{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DHGNJJB6ONNNNMOJSP3EJY5OJ2","short_pith_number":"pith:DHGNJJB6","canonical_record":{"source":{"id":"1604.03302","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-04-12T08:45:43Z","cross_cats_sorted":[],"title_canon_sha256":"a135d1e26587eb7fad9dcf62eb0094ce873e6949ae26aa22dd1e369b5e23f7f3","abstract_canon_sha256":"7f4b01de4a4e7c0a7faeafa6570bf8538f83e0eb48022339a4a18798170ba954"},"schema_version":"1.0"},"canonical_sha256":"19ccd4a43e735ad6b1c993f644e3ae4eb3050cfeaa7cffe8f3586b163f87b283","source":{"kind":"arxiv","id":"1604.03302","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03302","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03302v2","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03302","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"DHGNJJB6ONNN","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DHGNJJB6ONNNNMOJ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DHGNJJB6","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DHGNJJB6ONNNNMOJSP3EJY5OJ2","target":"record","payload":{"canonical_record":{"source":{"id":"1604.03302","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-04-12T08:45:43Z","cross_cats_sorted":[],"title_canon_sha256":"a135d1e26587eb7fad9dcf62eb0094ce873e6949ae26aa22dd1e369b5e23f7f3","abstract_canon_sha256":"7f4b01de4a4e7c0a7faeafa6570bf8538f83e0eb48022339a4a18798170ba954"},"schema_version":"1.0"},"canonical_sha256":"19ccd4a43e735ad6b1c993f644e3ae4eb3050cfeaa7cffe8f3586b163f87b283","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:59.194539Z","signature_b64":"VPLWKRm78FSpLXIeb0JMbchc/zTcImxfeiljOoumLJcQvb7M4yMlhsWWACQLOG8hkRosV1hX7WwxiD992lXIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19ccd4a43e735ad6b1c993f644e3ae4eb3050cfeaa7cffe8f3586b163f87b283","last_reissued_at":"2026-05-18T01:16:59.193809Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:59.193809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.03302","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4rUUqc78tDq/ZqUzZ/PGyzefvqmekesppX3/g7+iDEj0TnHPCKrjYLtqzrc0P1TEkC7g2SbrjCVb37uFF4RkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:05:52.611993Z"},"content_sha256":"2e8d7e7e3a0ff38c500ffeef5479a205f7320560c21489d633a5a3bd4baaaa43","schema_version":"1.0","event_id":"sha256:2e8d7e7e3a0ff38c500ffeef5479a205f7320560c21489d633a5a3bd4baaaa43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DHGNJJB6ONNNNMOJSP3EJY5OJ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homotopy equivalence between Voronoi medusa and Delaunay medusa","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Michael Kerber, Siddharth Pritam","submitted_at":"2016-04-12T08:45:43Z","abstract_excerpt":"We trace movements of certain points in space-time along their corresponding continuous path. We partition the space at every moment of time using alpha-Complexes, Voronoi medusa is then the collection or union of restricted Voronoi cells at every moment in time. We can imagine them as a four dimensional structure formed when three dimensional restricted Voronoi cells sweeps continuously through the extra dimension of time. Similarly Delaunay medusa is the collection of the corresponding Delaunay triangulations at each moment in time. In this article we prove that these two structures are homo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03302","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l8bmJRcpjBNW8Oc8QlE6TB8lsxSVRpZQM6NqFBXV41RblZHnqfW1J0Fm9o2AdR5WjALUmNfsaoMMk0kb3XRwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T16:05:52.612356Z"},"content_sha256":"d04f8a849e23236341b767dd4ba4c34512843c477906f6757277008435dff4cc","schema_version":"1.0","event_id":"sha256:d04f8a849e23236341b767dd4ba4c34512843c477906f6757277008435dff4cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DHGNJJB6ONNNNMOJSP3EJY5OJ2/bundle.json","state_url":"https://pith.science/pith/DHGNJJB6ONNNNMOJSP3EJY5OJ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DHGNJJB6ONNNNMOJSP3EJY5OJ2/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":"2026-06-26T16:05:52Z","links":{"resolver":"https://pith.science/pith/DHGNJJB6ONNNNMOJSP3EJY5OJ2","bundle":"https://pith.science/pith/DHGNJJB6ONNNNMOJSP3EJY5OJ2/bundle.json","state":"https://pith.science/pith/DHGNJJB6ONNNNMOJSP3EJY5OJ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DHGNJJB6ONNNNMOJSP3EJY5OJ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DHGNJJB6ONNNNMOJSP3EJY5OJ2","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":"7f4b01de4a4e7c0a7faeafa6570bf8538f83e0eb48022339a4a18798170ba954","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-04-12T08:45:43Z","title_canon_sha256":"a135d1e26587eb7fad9dcf62eb0094ce873e6949ae26aa22dd1e369b5e23f7f3"},"schema_version":"1.0","source":{"id":"1604.03302","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.03302","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"arxiv_version","alias_value":"1604.03302v2","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.03302","created_at":"2026-05-18T01:16:59Z"},{"alias_kind":"pith_short_12","alias_value":"DHGNJJB6ONNN","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DHGNJJB6ONNNNMOJ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DHGNJJB6","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:d04f8a849e23236341b767dd4ba4c34512843c477906f6757277008435dff4cc","target":"graph","created_at":"2026-05-18T01:16:59Z","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":"We trace movements of certain points in space-time along their corresponding continuous path. We partition the space at every moment of time using alpha-Complexes, Voronoi medusa is then the collection or union of restricted Voronoi cells at every moment in time. We can imagine them as a four dimensional structure formed when three dimensional restricted Voronoi cells sweeps continuously through the extra dimension of time. Similarly Delaunay medusa is the collection of the corresponding Delaunay triangulations at each moment in time. In this article we prove that these two structures are homo","authors_text":"Michael Kerber, Siddharth Pritam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-04-12T08:45:43Z","title":"Homotopy equivalence between Voronoi medusa and Delaunay medusa"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03302","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":"sha256:2e8d7e7e3a0ff38c500ffeef5479a205f7320560c21489d633a5a3bd4baaaa43","target":"record","created_at":"2026-05-18T01:16:59Z","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":"7f4b01de4a4e7c0a7faeafa6570bf8538f83e0eb48022339a4a18798170ba954","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-04-12T08:45:43Z","title_canon_sha256":"a135d1e26587eb7fad9dcf62eb0094ce873e6949ae26aa22dd1e369b5e23f7f3"},"schema_version":"1.0","source":{"id":"1604.03302","kind":"arxiv","version":2}},"canonical_sha256":"19ccd4a43e735ad6b1c993f644e3ae4eb3050cfeaa7cffe8f3586b163f87b283","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19ccd4a43e735ad6b1c993f644e3ae4eb3050cfeaa7cffe8f3586b163f87b283","first_computed_at":"2026-05-18T01:16:59.193809Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:59.193809Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VPLWKRm78FSpLXIeb0JMbchc/zTcImxfeiljOoumLJcQvb7M4yMlhsWWACQLOG8hkRosV1hX7WwxiD992lXIDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:59.194539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.03302","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e8d7e7e3a0ff38c500ffeef5479a205f7320560c21489d633a5a3bd4baaaa43","sha256:d04f8a849e23236341b767dd4ba4c34512843c477906f6757277008435dff4cc"],"state_sha256":"c016c65e35f86f3a7af0fc062ff4d2de159881c207649733ecb1d40780182ee7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rPYnqKkIPYyJP+eNnybgzwDsTYhKfOGP4/VToO2JkFEtJKE3OY1XleIHUq5CELWouIGQRosr7rylACEcelFzDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T16:05:52.614289Z","bundle_sha256":"6eb3b0b933e8269afae9caf8f88392ebf05f7428df3c6fe98a2179cfaffdb2f9"}}