{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Z5YW6MQCYOBKTWXI2HCEFDHND5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d84354b619b7c8e271d17c8cc8801a062ed00a12feba51fc863b4ebc68af6ca7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-12-11T12:33:09Z","title_canon_sha256":"e4c968964c07743e406c069f035359d17bda908342c21fd791d2a1621f0593b5"},"schema_version":"1.0","source":{"id":"2512.10590","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.10590","created_at":"2026-06-19T16:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"2512.10590v2","created_at":"2026-06-19T16:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.10590","created_at":"2026-06-19T16:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"Z5YW6MQCYOBK","created_at":"2026-06-19T16:11:18Z"},{"alias_kind":"pith_short_16","alias_value":"Z5YW6MQCYOBKTWXI","created_at":"2026-06-19T16:11:18Z"},{"alias_kind":"pith_short_8","alias_value":"Z5YW6MQC","created_at":"2026-06-19T16:11:18Z"}],"graph_snapshots":[{"event_id":"sha256:5e6e354f715c61873d83cff7848f1359e503b6a7ae5cdcb24793c813eab76f03","target":"graph","created_at":"2026-06-19T16:11:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2512.10590/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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.","authors_text":"G. Arunkumar, Puja Samanta","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-12-11T12:33:09Z","title":"On the $P$-vertex problem in Bipartite Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.10590","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8565f086d640e359bc176f6ccb29254c96890a5b084dfad62d68937639d7eb42","target":"record","created_at":"2026-06-19T16:11:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d84354b619b7c8e271d17c8cc8801a062ed00a12feba51fc863b4ebc68af6ca7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-12-11T12:33:09Z","title_canon_sha256":"e4c968964c07743e406c069f035359d17bda908342c21fd791d2a1621f0593b5"},"schema_version":"1.0","source":{"id":"2512.10590","kind":"arxiv","version":2}},"canonical_sha256":"cf716f3202c382a9dae8d1c4428ced1f7f77c8e4ca1bf0aeb71e6ef033a8bd01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf716f3202c382a9dae8d1c4428ced1f7f77c8e4ca1bf0aeb71e6ef033a8bd01","first_computed_at":"2026-06-19T16:11:18.349795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:18.349795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R3bVI3PwXC9J+DneftuqKx/eRlhFLrMeYS02ubqfzLaSJ2J9DweVwJh/74AEcO0CBbh5l6WHU57bgKy5sYQMBA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:18.350420Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.10590","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8565f086d640e359bc176f6ccb29254c96890a5b084dfad62d68937639d7eb42","sha256:5e6e354f715c61873d83cff7848f1359e503b6a7ae5cdcb24793c813eab76f03"],"state_sha256":"cdb953d6745732b026a12a075d8e50001e87dfbb4d3e374eff94e537c16a78c6"}