{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:3IQIUZNNQFZPDZCEUQN7MHQMPS","short_pith_number":"pith:3IQIUZNN","canonical_record":{"source":{"id":"2005.01937","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-05-05T04:06:25Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ff8b7da97cda059042d0b59c5992caca0d9091d026cec9044e5620cd2ce45f75","abstract_canon_sha256":"0645223c1aaea4a21a602b3bae510edaec3d5921e0a56fefe28f2f718dff4414"},"schema_version":"1.0"},"canonical_sha256":"da208a65ad8172f1e444a41bf61e0c7ca223224a098987f4e9359dcc83f34995","source":{"kind":"arxiv","id":"2005.01937","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.01937","created_at":"2026-07-05T05:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"2005.01937v3","created_at":"2026-07-05T05:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.01937","created_at":"2026-07-05T05:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"3IQIUZNNQFZP","created_at":"2026-07-05T05:54:03Z"},{"alias_kind":"pith_short_16","alias_value":"3IQIUZNNQFZPDZCE","created_at":"2026-07-05T05:54:03Z"},{"alias_kind":"pith_short_8","alias_value":"3IQIUZNN","created_at":"2026-07-05T05:54:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:3IQIUZNNQFZPDZCEUQN7MHQMPS","target":"record","payload":{"canonical_record":{"source":{"id":"2005.01937","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-05-05T04:06:25Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ff8b7da97cda059042d0b59c5992caca0d9091d026cec9044e5620cd2ce45f75","abstract_canon_sha256":"0645223c1aaea4a21a602b3bae510edaec3d5921e0a56fefe28f2f718dff4414"},"schema_version":"1.0"},"canonical_sha256":"da208a65ad8172f1e444a41bf61e0c7ca223224a098987f4e9359dcc83f34995","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:54:03.340763Z","signature_b64":"3xJ5uT5kOLns7KIpirfwSmxkCfougttwpSgjsKFvfv7P4mZ55NS8Q7yghY2camWQDQgOiQjxWskyxfpE/44fAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da208a65ad8172f1e444a41bf61e0c7ca223224a098987f4e9359dcc83f34995","last_reissued_at":"2026-07-05T05:54:03.340366Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:54:03.340366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2005.01937","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EEle2uOlNNH/M1nKbgrc2976S/fatOkSyG0TPL3KCbpQVI1JnH+L8enfsDYX/jPZRaDOcPoEgUq6iT285PUPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T15:41:40.004492Z"},"content_sha256":"7200ff23e8aa1eabfb76e367dc3a12056996e237182cf210ce4a86305cb4549f","schema_version":"1.0","event_id":"sha256:7200ff23e8aa1eabfb76e367dc3a12056996e237182cf210ce4a86305cb4549f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:3IQIUZNNQFZPDZCEUQN7MHQMPS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Log-concavity of matroid h-vectors and mixed Eulerian numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Andrew Berget, Dennis Tseng, Hunter Spink","submitted_at":"2020-05-05T04:06:25Z","abstract_excerpt":"For any matroid $M$, we compute the Tutte polynomial $T_M(x,y)$ using the mixed intersection numbers of certain classes in the combinatorial Chow ring $A^\\bullet(M)$ arising from hypersimplices. Using the mixed Hodge-Riemann relations, we deduce a strengthening of the log-concavity of the $h$-vector of a matroid complex, improving on an old conjecture of Dawson."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.01937","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2005.01937/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kZuud3z5mgmstEigrXSPo9xIVG7sDpOeObKrsBoccr/P1KbbW7C41n0idYKHfgdY1OKlVhPI6f3n6M3M6OdgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T15:41:40.005196Z"},"content_sha256":"77cfecdcf7b0ec76abda2d6930edb78485b9cfea21687d72ed02c8239f37e167","schema_version":"1.0","event_id":"sha256:77cfecdcf7b0ec76abda2d6930edb78485b9cfea21687d72ed02c8239f37e167"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3IQIUZNNQFZPDZCEUQN7MHQMPS/bundle.json","state_url":"https://pith.science/pith/3IQIUZNNQFZPDZCEUQN7MHQMPS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3IQIUZNNQFZPDZCEUQN7MHQMPS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-21T15:41:40Z","links":{"resolver":"https://pith.science/pith/3IQIUZNNQFZPDZCEUQN7MHQMPS","bundle":"https://pith.science/pith/3IQIUZNNQFZPDZCEUQN7MHQMPS/bundle.json","state":"https://pith.science/pith/3IQIUZNNQFZPDZCEUQN7MHQMPS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3IQIUZNNQFZPDZCEUQN7MHQMPS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:3IQIUZNNQFZPDZCEUQN7MHQMPS","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":"0645223c1aaea4a21a602b3bae510edaec3d5921e0a56fefe28f2f718dff4414","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-05-05T04:06:25Z","title_canon_sha256":"ff8b7da97cda059042d0b59c5992caca0d9091d026cec9044e5620cd2ce45f75"},"schema_version":"1.0","source":{"id":"2005.01937","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.01937","created_at":"2026-07-05T05:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"2005.01937v3","created_at":"2026-07-05T05:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.01937","created_at":"2026-07-05T05:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"3IQIUZNNQFZP","created_at":"2026-07-05T05:54:03Z"},{"alias_kind":"pith_short_16","alias_value":"3IQIUZNNQFZPDZCE","created_at":"2026-07-05T05:54:03Z"},{"alias_kind":"pith_short_8","alias_value":"3IQIUZNN","created_at":"2026-07-05T05:54:03Z"}],"graph_snapshots":[{"event_id":"sha256:77cfecdcf7b0ec76abda2d6930edb78485b9cfea21687d72ed02c8239f37e167","target":"graph","created_at":"2026-07-05T05:54:03Z","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/2005.01937/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For any matroid $M$, we compute the Tutte polynomial $T_M(x,y)$ using the mixed intersection numbers of certain classes in the combinatorial Chow ring $A^\\bullet(M)$ arising from hypersimplices. Using the mixed Hodge-Riemann relations, we deduce a strengthening of the log-concavity of the $h$-vector of a matroid complex, improving on an old conjecture of Dawson.","authors_text":"Andrew Berget, Dennis Tseng, Hunter Spink","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-05-05T04:06:25Z","title":"Log-concavity of matroid h-vectors and mixed Eulerian numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.01937","kind":"arxiv","version":3},"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":"sha256:7200ff23e8aa1eabfb76e367dc3a12056996e237182cf210ce4a86305cb4549f","target":"record","created_at":"2026-07-05T05:54:03Z","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":"0645223c1aaea4a21a602b3bae510edaec3d5921e0a56fefe28f2f718dff4414","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-05-05T04:06:25Z","title_canon_sha256":"ff8b7da97cda059042d0b59c5992caca0d9091d026cec9044e5620cd2ce45f75"},"schema_version":"1.0","source":{"id":"2005.01937","kind":"arxiv","version":3}},"canonical_sha256":"da208a65ad8172f1e444a41bf61e0c7ca223224a098987f4e9359dcc83f34995","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da208a65ad8172f1e444a41bf61e0c7ca223224a098987f4e9359dcc83f34995","first_computed_at":"2026-07-05T05:54:03.340366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:54:03.340366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3xJ5uT5kOLns7KIpirfwSmxkCfougttwpSgjsKFvfv7P4mZ55NS8Q7yghY2camWQDQgOiQjxWskyxfpE/44fAA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:54:03.340763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.01937","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7200ff23e8aa1eabfb76e367dc3a12056996e237182cf210ce4a86305cb4549f","sha256:77cfecdcf7b0ec76abda2d6930edb78485b9cfea21687d72ed02c8239f37e167"],"state_sha256":"73e3a7cafd02942e9388562f88b4f25ce45aa10a00c342157c21df75c2f99251"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zQo9EI4IZ649PiezBDjwcRCHOI1YOJ+z+jfwbPWlNxnFIWDdlnswFeWxVej+z8Jjq8VW/2JEbQ6wLzpwKtTuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T15:41:40.011539Z","bundle_sha256":"4ecf3da3815024758e98d987e5c93f2306e656aee880e49a0eb88a884c29d0a1"}}