{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:Z5YW6MQCYOBKTWXI2HCEFDHND5","short_pith_number":"pith:Z5YW6MQC","schema_version":"1.0","canonical_sha256":"cf716f3202c382a9dae8d1c4428ced1f7f77c8e4ca1bf0aeb71e6ef033a8bd01","source":{"kind":"arxiv","id":"2512.10590","version":2},"attestation_state":"computed","paper":{"title":"On the $P$-vertex problem in Bipartite Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G. Arunkumar, Puja Samanta","submitted_at":"2025-12-11T12:33:09Z","abstract_excerpt":"In a recent work, Sharma and Panda~\\cite{sharma} showed that every bipartite graph with a perfect matching has property (P). In this paper, we investigate the converse direction, i.e., when property (P) forces the existence of a perfect matching in bipartite graphs. We show that such graphs are balanced and establish that property (P) is equivalent to the existence of a perfect matching for several families of bipartite graphs."},"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":"2512.10590","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-12-11T12:33:09Z","cross_cats_sorted":[],"title_canon_sha256":"e4c968964c07743e406c069f035359d17bda908342c21fd791d2a1621f0593b5","abstract_canon_sha256":"d84354b619b7c8e271d17c8cc8801a062ed00a12feba51fc863b4ebc68af6ca7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:18.350420Z","signature_b64":"R3bVI3PwXC9J+DneftuqKx/eRlhFLrMeYS02ubqfzLaSJ2J9DweVwJh/74AEcO0CBbh5l6WHU57bgKy5sYQMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf716f3202c382a9dae8d1c4428ced1f7f77c8e4ca1bf0aeb71e6ef033a8bd01","last_reissued_at":"2026-06-19T16:11:18.349795Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:18.349795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the $P$-vertex problem in Bipartite Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G. Arunkumar, Puja Samanta","submitted_at":"2025-12-11T12:33:09Z","abstract_excerpt":"In a recent work, Sharma and Panda~\\cite{sharma} showed that every bipartite graph with a perfect matching has property (P). In this paper, we investigate the converse direction, i.e., when property (P) forces the existence of a perfect matching in bipartite graphs. We show that such graphs are balanced and establish that property (P) is equivalent to the existence of a perfect matching for several families of bipartite graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.10590","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/2512.10590/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":"2512.10590","created_at":"2026-06-19T16:11:18.349872+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.10590v2","created_at":"2026-06-19T16:11:18.349872+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.10590","created_at":"2026-06-19T16:11:18.349872+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z5YW6MQCYOBK","created_at":"2026-06-19T16:11:18.349872+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z5YW6MQCYOBKTWXI","created_at":"2026-06-19T16:11:18.349872+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z5YW6MQC","created_at":"2026-06-19T16:11:18.349872+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/Z5YW6MQCYOBKTWXI2HCEFDHND5","json":"https://pith.science/pith/Z5YW6MQCYOBKTWXI2HCEFDHND5.json","graph_json":"https://pith.science/api/pith-number/Z5YW6MQCYOBKTWXI2HCEFDHND5/graph.json","events_json":"https://pith.science/api/pith-number/Z5YW6MQCYOBKTWXI2HCEFDHND5/events.json","paper":"https://pith.science/paper/Z5YW6MQC"},"agent_actions":{"view_html":"https://pith.science/pith/Z5YW6MQCYOBKTWXI2HCEFDHND5","download_json":"https://pith.science/pith/Z5YW6MQCYOBKTWXI2HCEFDHND5.json","view_paper":"https://pith.science/paper/Z5YW6MQC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.10590&json=true","fetch_graph":"https://pith.science/api/pith-number/Z5YW6MQCYOBKTWXI2HCEFDHND5/graph.json","fetch_events":"https://pith.science/api/pith-number/Z5YW6MQCYOBKTWXI2HCEFDHND5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z5YW6MQCYOBKTWXI2HCEFDHND5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z5YW6MQCYOBKTWXI2HCEFDHND5/action/storage_attestation","attest_author":"https://pith.science/pith/Z5YW6MQCYOBKTWXI2HCEFDHND5/action/author_attestation","sign_citation":"https://pith.science/pith/Z5YW6MQCYOBKTWXI2HCEFDHND5/action/citation_signature","submit_replication":"https://pith.science/pith/Z5YW6MQCYOBKTWXI2HCEFDHND5/action/replication_record"}},"created_at":"2026-06-19T16:11:18.349872+00:00","updated_at":"2026-06-19T16:11:18.349872+00:00"}