{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BRCRCPJ673S5ZZHZUP5CZT3V6S","short_pith_number":"pith:BRCRCPJ6","canonical_record":{"source":{"id":"1304.0662","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-04-02T15:11:23Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"afd646ca8a4df89de6678c199b619b125a236ff0ede82ddfca65f6e6594447a3","abstract_canon_sha256":"cbfd2b2a841fd4dd87f54a76e50d8b5ac95091c3b10024406a475f41f0f4f22b"},"schema_version":"1.0"},"canonical_sha256":"0c45113d3efee5dce4f9a3fa2ccf75f4ae80dcc4b1718e84d33ea6d45a3bc209","source":{"kind":"arxiv","id":"1304.0662","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0662","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0662v1","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0662","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"BRCRCPJ673S5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BRCRCPJ673S5ZZHZ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BRCRCPJ6","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BRCRCPJ673S5ZZHZUP5CZT3V6S","target":"record","payload":{"canonical_record":{"source":{"id":"1304.0662","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-04-02T15:11:23Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"afd646ca8a4df89de6678c199b619b125a236ff0ede82ddfca65f6e6594447a3","abstract_canon_sha256":"cbfd2b2a841fd4dd87f54a76e50d8b5ac95091c3b10024406a475f41f0f4f22b"},"schema_version":"1.0"},"canonical_sha256":"0c45113d3efee5dce4f9a3fa2ccf75f4ae80dcc4b1718e84d33ea6d45a3bc209","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:14.709517Z","signature_b64":"zych/+7DFcivl31eZemcvamsf+OydozITxSX2U6DwL8c5gnmxpXRh7ZhfLt5wtOX0QSSu6jmlOAYC3e8nmEiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c45113d3efee5dce4f9a3fa2ccf75f4ae80dcc4b1718e84d33ea6d45a3bc209","last_reissued_at":"2026-05-18T03:29:14.708659Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:14.708659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.0662","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sgzUPZQTKWnYSK0bUMQFnnV4nH9gyvLebJKFTegcn0FuPYI9+y32g9dqPFMT9MXeZIobv70CK5eC9L3NA66tBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:42:59.534139Z"},"content_sha256":"25141dbc8dfc5b2a16c74c8a44b77d0a0c7540e7f0fce7feafdb9d9501df5f82","schema_version":"1.0","event_id":"sha256:25141dbc8dfc5b2a16c74c8a44b77d0a0c7540e7f0fce7feafdb9d9501df5f82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BRCRCPJ673S5ZZHZUP5CZT3V6S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph Induced Complex on Point Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"cs.CG","authors_text":"Fengtao Fan, Tamal K. Dey, Yusu Wang","submitted_at":"2013-04-02T15:11:23Z","abstract_excerpt":"The efficiency of extracting topological information from point data depends largely on the complex that is built on top of the data points. From a computational viewpoint, the most favored complexes for this purpose have so far been Vietoris-Rips and witness complexes. While the Vietoris-Rips complex is simple to compute and is a good vehicle for extracting topology of sampled spaces, its size is huge--particularly in high dimensions. The witness complex on the other hand enjoys a smaller size because of a subsampling, but fails to capture the topology in high dimensions unless imposed with e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0662","kind":"arxiv","version":1},"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":"2026-05-18T03:29:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5PU3QGzNqkZBBZykgm3/QbbfpGUyl2xx9tNlqVZq03pOsTpkB+Et5t/lA9EAYTQ3dQZeX6ZqrfmyoqM84UTvBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:42:59.534812Z"},"content_sha256":"9b4deaf364b3d476b360e872013450f6d11bc494575c0f63997f1071f0ec3fca","schema_version":"1.0","event_id":"sha256:9b4deaf364b3d476b360e872013450f6d11bc494575c0f63997f1071f0ec3fca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BRCRCPJ673S5ZZHZUP5CZT3V6S/bundle.json","state_url":"https://pith.science/pith/BRCRCPJ673S5ZZHZUP5CZT3V6S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BRCRCPJ673S5ZZHZUP5CZT3V6S/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":"2026-05-26T14:42:59Z","links":{"resolver":"https://pith.science/pith/BRCRCPJ673S5ZZHZUP5CZT3V6S","bundle":"https://pith.science/pith/BRCRCPJ673S5ZZHZUP5CZT3V6S/bundle.json","state":"https://pith.science/pith/BRCRCPJ673S5ZZHZUP5CZT3V6S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BRCRCPJ673S5ZZHZUP5CZT3V6S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BRCRCPJ673S5ZZHZUP5CZT3V6S","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":"cbfd2b2a841fd4dd87f54a76e50d8b5ac95091c3b10024406a475f41f0f4f22b","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-04-02T15:11:23Z","title_canon_sha256":"afd646ca8a4df89de6678c199b619b125a236ff0ede82ddfca65f6e6594447a3"},"schema_version":"1.0","source":{"id":"1304.0662","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.0662","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"1304.0662v1","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.0662","created_at":"2026-05-18T03:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"BRCRCPJ673S5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BRCRCPJ673S5ZZHZ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BRCRCPJ6","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:9b4deaf364b3d476b360e872013450f6d11bc494575c0f63997f1071f0ec3fca","target":"graph","created_at":"2026-05-18T03:29:14Z","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":"The efficiency of extracting topological information from point data depends largely on the complex that is built on top of the data points. From a computational viewpoint, the most favored complexes for this purpose have so far been Vietoris-Rips and witness complexes. While the Vietoris-Rips complex is simple to compute and is a good vehicle for extracting topology of sampled spaces, its size is huge--particularly in high dimensions. The witness complex on the other hand enjoys a smaller size because of a subsampling, but fails to capture the topology in high dimensions unless imposed with e","authors_text":"Fengtao Fan, Tamal K. Dey, Yusu Wang","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-04-02T15:11:23Z","title":"Graph Induced Complex on Point Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0662","kind":"arxiv","version":1},"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":"sha256:25141dbc8dfc5b2a16c74c8a44b77d0a0c7540e7f0fce7feafdb9d9501df5f82","target":"record","created_at":"2026-05-18T03:29:14Z","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":"cbfd2b2a841fd4dd87f54a76e50d8b5ac95091c3b10024406a475f41f0f4f22b","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-04-02T15:11:23Z","title_canon_sha256":"afd646ca8a4df89de6678c199b619b125a236ff0ede82ddfca65f6e6594447a3"},"schema_version":"1.0","source":{"id":"1304.0662","kind":"arxiv","version":1}},"canonical_sha256":"0c45113d3efee5dce4f9a3fa2ccf75f4ae80dcc4b1718e84d33ea6d45a3bc209","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c45113d3efee5dce4f9a3fa2ccf75f4ae80dcc4b1718e84d33ea6d45a3bc209","first_computed_at":"2026-05-18T03:29:14.708659Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:14.708659Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zych/+7DFcivl31eZemcvamsf+OydozITxSX2U6DwL8c5gnmxpXRh7ZhfLt5wtOX0QSSu6jmlOAYC3e8nmEiDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:14.709517Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.0662","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25141dbc8dfc5b2a16c74c8a44b77d0a0c7540e7f0fce7feafdb9d9501df5f82","sha256:9b4deaf364b3d476b360e872013450f6d11bc494575c0f63997f1071f0ec3fca"],"state_sha256":"cc4ed7b0e05d74cc6af65bf697b09334361bb0ced239a0678f2272fe50c4a408"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0WbWTml6/VGnY2qk0TQL67uekIQ/Ai1a43sGV3+v1Yzg3EVWlRbIRCIBHpDyzMqC8VoyoYz0QjSyEn7bBKNPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:42:59.538280Z","bundle_sha256":"f6b1d24dfe353f85b22e6247fd42fa25a26593fdcf52f816237eb36670627828"}}