{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TPHJ2W5NUYFH53ULK2D2HDTDGK","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":"4f780c351e39f0a40a5f177148eb1fb6da7173b9c4ff15c62fd376ab226b3561","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-13T14:51:29Z","title_canon_sha256":"99864ce72ad72643b283c35d938adc6ca3ef5a8ce3251bce6aa0b7de59acf027"},"schema_version":"1.0","source":{"id":"1104.2519","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2519","created_at":"2026-05-18T04:02:15Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2519v2","created_at":"2026-05-18T04:02:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2519","created_at":"2026-05-18T04:02:15Z"},{"alias_kind":"pith_short_12","alias_value":"TPHJ2W5NUYFH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TPHJ2W5NUYFH53UL","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TPHJ2W5N","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:bda516bfb6cf995f8067695810b5f2e389678e7c9eee52261be9e8648536a39d","target":"graph","created_at":"2026-05-18T04:02:15Z","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":"In a recent paper, the first author proved the log-concavity of the coefficients of the characteristic polynomial of a matroid realizable over a field of characteristic 0, answering a long-standing conjecture of Read in graph theory. We extend the proof to all realizable matroids, making progress towards a more general conjecture of Rota-Heron-Welsh. Our proof follows from an identification of the coefficients of the reduced characteristic polynomial as answers to particular intersection problems on a toric variety. The log-concavity then follows from an inequality of Hodge type.","authors_text":"Eric Katz, June Huh","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-13T14:51:29Z","title":"Log-concavity of characteristic polynomials and the Bergman fan of matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2519","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:cd4bcd6ea77ba7870dbebde2e3d87b8d855896e2a7651b7eb21cc9c06c8c7fce","target":"record","created_at":"2026-05-18T04:02:15Z","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":"4f780c351e39f0a40a5f177148eb1fb6da7173b9c4ff15c62fd376ab226b3561","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-13T14:51:29Z","title_canon_sha256":"99864ce72ad72643b283c35d938adc6ca3ef5a8ce3251bce6aa0b7de59acf027"},"schema_version":"1.0","source":{"id":"1104.2519","kind":"arxiv","version":2}},"canonical_sha256":"9bce9d5bada60a7eee8b5687a38e6332af2efcc7128b2fd2c5c34d3a9cac5925","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bce9d5bada60a7eee8b5687a38e6332af2efcc7128b2fd2c5c34d3a9cac5925","first_computed_at":"2026-05-18T04:02:15.142779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:15.142779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OjJQp7rYi9n8lu0DUFbaRNOdfL8gRVwXtsnJmDY1+GA1hhV3pmy3vX63D7VFC9J2gBRhaKKtH9C0Br86xHHKDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:15.143476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2519","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd4bcd6ea77ba7870dbebde2e3d87b8d855896e2a7651b7eb21cc9c06c8c7fce","sha256:bda516bfb6cf995f8067695810b5f2e389678e7c9eee52261be9e8648536a39d"],"state_sha256":"5ff822d727e1d4976e33da42f0b720f416b7df66a43a1ca7a37dbba4cccc7758"}