{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:3LJM4NMCWPFOOQWFUNRR52HFYC","short_pith_number":"pith:3LJM4NMC","schema_version":"1.0","canonical_sha256":"dad2ce3582b3cae742c5a3631ee8e5c08e933a059db1a2571ba2f2990f54c866","source":{"kind":"arxiv","id":"1704.05727","version":4},"attestation_state":"computed","paper":{"title":"Proximal Planar Cech Nerves. An Approach to Approximating the Shapes of Irregular, Finite, Bounded Planar Regions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"J.F. Peters","submitted_at":"2017-04-19T13:35:30Z","abstract_excerpt":"This article introduces proximal Cech nerves and Cech complexes, restricted to finite, bounded regions $K$ of the Euclidean plane. A Cech nerve is a collection of intersecting balls. A Cech complex is a collection of nerves that cover $K$. Cech nerves are proximal, provided the nerves are close to each other, either spatially or descriptively. A Cech nerve has an advantage over the usual Alexandroff nerve, since we need only identify the center and fixed radius of each ball in a Cech nerve instead of identifying the three vertices of intersecting filled triangles (2-simplexes) in an Alexandrof"},"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":"1704.05727","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-04-19T13:35:30Z","cross_cats_sorted":[],"title_canon_sha256":"a7a3b5ea350c0a0ecd047bb48c971089b07326150d398b0cb7ca64c6e1e90f82","abstract_canon_sha256":"e27b9d5807e437f89667198eeb8080b54db7d57f32bd584a6b86cc5281756305"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:41.471746Z","signature_b64":"1+LwyIe4+jOE9qSlqV4CbAfERGOSf63njiI7Y+ehpW9ZQKcOO938t2GxP4DPzO1FOaYKYpPDouDE2wuwxhCYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dad2ce3582b3cae742c5a3631ee8e5c08e933a059db1a2571ba2f2990f54c866","last_reissued_at":"2026-05-18T00:35:41.470828Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:41.470828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proximal Planar Cech Nerves. An Approach to Approximating the Shapes of Irregular, Finite, Bounded Planar Regions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"J.F. Peters","submitted_at":"2017-04-19T13:35:30Z","abstract_excerpt":"This article introduces proximal Cech nerves and Cech complexes, restricted to finite, bounded regions $K$ of the Euclidean plane. A Cech nerve is a collection of intersecting balls. A Cech complex is a collection of nerves that cover $K$. Cech nerves are proximal, provided the nerves are close to each other, either spatially or descriptively. A Cech nerve has an advantage over the usual Alexandroff nerve, since we need only identify the center and fixed radius of each ball in a Cech nerve instead of identifying the three vertices of intersecting filled triangles (2-simplexes) in an Alexandrof"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05727","kind":"arxiv","version":4},"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":"1704.05727","created_at":"2026-05-18T00:35:41.470967+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.05727v4","created_at":"2026-05-18T00:35:41.470967+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05727","created_at":"2026-05-18T00:35:41.470967+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/3LJM4NMCWPFOOQWFUNRR52HFYC","json":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC.json","graph_json":"https://pith.science/api/pith-number/3LJM4NMCWPFOOQWFUNRR52HFYC/graph.json","events_json":"https://pith.science/api/pith-number/3LJM4NMCWPFOOQWFUNRR52HFYC/events.json","paper":"https://pith.science/paper/3LJM4NMC"},"agent_actions":{"view_html":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC","download_json":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC.json","view_paper":"https://pith.science/paper/3LJM4NMC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.05727&json=true","fetch_graph":"https://pith.science/api/pith-number/3LJM4NMCWPFOOQWFUNRR52HFYC/graph.json","fetch_events":"https://pith.science/api/pith-number/3LJM4NMCWPFOOQWFUNRR52HFYC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC/action/storage_attestation","attest_author":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC/action/author_attestation","sign_citation":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC/action/citation_signature","submit_replication":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC/action/replication_record"}},"created_at":"2026-05-18T00:35:41.470967+00:00","updated_at":"2026-05-18T00:35:41.470967+00:00"}