{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XXDNDNU36GR4NJS5KM27LWEWSC","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":"2a1769e82b699cc01c3c6f25d9005df23120b51d820eef6a963030e8150d005e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-07-10T13:40:40Z","title_canon_sha256":"ab22318a2e164912d90bc73557664ce7ad7e544b0d3a58bd059caa38cfd4ce7d"},"schema_version":"1.0","source":{"id":"1207.2346","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2346","created_at":"2026-05-18T03:18:51Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2346v3","created_at":"2026-05-18T03:18:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2346","created_at":"2026-05-18T03:18:51Z"},{"alias_kind":"pith_short_12","alias_value":"XXDNDNU36GR4","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XXDNDNU36GR4NJS5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XXDNDNU3","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:dd23d30c7e1bc60431f1bb2d0bda44bf24fc7ff41981dbe1e373d32f00325472","target":"graph","created_at":"2026-05-18T03:18:51Z","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":"Let $I=(\\mathbb{Z}^3,26,6,B)$ be a 3D digital image, let $Q(I)$ be the associated cubical complex and let $\\partial Q(I)$ be the subcomplex of $Q(I)$ whose maximal cells are the quadrangles of $Q(I)$ shared by a voxel of $B$ in the foreground -- the object under study -- and by a voxel of $\\mathbb{Z}^3\\smallsetminus B$ in the background -- the ambient space. We show how to simplify the combinatorial structure of $\\partial Q(I)$ and obtain a 3D polyhedral complex $P(I)$ homeomorphic to $\\partial Q(I)$ but with fewer cells. We introduce an algorithm that computes cup products on $H^*(P(I);\\mathb","authors_text":"Javier Lamar, Rocio Gonalez-Diaz, Ronald Umble","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-07-10T13:40:40Z","title":"Cups Products in Z2-Cohomology of 3D Polyhedral Complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2346","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:db3b6dfefa0d5726d29f114347b59c6c8f8eec9d4e26970a5f831915edaae9d4","target":"record","created_at":"2026-05-18T03:18:51Z","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":"2a1769e82b699cc01c3c6f25d9005df23120b51d820eef6a963030e8150d005e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2012-07-10T13:40:40Z","title_canon_sha256":"ab22318a2e164912d90bc73557664ce7ad7e544b0d3a58bd059caa38cfd4ce7d"},"schema_version":"1.0","source":{"id":"1207.2346","kind":"arxiv","version":3}},"canonical_sha256":"bdc6d1b69bf1a3c6a65d5335f5d89690aa2921c4568cb9068e687fc2a6a08456","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdc6d1b69bf1a3c6a65d5335f5d89690aa2921c4568cb9068e687fc2a6a08456","first_computed_at":"2026-05-18T03:18:51.820418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:51.820418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"69q4yXPP0+ddc3JGh4qgRKBp6Z+Fw3OJ6YOjp00BWnDfq8KdtLjFKGjGevJ2VSLbfrXYIAW25gN5gl/G6W9XAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:51.820903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2346","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db3b6dfefa0d5726d29f114347b59c6c8f8eec9d4e26970a5f831915edaae9d4","sha256:dd23d30c7e1bc60431f1bb2d0bda44bf24fc7ff41981dbe1e373d32f00325472"],"state_sha256":"4ee890965d9ff1d298c56fe4598f57f33b4f72cb2ed59d10499dc0eaf83aa3c8"}