{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EMSDNWBWQANLDSA7MSTXFBF5OK","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":"b85ae9a3d969aba70a41d90236494ef407f8947333e356f67882b27fabab01ec","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-30T08:18:14Z","title_canon_sha256":"1a4733287a79741fca71a75929ab883ded6967584e90b8f852232813e55547a7"},"schema_version":"1.0","source":{"id":"1404.7623","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7623","created_at":"2026-05-18T02:52:55Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7623v1","created_at":"2026-05-18T02:52:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7623","created_at":"2026-05-18T02:52:55Z"},{"alias_kind":"pith_short_12","alias_value":"EMSDNWBWQANL","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EMSDNWBWQANLDSA7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EMSDNWBW","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:d45076638f5a5a0a82d1c9e88250baf9d045a19650e566405fd7b5cddd61e234","target":"graph","created_at":"2026-05-18T02:52:55Z","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"},"paper":{"abstract_excerpt":"The stable set polytope of a graph $G$, denoted as STAB($G$), is the convex hull of all the incidence vectors of stable sets of $G$. To describe a linear system which defines STAB($G$) seems to be a difficult task in the general case. In this paper we present a complete description of the stable set polytope of ($P_6$,triangle)-free graphs (and more generally of ($P_6$,paw)-free graphs). For that we combine different tools, in the context of a well known result of Chv\\'atal \\cite{Chvatal1975} which allows to focus just on prime facet-inducing graphs, with particular reference to a structure re","authors_text":"Raffaele Mosca","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-30T08:18:14Z","title":"The stable set polytope of ($P_6$,triangle)-free graphs and new facet-inducing graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7623","kind":"arxiv","version":1},"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":"sha256:85c5ff0fb3de28e68bb5ba3a1bfc66a71d00e16e46cadc74a35a115283e35fc9","target":"record","created_at":"2026-05-18T02:52:55Z","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":"b85ae9a3d969aba70a41d90236494ef407f8947333e356f67882b27fabab01ec","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-04-30T08:18:14Z","title_canon_sha256":"1a4733287a79741fca71a75929ab883ded6967584e90b8f852232813e55547a7"},"schema_version":"1.0","source":{"id":"1404.7623","kind":"arxiv","version":1}},"canonical_sha256":"232436d836801ab1c81f64a77284bd72807b0744c3ce8fd62ae7d6fcc6581097","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"232436d836801ab1c81f64a77284bd72807b0744c3ce8fd62ae7d6fcc6581097","first_computed_at":"2026-05-18T02:52:55.199754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:55.199754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QuBcbNmks11wlOr8hpIgiSnLTS3MdTSEZizZoWPqoPxSSSHnR11eAaPT8WPuN2kPdjQQLO20UUqugpnL0ettCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:55.200360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7623","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85c5ff0fb3de28e68bb5ba3a1bfc66a71d00e16e46cadc74a35a115283e35fc9","sha256:d45076638f5a5a0a82d1c9e88250baf9d045a19650e566405fd7b5cddd61e234"],"state_sha256":"7c073602745376c4b67b836bacea9645b8187f623c2a58c9c6f0937fe1648ec3"}