{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RGXXLU3NU2HCEBUHQBCWYQPDVF","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":"8b270c5a2983a529d42477aa0d594fc7d77eb0bdc37de80d3a46c3d9bf6c8934","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-23T09:45:10Z","title_canon_sha256":"53a5f2ce492377976a7521a25cc5738a0381e286d1690264a5b74b3323c016e4"},"schema_version":"1.0","source":{"id":"1512.07409","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07409","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07409v3","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07409","created_at":"2026-05-18T00:20:07Z"},{"alias_kind":"pith_short_12","alias_value":"RGXXLU3NU2HC","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RGXXLU3NU2HCEBUH","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RGXXLU3N","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:07c5660daf5cb8b3c01c2aefb64e30d7f334f05f401c2a1a12542684f1a16651","target":"graph","created_at":"2026-05-18T00:20:07Z","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 establish a canonical isomorphism between two bigraded cohomology theories for polyhedral spaces: Dolbeault cohomology of superforms and tropical cohomology. Furthermore, we prove Poincar\\'e duality for cohomology of tropical manifolds, which are polyhedral spaces locally given by Bergman fans of matroids.","authors_text":"Jascha Smacka, Kristin Shaw, Philipp Jell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-23T09:45:10Z","title":"Superforms, Tropical Cohomology, and Poincar\\'e Duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07409","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":"sha256:3f2a1d70478091a3f5c8d9881e3fbe8149e2efd35bfa09ab2cdefe4d31ccdfa2","target":"record","created_at":"2026-05-18T00:20:07Z","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":"8b270c5a2983a529d42477aa0d594fc7d77eb0bdc37de80d3a46c3d9bf6c8934","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-23T09:45:10Z","title_canon_sha256":"53a5f2ce492377976a7521a25cc5738a0381e286d1690264a5b74b3323c016e4"},"schema_version":"1.0","source":{"id":"1512.07409","kind":"arxiv","version":3}},"canonical_sha256":"89af75d36da68e22068780456c41e3a942a16e49b0d166aaafa2cc9ab4a3793c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89af75d36da68e22068780456c41e3a942a16e49b0d166aaafa2cc9ab4a3793c","first_computed_at":"2026-05-18T00:20:07.671201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:07.671201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vOBs+XTetfItcSq0W6T9iPfxMsIReCQ4WfDPprYROQXg+uloFwZlP8cQTY61XBl9DRnEQlIC45rwum566dJfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:07.671874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07409","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f2a1d70478091a3f5c8d9881e3fbe8149e2efd35bfa09ab2cdefe4d31ccdfa2","sha256:07c5660daf5cb8b3c01c2aefb64e30d7f334f05f401c2a1a12542684f1a16651"],"state_sha256":"3d58c7dcab4ce876096414eaab0a3ca7763491ab22b0050faaa77dfb051e68bb"}