{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:UCLW3UUFZ6QOBRYULEKAIWSIBR","short_pith_number":"pith:UCLW3UUF","schema_version":"1.0","canonical_sha256":"a0976dd285cfa0e0c7145914045a480c5779163ead8b8a894616a629ab9b5719","source":{"kind":"arxiv","id":"2505.22766","version":2},"attestation_state":"computed","paper":{"title":"On the independent set polynomial of graphs and claw-free graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"Aldo Procacci, Paula M. S. Fialho","submitted_at":"2025-05-28T18:34:34Z","abstract_excerpt":"We present two new contributions to the study of the independence polynomial $Z_G(z)$ of a finite simple graph $G = (V,E)$. First, we provide an improved lower bound for the zero-free region of $Z_G(z)$ for the important class of claw-free graphs. Our bound exceeds the classical Shearer radius and it is derived through a refined application of the Fern\\'andez-Procacci criterion using properties of the local neighborhood structure in claw-free graphs. Second, we establish a novel combinatorial expression for $Z_G(z)$, inspired by the connection with the abstract polymer gas models in statistica"},"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":"2505.22766","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T18:34:34Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"cdee4f11f44ab992384c9c72815ab80f8d00b75a674ef4eb15c5507064f03d87","abstract_canon_sha256":"c094902dd4a2512f6c6404a857de9e2970c8f79b425885b048281a0716c8fcbc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:53:27.771142Z","signature_b64":"2nvVo2tK3//X5HICZ67EVLQWltok6P3NLq662G+OGMqK3KfnQQ1KorwrClP+pL3Gso5O+zRUB8e+5Ay+19OHDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0976dd285cfa0e0c7145914045a480c5779163ead8b8a894616a629ab9b5719","last_reissued_at":"2026-07-05T11:53:27.770615Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:53:27.770615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the independent set polynomial of graphs and claw-free graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"Aldo Procacci, Paula M. S. Fialho","submitted_at":"2025-05-28T18:34:34Z","abstract_excerpt":"We present two new contributions to the study of the independence polynomial $Z_G(z)$ of a finite simple graph $G = (V,E)$. First, we provide an improved lower bound for the zero-free region of $Z_G(z)$ for the important class of claw-free graphs. Our bound exceeds the classical Shearer radius and it is derived through a refined application of the Fern\\'andez-Procacci criterion using properties of the local neighborhood structure in claw-free graphs. Second, we establish a novel combinatorial expression for $Z_G(z)$, inspired by the connection with the abstract polymer gas models in statistica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22766","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/2505.22766/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":"2505.22766","created_at":"2026-07-05T11:53:27.770696+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.22766v2","created_at":"2026-07-05T11:53:27.770696+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22766","created_at":"2026-07-05T11:53:27.770696+00:00"},{"alias_kind":"pith_short_12","alias_value":"UCLW3UUFZ6QO","created_at":"2026-07-05T11:53:27.770696+00:00"},{"alias_kind":"pith_short_16","alias_value":"UCLW3UUFZ6QOBRYU","created_at":"2026-07-05T11:53:27.770696+00:00"},{"alias_kind":"pith_short_8","alias_value":"UCLW3UUF","created_at":"2026-07-05T11:53:27.770696+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/UCLW3UUFZ6QOBRYULEKAIWSIBR","json":"https://pith.science/pith/UCLW3UUFZ6QOBRYULEKAIWSIBR.json","graph_json":"https://pith.science/api/pith-number/UCLW3UUFZ6QOBRYULEKAIWSIBR/graph.json","events_json":"https://pith.science/api/pith-number/UCLW3UUFZ6QOBRYULEKAIWSIBR/events.json","paper":"https://pith.science/paper/UCLW3UUF"},"agent_actions":{"view_html":"https://pith.science/pith/UCLW3UUFZ6QOBRYULEKAIWSIBR","download_json":"https://pith.science/pith/UCLW3UUFZ6QOBRYULEKAIWSIBR.json","view_paper":"https://pith.science/paper/UCLW3UUF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.22766&json=true","fetch_graph":"https://pith.science/api/pith-number/UCLW3UUFZ6QOBRYULEKAIWSIBR/graph.json","fetch_events":"https://pith.science/api/pith-number/UCLW3UUFZ6QOBRYULEKAIWSIBR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UCLW3UUFZ6QOBRYULEKAIWSIBR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UCLW3UUFZ6QOBRYULEKAIWSIBR/action/storage_attestation","attest_author":"https://pith.science/pith/UCLW3UUFZ6QOBRYULEKAIWSIBR/action/author_attestation","sign_citation":"https://pith.science/pith/UCLW3UUFZ6QOBRYULEKAIWSIBR/action/citation_signature","submit_replication":"https://pith.science/pith/UCLW3UUFZ6QOBRYULEKAIWSIBR/action/replication_record"}},"created_at":"2026-07-05T11:53:27.770696+00:00","updated_at":"2026-07-05T11:53:27.770696+00:00"}