{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HVOLZD6TFZ2YNTZ3FJ3K3X4RNK","short_pith_number":"pith:HVOLZD6T","canonical_record":{"source":{"id":"1205.1669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-05-08T12:19:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5ea669f4cb0d866e299c69792b44ea95b123e83c35902b75b404796ba48aa53f","abstract_canon_sha256":"ac0826ceed4fc8963e53c7ad38774a29cf139d07288b20bfac07ba180b31255a"},"schema_version":"1.0"},"canonical_sha256":"3d5cbc8fd32e7586cf3b2a76addf916aa283523dd85371bd4a1cdeb94319a8a7","source":{"kind":"arxiv","id":"1205.1669","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1669","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1669v1","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1669","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"HVOLZD6TFZ2Y","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HVOLZD6TFZ2YNTZ3","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HVOLZD6T","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HVOLZD6TFZ2YNTZ3FJ3K3X4RNK","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-05-08T12:19:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5ea669f4cb0d866e299c69792b44ea95b123e83c35902b75b404796ba48aa53f","abstract_canon_sha256":"ac0826ceed4fc8963e53c7ad38774a29cf139d07288b20bfac07ba180b31255a"},"schema_version":"1.0"},"canonical_sha256":"3d5cbc8fd32e7586cf3b2a76addf916aa283523dd85371bd4a1cdeb94319a8a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:09.502162Z","signature_b64":"ssXPMgjz1sWMEMxjscnCDr7YqppBbttg5STKE16MR/TYW9lsE/owGMsfrT9jo1I4MZeFC/Ey8WelUi6irg4bBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d5cbc8fd32e7586cf3b2a76addf916aa283523dd85371bd4a1cdeb94319a8a7","last_reissued_at":"2026-05-18T03:56:09.501526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:09.501526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1669","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":"2026-05-18T03:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bA0RkUk8brUDpeAaTtq+wuw8pIFtst2HtxWC1qDtl/7ELumIE38XrV3ipLuvx9PhUf51F4Tm4dOEShu+jgfMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:22:51.068380Z"},"content_sha256":"14587a256038627726a1a793a53f59ffd4a452f25a73aa1ead7b00112f365b16","schema_version":"1.0","event_id":"sha256:14587a256038627726a1a793a53f59ffd4a452f25a73aa1ead7b00112f365b16"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HVOLZD6TFZ2YNTZ3FJ3K3X4RNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Sticky Geometry of the Cosmic Web","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"astro-ph.CO","authors_text":"Bernard J.T. Jones, Gert Vegter, Johan Hidding, Monique Teillaud, Rien van de Weygaert","submitted_at":"2012-05-08T12:19:28Z","abstract_excerpt":"In this video we highlight the application of Computational Geometry to our understanding of the formation and dynamics of the Cosmic Web. The emergence of this intricate and pervasive weblike structure of the Universe on Megaparsec scales can be approximated by a well-known equation from fluid mechanics, the Burgers' equation. The solution to this equation can be obtained from a geometrical formalism. We have extended and improved this method by invoking weighted Delaunay and Voronoi tessellations. The duality between these tessellations finds a remarkable and profound reflection in the descr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1669","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":"2026-05-18T03:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XTvccjfV0AgPmFwQIVhwCoraCEPjP+5skMBkSLNt5V1+Bc87YFOI4Ym2IjYGe+cXyz5GqRn1WMpizxs2mq2vCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:22:51.069016Z"},"content_sha256":"88cc352562e68a413931b5b9c92072d19d0c8eee7e65fb53e143cddb9ee5e703","schema_version":"1.0","event_id":"sha256:88cc352562e68a413931b5b9c92072d19d0c8eee7e65fb53e143cddb9ee5e703"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HVOLZD6TFZ2YNTZ3FJ3K3X4RNK/bundle.json","state_url":"https://pith.science/pith/HVOLZD6TFZ2YNTZ3FJ3K3X4RNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HVOLZD6TFZ2YNTZ3FJ3K3X4RNK/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":"2026-05-26T14:22:51Z","links":{"resolver":"https://pith.science/pith/HVOLZD6TFZ2YNTZ3FJ3K3X4RNK","bundle":"https://pith.science/pith/HVOLZD6TFZ2YNTZ3FJ3K3X4RNK/bundle.json","state":"https://pith.science/pith/HVOLZD6TFZ2YNTZ3FJ3K3X4RNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HVOLZD6TFZ2YNTZ3FJ3K3X4RNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HVOLZD6TFZ2YNTZ3FJ3K3X4RNK","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":"ac0826ceed4fc8963e53c7ad38774a29cf139d07288b20bfac07ba180b31255a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-05-08T12:19:28Z","title_canon_sha256":"5ea669f4cb0d866e299c69792b44ea95b123e83c35902b75b404796ba48aa53f"},"schema_version":"1.0","source":{"id":"1205.1669","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1669","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1669v1","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1669","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"HVOLZD6TFZ2Y","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HVOLZD6TFZ2YNTZ3","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HVOLZD6T","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:88cc352562e68a413931b5b9c92072d19d0c8eee7e65fb53e143cddb9ee5e703","target":"graph","created_at":"2026-05-18T03:56:09Z","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":"In this video we highlight the application of Computational Geometry to our understanding of the formation and dynamics of the Cosmic Web. The emergence of this intricate and pervasive weblike structure of the Universe on Megaparsec scales can be approximated by a well-known equation from fluid mechanics, the Burgers' equation. The solution to this equation can be obtained from a geometrical formalism. We have extended and improved this method by invoking weighted Delaunay and Voronoi tessellations. The duality between these tessellations finds a remarkable and profound reflection in the descr","authors_text":"Bernard J.T. Jones, Gert Vegter, Johan Hidding, Monique Teillaud, Rien van de Weygaert","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-05-08T12:19:28Z","title":"The Sticky Geometry of the Cosmic Web"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1669","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":"sha256:14587a256038627726a1a793a53f59ffd4a452f25a73aa1ead7b00112f365b16","target":"record","created_at":"2026-05-18T03:56:09Z","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":"ac0826ceed4fc8963e53c7ad38774a29cf139d07288b20bfac07ba180b31255a","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-05-08T12:19:28Z","title_canon_sha256":"5ea669f4cb0d866e299c69792b44ea95b123e83c35902b75b404796ba48aa53f"},"schema_version":"1.0","source":{"id":"1205.1669","kind":"arxiv","version":1}},"canonical_sha256":"3d5cbc8fd32e7586cf3b2a76addf916aa283523dd85371bd4a1cdeb94319a8a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d5cbc8fd32e7586cf3b2a76addf916aa283523dd85371bd4a1cdeb94319a8a7","first_computed_at":"2026-05-18T03:56:09.501526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:09.501526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ssXPMgjz1sWMEMxjscnCDr7YqppBbttg5STKE16MR/TYW9lsE/owGMsfrT9jo1I4MZeFC/Ey8WelUi6irg4bBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:09.502162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1669","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14587a256038627726a1a793a53f59ffd4a452f25a73aa1ead7b00112f365b16","sha256:88cc352562e68a413931b5b9c92072d19d0c8eee7e65fb53e143cddb9ee5e703"],"state_sha256":"5942e7a3306b7e6cc51da2c35f606aa9f320f438a36b82b3e21380e10de01da7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QOn9sBuVcUWV5kCP0k8DxejsleD4bJTSmLRuMlCjqxzaC7MlJPEtpr/H/hceBMmazYqJyCMAI8rKHnO3OXe1Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:22:51.071813Z","bundle_sha256":"3f111054726230c499f2a95b582f1390cf2f36a0cb9f434b11b22c094ee32dab"}}