{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:H27TIXMG2CVPKO6SE3F7ULHC3C","short_pith_number":"pith:H27TIXMG","canonical_record":{"source":{"id":"2210.15584","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-10-27T16:18:10Z","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"title_canon_sha256":"d23ed84ce9c70121cc364706befba8fea986f678942587e8048f157adc87435e","abstract_canon_sha256":"5c8ae3b6064b93968307942d8cd58b2daaf470f398af586fd1c9506fb4921acf"},"schema_version":"1.0"},"canonical_sha256":"3ebf345d86d0aaf53bd226cbfa2ce2d8a41ae2c41827a5108c8805d25660736e","source":{"kind":"arxiv","id":"2210.15584","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.15584","created_at":"2026-07-05T05:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"2210.15584v1","created_at":"2026-07-05T05:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.15584","created_at":"2026-07-05T05:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"H27TIXMG2CVP","created_at":"2026-07-05T05:11:07Z"},{"alias_kind":"pith_short_16","alias_value":"H27TIXMG2CVPKO6S","created_at":"2026-07-05T05:11:07Z"},{"alias_kind":"pith_short_8","alias_value":"H27TIXMG","created_at":"2026-07-05T05:11:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:H27TIXMG2CVPKO6SE3F7ULHC3C","target":"record","payload":{"canonical_record":{"source":{"id":"2210.15584","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-10-27T16:18:10Z","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"title_canon_sha256":"d23ed84ce9c70121cc364706befba8fea986f678942587e8048f157adc87435e","abstract_canon_sha256":"5c8ae3b6064b93968307942d8cd58b2daaf470f398af586fd1c9506fb4921acf"},"schema_version":"1.0"},"canonical_sha256":"3ebf345d86d0aaf53bd226cbfa2ce2d8a41ae2c41827a5108c8805d25660736e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:11:07.962242Z","signature_b64":"N/pjjmp/iPkNOh/b1i3azIx3EeD9tQW2AdDCN2Xtc2qjmYfeOALbVMFrfOaa4M3OaGzQtoYbP84Ly1eT0SIMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ebf345d86d0aaf53bd226cbfa2ce2d8a41ae2c41827a5108c8805d25660736e","last_reissued_at":"2026-07-05T05:11:07.961838Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:11:07.961838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.15584","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":"2026-07-05T05:11:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pumxrzrUxx4sn2wjRr0nNPhnS87/uBVl3iG+Lvm0QeNde5zn0GwtDrgG2CDtbMiBuJ1gRw9APlMLLnqWBr3FDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T09:13:52.132673Z"},"content_sha256":"b5de9f3e7dc777ef071ddebc2298ff6a847486a1b5106e227931673cb653a51c","schema_version":"1.0","event_id":"sha256:b5de9f3e7dc777ef071ddebc2298ff6a847486a1b5106e227931673cb653a51c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:H27TIXMG2CVPKO6SE3F7ULHC3C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The statistical theory of the angiogenesis equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.PS"],"primary_cat":"math.AP","authors_text":"Bj\\\"orn Birnir (CNLS, Department of Mathematics, Department of Mathematics Universidad de Carlos III, Filippo Terragni (G. Mill\\'an Institute, Luis Bonilla, Madrid, Manuel Carretero, Spain), UC Santa Barbara, USA)","submitted_at":"2022-10-27T16:18:10Z","abstract_excerpt":"Angiogenesis is a multiscale process by which a primary blood vessel issues secondary vessel sprouts that reach regions lacking oxygen. Angiogenesis can be a natural process of organ growth and development or a pathological induced by a cancerous tumor. A mean field approximation for a stochastic model of angiogenesis consists of partial differential equation (PDE) for the density of active tip vessels. Addition of Gaussian and jump noise terms to this equation produces a stochastic PDE that defines an infinite dimensional L\\'evy process and is the basis of a statistical theory of angiogenesis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.15584","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.15584/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:11:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xyc3c7TXKa/uCHJsv08KHR7nicTxCTImgn1cyX/yaXbkES5bQGZDQ/5MILvtqalRx97pisamKmwt18xeDURXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T09:13:52.133293Z"},"content_sha256":"3948c683e099db3bb22af9107fa24b52fd061bada9032ea637e9774850217085","schema_version":"1.0","event_id":"sha256:3948c683e099db3bb22af9107fa24b52fd061bada9032ea637e9774850217085"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H27TIXMG2CVPKO6SE3F7ULHC3C/bundle.json","state_url":"https://pith.science/pith/H27TIXMG2CVPKO6SE3F7ULHC3C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H27TIXMG2CVPKO6SE3F7ULHC3C/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":"2026-08-12T09:13:52Z","links":{"resolver":"https://pith.science/pith/H27TIXMG2CVPKO6SE3F7ULHC3C","bundle":"https://pith.science/pith/H27TIXMG2CVPKO6SE3F7ULHC3C/bundle.json","state":"https://pith.science/pith/H27TIXMG2CVPKO6SE3F7ULHC3C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H27TIXMG2CVPKO6SE3F7ULHC3C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:H27TIXMG2CVPKO6SE3F7ULHC3C","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":"5c8ae3b6064b93968307942d8cd58b2daaf470f398af586fd1c9506fb4921acf","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-10-27T16:18:10Z","title_canon_sha256":"d23ed84ce9c70121cc364706befba8fea986f678942587e8048f157adc87435e"},"schema_version":"1.0","source":{"id":"2210.15584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.15584","created_at":"2026-07-05T05:11:07Z"},{"alias_kind":"arxiv_version","alias_value":"2210.15584v1","created_at":"2026-07-05T05:11:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.15584","created_at":"2026-07-05T05:11:07Z"},{"alias_kind":"pith_short_12","alias_value":"H27TIXMG2CVP","created_at":"2026-07-05T05:11:07Z"},{"alias_kind":"pith_short_16","alias_value":"H27TIXMG2CVPKO6S","created_at":"2026-07-05T05:11:07Z"},{"alias_kind":"pith_short_8","alias_value":"H27TIXMG","created_at":"2026-07-05T05:11:07Z"}],"graph_snapshots":[{"event_id":"sha256:3948c683e099db3bb22af9107fa24b52fd061bada9032ea637e9774850217085","target":"graph","created_at":"2026-07-05T05:11:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2210.15584/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Angiogenesis is a multiscale process by which a primary blood vessel issues secondary vessel sprouts that reach regions lacking oxygen. Angiogenesis can be a natural process of organ growth and development or a pathological induced by a cancerous tumor. A mean field approximation for a stochastic model of angiogenesis consists of partial differential equation (PDE) for the density of active tip vessels. Addition of Gaussian and jump noise terms to this equation produces a stochastic PDE that defines an infinite dimensional L\\'evy process and is the basis of a statistical theory of angiogenesis","authors_text":"Bj\\\"orn Birnir (CNLS, Department of Mathematics, Department of Mathematics Universidad de Carlos III, Filippo Terragni (G. Mill\\'an Institute, Luis Bonilla, Madrid, Manuel Carretero, Spain), UC Santa Barbara, USA)","cross_cats":["math-ph","math.MP","nlin.PS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-10-27T16:18:10Z","title":"The statistical theory of the angiogenesis equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.15584","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:b5de9f3e7dc777ef071ddebc2298ff6a847486a1b5106e227931673cb653a51c","target":"record","created_at":"2026-07-05T05:11:07Z","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":"5c8ae3b6064b93968307942d8cd58b2daaf470f398af586fd1c9506fb4921acf","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-10-27T16:18:10Z","title_canon_sha256":"d23ed84ce9c70121cc364706befba8fea986f678942587e8048f157adc87435e"},"schema_version":"1.0","source":{"id":"2210.15584","kind":"arxiv","version":1}},"canonical_sha256":"3ebf345d86d0aaf53bd226cbfa2ce2d8a41ae2c41827a5108c8805d25660736e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ebf345d86d0aaf53bd226cbfa2ce2d8a41ae2c41827a5108c8805d25660736e","first_computed_at":"2026-07-05T05:11:07.961838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:11:07.961838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N/pjjmp/iPkNOh/b1i3azIx3EeD9tQW2AdDCN2Xtc2qjmYfeOALbVMFrfOaa4M3OaGzQtoYbP84Ly1eT0SIMDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:11:07.962242Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.15584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5de9f3e7dc777ef071ddebc2298ff6a847486a1b5106e227931673cb653a51c","sha256:3948c683e099db3bb22af9107fa24b52fd061bada9032ea637e9774850217085"],"state_sha256":"d46a046377d30a542b2e4692b1be2187b193e5378b52f163e74b152d53b0d183"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jG5ZhsQziMaHY96+t5RSQBnDj0TyTCaSo78ba9MaKio/bPD3+5y4VSoWLC1U+phlvl2vpK+5vL1661mqiCJJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T09:13:52.137101Z","bundle_sha256":"e91426d6338934d14773ba9f6f6d2b82a8cff1f8d25bb3333e4adc852660ef16"}}