{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3LJM4NMCWPFOOQWFUNRR52HFYC","short_pith_number":"pith:3LJM4NMC","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"},"canonical_sha256":"dad2ce3582b3cae742c5a3631ee8e5c08e933a059db1a2571ba2f2990f54c866","source":{"kind":"arxiv","id":"1704.05727","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05727","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05727v4","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05727","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"pith_short_12","alias_value":"3LJM4NMCWPFO","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3LJM4NMCWPFOOQWF","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3LJM4NMC","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3LJM4NMCWPFOOQWFUNRR52HFYC","target":"record","payload":{"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"},"canonical_sha256":"dad2ce3582b3cae742c5a3631ee8e5c08e933a059db1a2571ba2f2990f54c866","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"},"source_kind":"arxiv","source_id":"1704.05727","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dTVvNqBzBIZdTXJdnQQpscPavxgJA3lhpJBcZqMJcAM5XsMfa9jiYned9aT256ozvmLx3Z8nGPm4UYcZ+s2lDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:21:54.626658Z"},"content_sha256":"760baad6e4f2cb92f414a7cfbc0426d70db81c8508b2a82c740c9949f913b9e0","schema_version":"1.0","event_id":"sha256:760baad6e4f2cb92f414a7cfbc0426d70db81c8508b2a82c740c9949f913b9e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3LJM4NMCWPFOOQWFUNRR52HFYC","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqmHJ+LiWqMdhuo/6jaIryO6Z5t+cVBE9VRLB0lxZolQC0WyITzhEDksjCPrSkc7vEdgMKbhjlVqdX9uBKTDDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:21:54.627005Z"},"content_sha256":"e1a93ee2036bf92e661001978c9bedccb3ce4705909eefa91e1da228e04bccf4","schema_version":"1.0","event_id":"sha256:e1a93ee2036bf92e661001978c9bedccb3ce4705909eefa91e1da228e04bccf4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC/bundle.json","state_url":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LJM4NMCWPFOOQWFUNRR52HFYC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T13:21:54Z","links":{"resolver":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC","bundle":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC/bundle.json","state":"https://pith.science/pith/3LJM4NMCWPFOOQWFUNRR52HFYC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LJM4NMCWPFOOQWFUNRR52HFYC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3LJM4NMCWPFOOQWFUNRR52HFYC","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":"e27b9d5807e437f89667198eeb8080b54db7d57f32bd584a6b86cc5281756305","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-04-19T13:35:30Z","title_canon_sha256":"a7a3b5ea350c0a0ecd047bb48c971089b07326150d398b0cb7ca64c6e1e90f82"},"schema_version":"1.0","source":{"id":"1704.05727","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05727","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05727v4","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05727","created_at":"2026-05-18T00:35:41Z"},{"alias_kind":"pith_short_12","alias_value":"3LJM4NMCWPFO","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3LJM4NMCWPFOOQWF","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3LJM4NMC","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:e1a93ee2036bf92e661001978c9bedccb3ce4705909eefa91e1da228e04bccf4","target":"graph","created_at":"2026-05-18T00:35:41Z","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":"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","authors_text":"J.F. Peters","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-04-19T13:35:30Z","title":"Proximal Planar Cech Nerves. An Approach to Approximating the Shapes of Irregular, Finite, Bounded Planar Regions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05727","kind":"arxiv","version":4},"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":"sha256:760baad6e4f2cb92f414a7cfbc0426d70db81c8508b2a82c740c9949f913b9e0","target":"record","created_at":"2026-05-18T00:35:41Z","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":"e27b9d5807e437f89667198eeb8080b54db7d57f32bd584a6b86cc5281756305","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-04-19T13:35:30Z","title_canon_sha256":"a7a3b5ea350c0a0ecd047bb48c971089b07326150d398b0cb7ca64c6e1e90f82"},"schema_version":"1.0","source":{"id":"1704.05727","kind":"arxiv","version":4}},"canonical_sha256":"dad2ce3582b3cae742c5a3631ee8e5c08e933a059db1a2571ba2f2990f54c866","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dad2ce3582b3cae742c5a3631ee8e5c08e933a059db1a2571ba2f2990f54c866","first_computed_at":"2026-05-18T00:35:41.470828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:41.470828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1+LwyIe4+jOE9qSlqV4CbAfERGOSf63njiI7Y+ehpW9ZQKcOO938t2GxP4DPzO1FOaYKYpPDouDE2wuwxhCYCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:41.471746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05727","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:760baad6e4f2cb92f414a7cfbc0426d70db81c8508b2a82c740c9949f913b9e0","sha256:e1a93ee2036bf92e661001978c9bedccb3ce4705909eefa91e1da228e04bccf4"],"state_sha256":"e1365e11ce7991c10b693332948a4ad9bf0b407d20a9c5a8bd33a77418c891cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BsYPFPcrkIz5Wys5szpYQP14W4EbcCdnhEnLw5ATU66PbJDSrB+pxZTuzBRZ3d71SeiXRo9JgrNGGSvFzCjRDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T13:21:54.629196Z","bundle_sha256":"e26a632e96fea3e5ae8005733d914e05a17a235c42e41a0cdeeb5c12d6e4f800"}}