{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HOI55UN77QWD4FNAOKORIZ2ZJZ","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":"ce91975d7c34209bf26dedde08030ea7b75137a2dd22ebb40ab0178b6bf32c96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-07-16T20:00:00Z","title_canon_sha256":"35fd62f3d7685256849f8f24bb4e0496a77c1edd43b0a0c4deb5c5eebb9d1407"},"schema_version":"1.0","source":{"id":"1507.04741","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04741","created_at":"2026-05-18T01:13:09Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04741v2","created_at":"2026-05-18T01:13:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04741","created_at":"2026-05-18T01:13:09Z"},{"alias_kind":"pith_short_12","alias_value":"HOI55UN77QWD","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HOI55UN77QWD4FNA","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HOI55UN7","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:6c2c211f477a110f4da9ad624e92674f5fc0c245275a6dd805e96b849d412527","target":"graph","created_at":"2026-05-18T01:13:09Z","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":"Considered is a class of pursuit-evasion games, in which an evader tries to avoid detection. Such games can be formulated as the search for sections to the complement of a coverage region in a Euclidean space over a timeline. Prior results give homological criteria for evasion in the general case that are not necessary and sufficient. This paper provides a necessary and sufficient positive cohomological criterion for evasion in a general case. The principal tools are (1) a refinement of the Cech cohomology of a coverage region with a positive cone encoding spatial orientation, (2) a refinement","authors_text":"Robert Ghrist, Sanjeevi Krishnan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-07-16T20:00:00Z","title":"Positive Alexander Duality for Pursuit and Evasion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04741","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:e9b29e9b1b000f526c843b380ad30a0153e5fd5d6e53db0c54866173cfa6b49f","target":"record","created_at":"2026-05-18T01:13:09Z","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":"ce91975d7c34209bf26dedde08030ea7b75137a2dd22ebb40ab0178b6bf32c96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-07-16T20:00:00Z","title_canon_sha256":"35fd62f3d7685256849f8f24bb4e0496a77c1edd43b0a0c4deb5c5eebb9d1407"},"schema_version":"1.0","source":{"id":"1507.04741","kind":"arxiv","version":2}},"canonical_sha256":"3b91ded1bffc2c3e15a0729d1467594e7d7d6440d94a4afed4e527fe989abab1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b91ded1bffc2c3e15a0729d1467594e7d7d6440d94a4afed4e527fe989abab1","first_computed_at":"2026-05-18T01:13:09.660855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:09.660855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"16+MCb2RC5GXWjsEzYsAAlwlSKtdbufgORTRi6ciKJov1ydq1uwqdS6vvSFL1fDT3mr18Kb9fSKIltbztMe3DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:09.661245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04741","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9b29e9b1b000f526c843b380ad30a0153e5fd5d6e53db0c54866173cfa6b49f","sha256:6c2c211f477a110f4da9ad624e92674f5fc0c245275a6dd805e96b849d412527"],"state_sha256":"689b511fd3bece882a398eb9215680088a28edae83e27fc5fb9aeff5d6dac513"}