{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PXV5WVG76S5PTDELMBNYBDY6M6","short_pith_number":"pith:PXV5WVG7","canonical_record":{"source":{"id":"1907.08711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2019-07-19T22:21:21Z","cross_cats_sorted":["math.AT","math.DS","q-bio.TO"],"title_canon_sha256":"c29cfc917349e9b0a4b17f24f9f6ec36708a27a5f463766dab2ab7c0e22943fa","abstract_canon_sha256":"913678c1f4fdf511caf3181ba2992077144258a4acd8c14767deac59272457fa"},"schema_version":"1.0"},"canonical_sha256":"7debdb54dff4baf98c8b605b808f1e6791333ea7a83f112240f44dbf1b61f886","source":{"kind":"arxiv","id":"1907.08711","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08711","created_at":"2026-05-17T23:40:05Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08711v1","created_at":"2026-05-17T23:40:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08711","created_at":"2026-05-17T23:40:05Z"},{"alias_kind":"pith_short_12","alias_value":"PXV5WVG76S5P","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PXV5WVG76S5PTDEL","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PXV5WVG7","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PXV5WVG76S5PTDELMBNYBDY6M6","target":"record","payload":{"canonical_record":{"source":{"id":"1907.08711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2019-07-19T22:21:21Z","cross_cats_sorted":["math.AT","math.DS","q-bio.TO"],"title_canon_sha256":"c29cfc917349e9b0a4b17f24f9f6ec36708a27a5f463766dab2ab7c0e22943fa","abstract_canon_sha256":"913678c1f4fdf511caf3181ba2992077144258a4acd8c14767deac59272457fa"},"schema_version":"1.0"},"canonical_sha256":"7debdb54dff4baf98c8b605b808f1e6791333ea7a83f112240f44dbf1b61f886","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:05.623028Z","signature_b64":"R8nT6xuge+TZI++6Rt0sikLDFdcfHidG7k3TpfAhHZiWPc8SnxAH7LIkXolEDGVQCbhME+gKSqQc6eS4BexXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7debdb54dff4baf98c8b605b808f1e6791333ea7a83f112240f44dbf1b61f886","last_reissued_at":"2026-05-17T23:40:05.622491Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:05.622491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.08711","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":"2026-05-17T23:40:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XYLOz2k0JJ/AmbJsEA9NV37y5ggsKRc7XzHe5HqSifjSk1fIvS5e3n7Ze9Gk1cQ/lChQ3LJHusmZv5FMctooAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:13:07.274327Z"},"content_sha256":"6887c36a8da6179aceede456b462e8e94522b9f1bfe665f0cc7abe4cd8d4da18","schema_version":"1.0","event_id":"sha256:6887c36a8da6179aceede456b462e8e94522b9f1bfe665f0cc7abe4cd8d4da18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PXV5WVG76S5PTDELMBNYBDY6M6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological Methods for Characterising Spatial Networks: A Case Study in Tumour Vasculature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DS","q-bio.TO"],"primary_cat":"q-bio.QM","authors_text":"Bernadette J Stolz, Gesine Reinert, Heather A Harrington, Helen M Byrne, Ruth Muschel, Ulrike Tillmann","submitted_at":"2019-07-19T22:21:21Z","abstract_excerpt":"Understanding how the spatial structure of blood vessel networks relates to their function in healthy and abnormal biological tissues could improve diagnosis and treatment for diseases such as cancer. New imaging techniques can generate multiple, high-resolution images of the same tissue region, and show how vessel networks evolve during disease onset and treatment. Such experimental advances have created an exciting opportunity for discovering new links between vessel structure and disease through the development of mathematical tools that can analyse these rich datasets. Here we explain how "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08711","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":"2026-05-17T23:40:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JtG66HwOkGWXOWbSh0dOaPZa+lCjndpHmcboqx/NvOJ2HfrnJAzTSO83i1ep5YfbydV2eamjPjZw3RzePU1NBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:13:07.274799Z"},"content_sha256":"10dda681847ad244b3cfc20c1aff8f7625b2acbe6df9646a3ad9f19a826ad0ff","schema_version":"1.0","event_id":"sha256:10dda681847ad244b3cfc20c1aff8f7625b2acbe6df9646a3ad9f19a826ad0ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PXV5WVG76S5PTDELMBNYBDY6M6/bundle.json","state_url":"https://pith.science/pith/PXV5WVG76S5PTDELMBNYBDY6M6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PXV5WVG76S5PTDELMBNYBDY6M6/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":"2026-05-29T15:13:07Z","links":{"resolver":"https://pith.science/pith/PXV5WVG76S5PTDELMBNYBDY6M6","bundle":"https://pith.science/pith/PXV5WVG76S5PTDELMBNYBDY6M6/bundle.json","state":"https://pith.science/pith/PXV5WVG76S5PTDELMBNYBDY6M6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PXV5WVG76S5PTDELMBNYBDY6M6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PXV5WVG76S5PTDELMBNYBDY6M6","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":"913678c1f4fdf511caf3181ba2992077144258a4acd8c14767deac59272457fa","cross_cats_sorted":["math.AT","math.DS","q-bio.TO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2019-07-19T22:21:21Z","title_canon_sha256":"c29cfc917349e9b0a4b17f24f9f6ec36708a27a5f463766dab2ab7c0e22943fa"},"schema_version":"1.0","source":{"id":"1907.08711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08711","created_at":"2026-05-17T23:40:05Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08711v1","created_at":"2026-05-17T23:40:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08711","created_at":"2026-05-17T23:40:05Z"},{"alias_kind":"pith_short_12","alias_value":"PXV5WVG76S5P","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PXV5WVG76S5PTDEL","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PXV5WVG7","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:10dda681847ad244b3cfc20c1aff8f7625b2acbe6df9646a3ad9f19a826ad0ff","target":"graph","created_at":"2026-05-17T23:40:05Z","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":"Understanding how the spatial structure of blood vessel networks relates to their function in healthy and abnormal biological tissues could improve diagnosis and treatment for diseases such as cancer. New imaging techniques can generate multiple, high-resolution images of the same tissue region, and show how vessel networks evolve during disease onset and treatment. Such experimental advances have created an exciting opportunity for discovering new links between vessel structure and disease through the development of mathematical tools that can analyse these rich datasets. Here we explain how ","authors_text":"Bernadette J Stolz, Gesine Reinert, Heather A Harrington, Helen M Byrne, Ruth Muschel, Ulrike Tillmann","cross_cats":["math.AT","math.DS","q-bio.TO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2019-07-19T22:21:21Z","title":"Topological Methods for Characterising Spatial Networks: A Case Study in Tumour Vasculature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08711","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":"sha256:6887c36a8da6179aceede456b462e8e94522b9f1bfe665f0cc7abe4cd8d4da18","target":"record","created_at":"2026-05-17T23:40:05Z","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":"913678c1f4fdf511caf3181ba2992077144258a4acd8c14767deac59272457fa","cross_cats_sorted":["math.AT","math.DS","q-bio.TO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2019-07-19T22:21:21Z","title_canon_sha256":"c29cfc917349e9b0a4b17f24f9f6ec36708a27a5f463766dab2ab7c0e22943fa"},"schema_version":"1.0","source":{"id":"1907.08711","kind":"arxiv","version":1}},"canonical_sha256":"7debdb54dff4baf98c8b605b808f1e6791333ea7a83f112240f44dbf1b61f886","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7debdb54dff4baf98c8b605b808f1e6791333ea7a83f112240f44dbf1b61f886","first_computed_at":"2026-05-17T23:40:05.622491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:05.622491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R8nT6xuge+TZI++6Rt0sikLDFdcfHidG7k3TpfAhHZiWPc8SnxAH7LIkXolEDGVQCbhME+gKSqQc6eS4BexXBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:05.623028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.08711","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6887c36a8da6179aceede456b462e8e94522b9f1bfe665f0cc7abe4cd8d4da18","sha256:10dda681847ad244b3cfc20c1aff8f7625b2acbe6df9646a3ad9f19a826ad0ff"],"state_sha256":"e9863c772c43125f7423541ba4223693a1180a00e1dc40fb39c49515f12047ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"weKnmbPC3N1vSNzsUSSs1+SpZElJxA/2WSY3W4tpUxA03MPdUhJAxr2gVQACJviePrNgbMVVgQCQLsg3XpW8Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:13:07.278177Z","bundle_sha256":"8727d0aebdfaea4d83c9ef975d2d3c592786d3b8b27885b620a6aa243d2fe66f"}}