{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IUMY5TKAXHF3KQEC3O7H25TLMW","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":"9a7214fdb0ffe822e62d0aa2097734313ab07024db326a516279c1eb464db060","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-12T01:12:45Z","title_canon_sha256":"20ebe617deb0797d57c5711075f3ad5ba05fb1328f1b9097f8c2fb75ace03a86"},"schema_version":"1.0","source":{"id":"1008.2031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2031","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2031v2","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2031","created_at":"2026-05-18T04:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"IUMY5TKAXHF3","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IUMY5TKAXHF3KQEC","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IUMY5TKA","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:7c49c83b2e3245bcf6ba57ca790a01e179efc8ef37af1a9ae486fe7271ae4bd2","target":"graph","created_at":"2026-05-18T04:42:13Z","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":"We give two proofs that the $h$-vector of any paving matroid is a pure O-sequence, thus answering in the affirmative a conjecture made by R. Stanley, for this particular class of matroids. We also investigate the problem of obtaining good lower bounds for the number of bases of a paving matroid given its rank and number of elements.","authors_text":"Criel Merino, Marcelino Ram\\'irez-Iba\\~nez, Rafael Villarroel, Steven D. Noble","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-12T01:12:45Z","title":"On the structure of the h-vector of a paving matroid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2031","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":"sha256:86e2715d64b5fa4180b6ef92621c6413ee12ccf64ff908d4bc19f9013fbd54cd","target":"record","created_at":"2026-05-18T04:42:13Z","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":"9a7214fdb0ffe822e62d0aa2097734313ab07024db326a516279c1eb464db060","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-08-12T01:12:45Z","title_canon_sha256":"20ebe617deb0797d57c5711075f3ad5ba05fb1328f1b9097f8c2fb75ace03a86"},"schema_version":"1.0","source":{"id":"1008.2031","kind":"arxiv","version":2}},"canonical_sha256":"45198ecd40b9cbb54082dbbe7d766b6599152fa8bece87bd5fe0946c0e4a5e4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45198ecd40b9cbb54082dbbe7d766b6599152fa8bece87bd5fe0946c0e4a5e4c","first_computed_at":"2026-05-18T04:42:13.440385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:13.440385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ndbdBKMx0UrOYUXiQFgN6RmIhnT5hQPftCzwU0AXpVHJAtHjeeSKhfbFaed+UNdtAfhhhSTk7YowoQ1uO7KpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:13.440958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86e2715d64b5fa4180b6ef92621c6413ee12ccf64ff908d4bc19f9013fbd54cd","sha256:7c49c83b2e3245bcf6ba57ca790a01e179efc8ef37af1a9ae486fe7271ae4bd2"],"state_sha256":"535ffe9f73d95e297d91e29fa0b2b9e65d30bb9be267e389ddf9fe1a8ed1bf1e"}