{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JORYRIPK6ORYB7WEPA5WCXY2CY","short_pith_number":"pith:JORYRIPK","schema_version":"1.0","canonical_sha256":"4ba388a1eaf3a380fec4783b615f1a160c42b8eccfb3fda119a345f92cee6665","source":{"kind":"arxiv","id":"1312.7563","version":1},"attestation_state":"computed","paper":{"title":"Weighted Well-Covered Claw-Free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"David Tankus, Vadim E. Levit","submitted_at":"2013-12-29T17:41:42Z","abstract_excerpt":"A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input claw-free graph G, we present an O(n^6)algortihm, whose input is a claw-free graph G, and output is the vector space of weight functions w, for which G is w-well-covered. A graph G is equimatchable if all its maximal matchings are of the same cardinality."},"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":"1312.7563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-29T17:41:42Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cf873518c1b63c2c11dcf0ea3ac57a14619aa8f1896a47e0c11e83c3f1033a8e","abstract_canon_sha256":"7558445a68e616b3e3600d2deec770e36b582addf17963a5cf8d7b9eb9b8ae4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:43.028561Z","signature_b64":"26EhFVl9ijmLo9cAtWNjZpmtUjP4lOCy4h6DJ9UpmH+KX4+ZrJGVPGPFvVDYQI8Uuzkvdsjri51H4aEr0h0kCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ba388a1eaf3a380fec4783b615f1a160c42b8eccfb3fda119a345f92cee6665","last_reissued_at":"2026-05-18T03:03:43.027834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:43.027834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weighted Well-Covered Claw-Free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"David Tankus, Vadim E. Levit","submitted_at":"2013-12-29T17:41:42Z","abstract_excerpt":"A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input claw-free graph G, we present an O(n^6)algortihm, whose input is a claw-free graph G, and output is the vector space of weight functions w, for which G is w-well-covered. A graph G is equimatchable if all its maximal matchings are of the same cardinality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7563","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":"1312.7563","created_at":"2026-05-18T03:03:43.027962+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.7563v1","created_at":"2026-05-18T03:03:43.027962+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7563","created_at":"2026-05-18T03:03:43.027962+00:00"},{"alias_kind":"pith_short_12","alias_value":"JORYRIPK6ORY","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JORYRIPK6ORYB7WE","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JORYRIPK","created_at":"2026-05-18T12:27:49.015174+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/JORYRIPK6ORYB7WEPA5WCXY2CY","json":"https://pith.science/pith/JORYRIPK6ORYB7WEPA5WCXY2CY.json","graph_json":"https://pith.science/api/pith-number/JORYRIPK6ORYB7WEPA5WCXY2CY/graph.json","events_json":"https://pith.science/api/pith-number/JORYRIPK6ORYB7WEPA5WCXY2CY/events.json","paper":"https://pith.science/paper/JORYRIPK"},"agent_actions":{"view_html":"https://pith.science/pith/JORYRIPK6ORYB7WEPA5WCXY2CY","download_json":"https://pith.science/pith/JORYRIPK6ORYB7WEPA5WCXY2CY.json","view_paper":"https://pith.science/paper/JORYRIPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.7563&json=true","fetch_graph":"https://pith.science/api/pith-number/JORYRIPK6ORYB7WEPA5WCXY2CY/graph.json","fetch_events":"https://pith.science/api/pith-number/JORYRIPK6ORYB7WEPA5WCXY2CY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JORYRIPK6ORYB7WEPA5WCXY2CY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JORYRIPK6ORYB7WEPA5WCXY2CY/action/storage_attestation","attest_author":"https://pith.science/pith/JORYRIPK6ORYB7WEPA5WCXY2CY/action/author_attestation","sign_citation":"https://pith.science/pith/JORYRIPK6ORYB7WEPA5WCXY2CY/action/citation_signature","submit_replication":"https://pith.science/pith/JORYRIPK6ORYB7WEPA5WCXY2CY/action/replication_record"}},"created_at":"2026-05-18T03:03:43.027962+00:00","updated_at":"2026-05-18T03:03:43.027962+00:00"}