{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BD7G2P4VIP3R3WM6BW3JD2UR2T","short_pith_number":"pith:BD7G2P4V","schema_version":"1.0","canonical_sha256":"08fe6d3f9543f71dd99e0db691ea91d4e7cc658b9de9c231f4104513978d4c1a","source":{"kind":"arxiv","id":"1205.6082","version":2},"attestation_state":"computed","paper":{"title":"Good covers are algorithmically unrecognizable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GT"],"primary_cat":"cs.CG","authors_text":"Dmitry Tonkonog, Martin Tancer","submitted_at":"2012-05-28T11:36:17Z","abstract_excerpt":"A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with convex sets, intersection patterns of good covers were studied intensively. Our main result is that intersection patterns of good covers are algorithmically unrecognizable.\n  More precisely, the intersection pattern of a good cover can be stored in a simplicial complex called nerve which records which subfamilies of the good cover intersect. A simplicial complex is topologically d-representable if it is isomorphic to "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1205.6082","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-05-28T11:36:17Z","cross_cats_sorted":["math.AT","math.GT"],"title_canon_sha256":"3b51c639556165959717643d24db4a651e347e0300858daa86a9b03e3fb37da5","abstract_canon_sha256":"9813ebd3e72d4d9835ce6dd276132b8a8a7415b10951e1cafd6144687fcf1167"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:05.303444Z","signature_b64":"4ApXRXEB+oYIisHyUufJl+/7ngj52xAcHrFQe6OHy4QvTgkZ7Jw7A3qsVSfug8SlpvLDushga1nJmvJ+jxGqBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08fe6d3f9543f71dd99e0db691ea91d4e7cc658b9de9c231f4104513978d4c1a","last_reissued_at":"2026-05-18T01:13:05.302901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:05.302901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Good covers are algorithmically unrecognizable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GT"],"primary_cat":"cs.CG","authors_text":"Dmitry Tonkonog, Martin Tancer","submitted_at":"2012-05-28T11:36:17Z","abstract_excerpt":"A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with convex sets, intersection patterns of good covers were studied intensively. Our main result is that intersection patterns of good covers are algorithmically unrecognizable.\n  More precisely, the intersection pattern of a good cover can be stored in a simplicial complex called nerve which records which subfamilies of the good cover intersect. A simplicial complex is topologically d-representable if it is isomorphic to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6082","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1205.6082","created_at":"2026-05-18T01:13:05.302967+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.6082v2","created_at":"2026-05-18T01:13:05.302967+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6082","created_at":"2026-05-18T01:13:05.302967+00:00"},{"alias_kind":"pith_short_12","alias_value":"BD7G2P4VIP3R","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"BD7G2P4VIP3R3WM6","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"BD7G2P4V","created_at":"2026-05-18T12:26:58.693483+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BD7G2P4VIP3R3WM6BW3JD2UR2T","json":"https://pith.science/pith/BD7G2P4VIP3R3WM6BW3JD2UR2T.json","graph_json":"https://pith.science/api/pith-number/BD7G2P4VIP3R3WM6BW3JD2UR2T/graph.json","events_json":"https://pith.science/api/pith-number/BD7G2P4VIP3R3WM6BW3JD2UR2T/events.json","paper":"https://pith.science/paper/BD7G2P4V"},"agent_actions":{"view_html":"https://pith.science/pith/BD7G2P4VIP3R3WM6BW3JD2UR2T","download_json":"https://pith.science/pith/BD7G2P4VIP3R3WM6BW3JD2UR2T.json","view_paper":"https://pith.science/paper/BD7G2P4V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.6082&json=true","fetch_graph":"https://pith.science/api/pith-number/BD7G2P4VIP3R3WM6BW3JD2UR2T/graph.json","fetch_events":"https://pith.science/api/pith-number/BD7G2P4VIP3R3WM6BW3JD2UR2T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BD7G2P4VIP3R3WM6BW3JD2UR2T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BD7G2P4VIP3R3WM6BW3JD2UR2T/action/storage_attestation","attest_author":"https://pith.science/pith/BD7G2P4VIP3R3WM6BW3JD2UR2T/action/author_attestation","sign_citation":"https://pith.science/pith/BD7G2P4VIP3R3WM6BW3JD2UR2T/action/citation_signature","submit_replication":"https://pith.science/pith/BD7G2P4VIP3R3WM6BW3JD2UR2T/action/replication_record"}},"created_at":"2026-05-18T01:13:05.302967+00:00","updated_at":"2026-05-18T01:13:05.302967+00:00"}