{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UD52ISTIBV7SMXVQJREK5UMFPJ","short_pith_number":"pith:UD52ISTI","canonical_record":{"source":{"id":"2401.04954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-01-10T06:38:15Z","cross_cats_sorted":["cs.NA","math.NA","q-bio.TO"],"title_canon_sha256":"ef78f8f0e3fa26c268b74bb645f639ed107d9fe0b8a317ed2ebd3f5c3e93dfbf","abstract_canon_sha256":"1db30adfdafb3e4ccec47875ea7f0b150e285daa18c4f66fbc4b1052ba02e899"},"schema_version":"1.0"},"canonical_sha256":"a0fba44a680d7f265eb04c48aed1857a5b909117f1e15d728277ead98538a7d8","source":{"kind":"arxiv","id":"2401.04954","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.04954","created_at":"2026-07-05T07:32:01Z"},{"alias_kind":"arxiv_version","alias_value":"2401.04954v1","created_at":"2026-07-05T07:32:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.04954","created_at":"2026-07-05T07:32:01Z"},{"alias_kind":"pith_short_12","alias_value":"UD52ISTIBV7S","created_at":"2026-07-05T07:32:01Z"},{"alias_kind":"pith_short_16","alias_value":"UD52ISTIBV7SMXVQ","created_at":"2026-07-05T07:32:01Z"},{"alias_kind":"pith_short_8","alias_value":"UD52ISTI","created_at":"2026-07-05T07:32:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UD52ISTIBV7SMXVQJREK5UMFPJ","target":"record","payload":{"canonical_record":{"source":{"id":"2401.04954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-01-10T06:38:15Z","cross_cats_sorted":["cs.NA","math.NA","q-bio.TO"],"title_canon_sha256":"ef78f8f0e3fa26c268b74bb645f639ed107d9fe0b8a317ed2ebd3f5c3e93dfbf","abstract_canon_sha256":"1db30adfdafb3e4ccec47875ea7f0b150e285daa18c4f66fbc4b1052ba02e899"},"schema_version":"1.0"},"canonical_sha256":"a0fba44a680d7f265eb04c48aed1857a5b909117f1e15d728277ead98538a7d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:32:01.044671Z","signature_b64":"rf2Ob7DFWsPiQDrrHJKFHjYVrwMzWzAZ4mEONRlH1TquWX3S6MCF1u9bpx0OR078EEeplIxmm6vfV9TlKIHKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0fba44a680d7f265eb04c48aed1857a5b909117f1e15d728277ead98538a7d8","last_reissued_at":"2026-07-05T07:32:01.044133Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:32:01.044133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.04954","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":"2026-07-05T07:32:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N2DGqgEjAXmG8ToW0nxPwP98T9Ay+AMRqTJHQzVaEmHEFtGzAiYTCiStnyO9tgAhob2qxqIZuxqSezVKDcXQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T01:08:09.172085Z"},"content_sha256":"09a61cdcacb97f8955ab7372be7e03553efe679bcabc61ae837b0c3f21f8ac38","schema_version":"1.0","event_id":"sha256:09a61cdcacb97f8955ab7372be7e03553efe679bcabc61ae837b0c3f21f8ac38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UD52ISTIBV7SMXVQJREK5UMFPJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Three-dimensional tumor growth model and its boundary instability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","q-bio.TO"],"primary_cat":"math.AP","authors_text":"Jian-Guo Liu, Jiaqi Zhang, Thomas Witelski, Xiaoqian Xu","submitted_at":"2024-01-10T06:38:15Z","abstract_excerpt":"In this paper, we investigate the tumor instability by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented in a prior study by Feng et al 2023. Building upon the insights derived from the analytical reconstruction of key results in the aforementioned work in one dimension (1D) and two dimensions (2D), we extend our analysis to three dimensions (3D). Specifically, we focus on the determination of boundary instability using perturbation and asymptotic analysis along with spherical harmonics. Additionally, we have validated "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04954","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/2401.04954/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":"2026-07-05T07:32:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6L9pibcloD/skDKNQOaaeii8ASHdZQu6iY+/FF3dLxgcnztL5cB+TlYSDTbN/v+sTd6SA2skpmgO7bvBi9Y1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T01:08:09.172781Z"},"content_sha256":"41731a8e7aef31ac270d5a153c75a1e38239c277db14a132a5f08f603078a7ef","schema_version":"1.0","event_id":"sha256:41731a8e7aef31ac270d5a153c75a1e38239c277db14a132a5f08f603078a7ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UD52ISTIBV7SMXVQJREK5UMFPJ/bundle.json","state_url":"https://pith.science/pith/UD52ISTIBV7SMXVQJREK5UMFPJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UD52ISTIBV7SMXVQJREK5UMFPJ/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":"2026-08-24T01:08:09Z","links":{"resolver":"https://pith.science/pith/UD52ISTIBV7SMXVQJREK5UMFPJ","bundle":"https://pith.science/pith/UD52ISTIBV7SMXVQJREK5UMFPJ/bundle.json","state":"https://pith.science/pith/UD52ISTIBV7SMXVQJREK5UMFPJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UD52ISTIBV7SMXVQJREK5UMFPJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UD52ISTIBV7SMXVQJREK5UMFPJ","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":"1db30adfdafb3e4ccec47875ea7f0b150e285daa18c4f66fbc4b1052ba02e899","cross_cats_sorted":["cs.NA","math.NA","q-bio.TO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-01-10T06:38:15Z","title_canon_sha256":"ef78f8f0e3fa26c268b74bb645f639ed107d9fe0b8a317ed2ebd3f5c3e93dfbf"},"schema_version":"1.0","source":{"id":"2401.04954","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.04954","created_at":"2026-07-05T07:32:01Z"},{"alias_kind":"arxiv_version","alias_value":"2401.04954v1","created_at":"2026-07-05T07:32:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.04954","created_at":"2026-07-05T07:32:01Z"},{"alias_kind":"pith_short_12","alias_value":"UD52ISTIBV7S","created_at":"2026-07-05T07:32:01Z"},{"alias_kind":"pith_short_16","alias_value":"UD52ISTIBV7SMXVQ","created_at":"2026-07-05T07:32:01Z"},{"alias_kind":"pith_short_8","alias_value":"UD52ISTI","created_at":"2026-07-05T07:32:01Z"}],"graph_snapshots":[{"event_id":"sha256:41731a8e7aef31ac270d5a153c75a1e38239c277db14a132a5f08f603078a7ef","target":"graph","created_at":"2026-07-05T07:32:01Z","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/2401.04954/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the tumor instability by employing both analytical and numerical techniques to validate previous results and extend the analytical findings presented in a prior study by Feng et al 2023. Building upon the insights derived from the analytical reconstruction of key results in the aforementioned work in one dimension (1D) and two dimensions (2D), we extend our analysis to three dimensions (3D). Specifically, we focus on the determination of boundary instability using perturbation and asymptotic analysis along with spherical harmonics. Additionally, we have validated ","authors_text":"Jian-Guo Liu, Jiaqi Zhang, Thomas Witelski, Xiaoqian Xu","cross_cats":["cs.NA","math.NA","q-bio.TO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-01-10T06:38:15Z","title":"A Three-dimensional tumor growth model and its boundary instability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04954","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":"sha256:09a61cdcacb97f8955ab7372be7e03553efe679bcabc61ae837b0c3f21f8ac38","target":"record","created_at":"2026-07-05T07:32:01Z","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":"1db30adfdafb3e4ccec47875ea7f0b150e285daa18c4f66fbc4b1052ba02e899","cross_cats_sorted":["cs.NA","math.NA","q-bio.TO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-01-10T06:38:15Z","title_canon_sha256":"ef78f8f0e3fa26c268b74bb645f639ed107d9fe0b8a317ed2ebd3f5c3e93dfbf"},"schema_version":"1.0","source":{"id":"2401.04954","kind":"arxiv","version":1}},"canonical_sha256":"a0fba44a680d7f265eb04c48aed1857a5b909117f1e15d728277ead98538a7d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0fba44a680d7f265eb04c48aed1857a5b909117f1e15d728277ead98538a7d8","first_computed_at":"2026-07-05T07:32:01.044133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:32:01.044133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rf2Ob7DFWsPiQDrrHJKFHjYVrwMzWzAZ4mEONRlH1TquWX3S6MCF1u9bpx0OR078EEeplIxmm6vfV9TlKIHKCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:32:01.044671Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.04954","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09a61cdcacb97f8955ab7372be7e03553efe679bcabc61ae837b0c3f21f8ac38","sha256:41731a8e7aef31ac270d5a153c75a1e38239c277db14a132a5f08f603078a7ef"],"state_sha256":"f0150a4749468948219f22166b4a8ca4b3bb56657e839934c0099dd17649bf7c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aHq5A5qOJw5wreUbXLuPdmJ6Eok4zHmziOZl27bmciiDSCc98cRfP+ejzewD2Ez9DcJqMGHHCwFLOMADAYffDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T01:08:09.178325Z","bundle_sha256":"269984267a733fb87c0b6114306b446c2d4e55b0d3bb38c3fd2ad0dd85a06bb9"}}