","created_at":"2026-05-18T12:32:59.047623+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/VCSYVYHJHXKJCVF5MLGEHJ4YBD","json":"https://pith.science/pith/VCSYVYHJHXKJCVF5MLGEHJ4YBD.json","graph_json":"https://pith.science/api/pith-number/VCSYVYHJHXKJCVF5MLGEHJ4YBD/graph.json","events_json":"https://pith.science/api/pith-number/VCSYVYHJHXKJCVF5MLGEHJ4YBD/events.json","paper":"https://pith.science/paper/VCSYVYHJ"},"agent_actions":{"view_html":"https://pith.science/pith/VCSYVYHJHXKJCVF5MLGEHJ4YBD","download_json":"https://pith.science/pith/VCSYVYHJHXKJCVF5MLGEHJ4YBD.json","view_paper":"https://pith.science/paper/VCSYVYHJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.00065&json=true","fetch_graph":"https://pith.science/api/pith-number/VCSYVYHJHXKJCVF5MLGEHJ4YBD/graph.json","fetch_events":"https://pith.science/api/pith-number/VCSYVYHJHXKJCVF5MLGEHJ4YBD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VCSYVYHJHXKJCVF5MLGEHJ4YBD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VCSYVYHJHXKJCVF5MLGEHJ4YBD/action/storage_attestation","attest_author":"https://pith.science/pith/VCSYVYHJHXKJCVF5MLGEHJ4YBD/action/author_attestation","sign_citation":"https://pith.science/pith/VCSYVYHJHXKJCVF5MLGEHJ4YBD/action/citation_signature","submit_replication":"https://pith.science/pith/VCSYVYHJHXKJCVF5MLGEHJ4YBD/action/replication_record"}},"created_at":"2026-05-18T00:04:28.948963+00:00","updated_at":"2026-05-18T00:04:28.948963+00:00"}