{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SSYJ4KCX2D4HD6GHXFEOJ6HLQD","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":"180779dbd1f0b7f6e52ad86a3a45d1adbb533d9b749219be4c0ff246854c930e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-07T21:12:11Z","title_canon_sha256":"ba7eaebbaa76155cfef718f91f6ba886fabf5dd33bb904234ebd076dd33c71ee"},"schema_version":"1.0","source":{"id":"1209.1651","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1651","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1651v2","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1651","created_at":"2026-05-18T03:11:09Z"},{"alias_kind":"pith_short_12","alias_value":"SSYJ4KCX2D4H","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"SSYJ4KCX2D4HD6GH","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"SSYJ4KCX","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:cef252d7d55a542fa7ff3502ff22a45dab2147f54817d0ed47663e07e73eca24","target":"graph","created_at":"2026-05-18T03:11:09Z","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":"Given a matroid $M$ one can define its Orlik-Solomon algebra $OS(M)$ and the Bergman fan $\\Sigma_0(M)$. On the other hand to any rational polyhedral fan $\\Sigma$ one can associate its tropical homology and cohomology groups $\\F_\\bullet(\\Sigma)$, $\\F^\\bullet (\\Sigma)$. We will show that the projective Orlik-Solomon algebra $OS_0(M)$ is canonically isomorphic to $\\F^\\bullet (\\Sigma_0(M))$.","authors_text":"Ilia Zharkov","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-07T21:12:11Z","title":"The Orlik-Solomon Algebra and the Bergman Fan of a Matroid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1651","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":"sha256:75801c3fe9a0eaf67693aab7ab9c9fae5763da0cb4900ba8b0f62b022e32e806","target":"record","created_at":"2026-05-18T03:11:09Z","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":"180779dbd1f0b7f6e52ad86a3a45d1adbb533d9b749219be4c0ff246854c930e","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-09-07T21:12:11Z","title_canon_sha256":"ba7eaebbaa76155cfef718f91f6ba886fabf5dd33bb904234ebd076dd33c71ee"},"schema_version":"1.0","source":{"id":"1209.1651","kind":"arxiv","version":2}},"canonical_sha256":"94b09e2857d0f871f8c7b948e4f8eb80cd252345406e8321f4db770e9b7987a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94b09e2857d0f871f8c7b948e4f8eb80cd252345406e8321f4db770e9b7987a0","first_computed_at":"2026-05-18T03:11:09.593990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:09.593990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UYWfBZz65ZrT69GSQ4bHQKDNcXMwlpNk4ud2y2dyfeZahhuQIenMw43okCreQvDKvGS8gamADsDqiHsQ9C3EDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:09.594791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1651","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75801c3fe9a0eaf67693aab7ab9c9fae5763da0cb4900ba8b0f62b022e32e806","sha256:cef252d7d55a542fa7ff3502ff22a45dab2147f54817d0ed47663e07e73eca24"],"state_sha256":"8d6f3dedf4a8f45aed72cdff807951a45d4a73985706da75a89bdfe159287e16"}