{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:HXHIL7RBJ4YVUG3Q2FLLUWVN2E","short_pith_number":"pith:HXHIL7RB","canonical_record":{"source":{"id":"2108.03737","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2021-08-08T21:23:48Z","cross_cats_sorted":[],"title_canon_sha256":"6c6616ab3e2842e0dffd63863ce8d20c7b4a8ab55b0509fb915592c97c5f67de","abstract_canon_sha256":"79db50235326c9a7f52e84fffc01f1dd023353e79928d9dd419b107423d5c577"},"schema_version":"1.0"},"canonical_sha256":"3dce85fe214f315a1b70d156ba5aadd13a2da2fc3e77aff09d0e43008503739d","source":{"kind":"arxiv","id":"2108.03737","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.03737","created_at":"2026-07-05T03:04:09Z"},{"alias_kind":"arxiv_version","alias_value":"2108.03737v1","created_at":"2026-07-05T03:04:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.03737","created_at":"2026-07-05T03:04:09Z"},{"alias_kind":"pith_short_12","alias_value":"HXHIL7RBJ4YV","created_at":"2026-07-05T03:04:09Z"},{"alias_kind":"pith_short_16","alias_value":"HXHIL7RBJ4YVUG3Q","created_at":"2026-07-05T03:04:09Z"},{"alias_kind":"pith_short_8","alias_value":"HXHIL7RB","created_at":"2026-07-05T03:04:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:HXHIL7RBJ4YVUG3Q2FLLUWVN2E","target":"record","payload":{"canonical_record":{"source":{"id":"2108.03737","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2021-08-08T21:23:48Z","cross_cats_sorted":[],"title_canon_sha256":"6c6616ab3e2842e0dffd63863ce8d20c7b4a8ab55b0509fb915592c97c5f67de","abstract_canon_sha256":"79db50235326c9a7f52e84fffc01f1dd023353e79928d9dd419b107423d5c577"},"schema_version":"1.0"},"canonical_sha256":"3dce85fe214f315a1b70d156ba5aadd13a2da2fc3e77aff09d0e43008503739d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:04:09.042420Z","signature_b64":"7t1uhkMsHQKAXxGD/HeTgWvWjDM0Za4W34YlJozJPAOsIH5rO6rbmCzRbFTJ/BvqaSXDb+XEeTZM5sllE2M4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dce85fe214f315a1b70d156ba5aadd13a2da2fc3e77aff09d0e43008503739d","last_reissued_at":"2026-07-05T03:04:09.042079Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:04:09.042079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2108.03737","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":"2026-07-05T03:04:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8l1scLNvkv9qjDU/UWJzeHbyeh8dxoWJ+RKwyrHKYEsv3RJ8OCOAZFYaibX+Z6fBDOAiK5bmOTzJLVm2kOsGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T04:27:29.038685Z"},"content_sha256":"8237126ab02a1be8e93b10501b2796197136386ebcea9ad3ef98b7abb70bdc29","schema_version":"1.0","event_id":"sha256:8237126ab02a1be8e93b10501b2796197136386ebcea9ad3ef98b7abb70bdc29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:HXHIL7RBJ4YVUG3Q2FLLUWVN2E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mathematical modelling of glioblastomas invasion within the brain: a 3D multi-scale moving-boundary approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dumitru Trucu, J. Douglas Steele, Kismet Hossain-Ibrahim, Raluca Eftimie, Szabolcs Suveges","submitted_at":"2021-08-08T21:23:48Z","abstract_excerpt":"Brain-related experiments are limited by nature, and so biological insights are often restricted or absent. This is particularly problematic in the context of brain cancers, which have very poor survival rates. To generate and test new biological hypotheses, researchers started using mathematical models that can simulate tumour evolution. However, most of these models focus on single-scale 2D cell dynamics, and cannot capture the complex multi-scale tumour invasion patterns in 3D brains. A particular role in these invasion patterns is likely played by the distribution of micro-fibres. To inves"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.03737","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/2108.03737/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":"2026-07-05T03:04:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KEERGxy079A1nnHI8whzaiddogbrVHXgJGMLl5vyIL6YXn0jd8dl/6oFl3znLDMQX/sgP+nyWxKu7Fi7eJwMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-17T04:27:29.039037Z"},"content_sha256":"aeb5b1e5f76391b3cf06bd4d4d60dd956a07ea0b5bc61afaf024eb2f2f878146","schema_version":"1.0","event_id":"sha256:aeb5b1e5f76391b3cf06bd4d4d60dd956a07ea0b5bc61afaf024eb2f2f878146"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HXHIL7RBJ4YVUG3Q2FLLUWVN2E/bundle.json","state_url":"https://pith.science/pith/HXHIL7RBJ4YVUG3Q2FLLUWVN2E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HXHIL7RBJ4YVUG3Q2FLLUWVN2E/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":"2026-07-17T04:27:29Z","links":{"resolver":"https://pith.science/pith/HXHIL7RBJ4YVUG3Q2FLLUWVN2E","bundle":"https://pith.science/pith/HXHIL7RBJ4YVUG3Q2FLLUWVN2E/bundle.json","state":"https://pith.science/pith/HXHIL7RBJ4YVUG3Q2FLLUWVN2E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HXHIL7RBJ4YVUG3Q2FLLUWVN2E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:HXHIL7RBJ4YVUG3Q2FLLUWVN2E","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":"79db50235326c9a7f52e84fffc01f1dd023353e79928d9dd419b107423d5c577","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2021-08-08T21:23:48Z","title_canon_sha256":"6c6616ab3e2842e0dffd63863ce8d20c7b4a8ab55b0509fb915592c97c5f67de"},"schema_version":"1.0","source":{"id":"2108.03737","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.03737","created_at":"2026-07-05T03:04:09Z"},{"alias_kind":"arxiv_version","alias_value":"2108.03737v1","created_at":"2026-07-05T03:04:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.03737","created_at":"2026-07-05T03:04:09Z"},{"alias_kind":"pith_short_12","alias_value":"HXHIL7RBJ4YV","created_at":"2026-07-05T03:04:09Z"},{"alias_kind":"pith_short_16","alias_value":"HXHIL7RBJ4YVUG3Q","created_at":"2026-07-05T03:04:09Z"},{"alias_kind":"pith_short_8","alias_value":"HXHIL7RB","created_at":"2026-07-05T03:04:09Z"}],"graph_snapshots":[{"event_id":"sha256:aeb5b1e5f76391b3cf06bd4d4d60dd956a07ea0b5bc61afaf024eb2f2f878146","target":"graph","created_at":"2026-07-05T03:04:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2108.03737/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Brain-related experiments are limited by nature, and so biological insights are often restricted or absent. This is particularly problematic in the context of brain cancers, which have very poor survival rates. To generate and test new biological hypotheses, researchers started using mathematical models that can simulate tumour evolution. However, most of these models focus on single-scale 2D cell dynamics, and cannot capture the complex multi-scale tumour invasion patterns in 3D brains. A particular role in these invasion patterns is likely played by the distribution of micro-fibres. To inves","authors_text":"Dumitru Trucu, J. Douglas Steele, Kismet Hossain-Ibrahim, Raluca Eftimie, Szabolcs Suveges","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2021-08-08T21:23:48Z","title":"Mathematical modelling of glioblastomas invasion within the brain: a 3D multi-scale moving-boundary approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.03737","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":"sha256:8237126ab02a1be8e93b10501b2796197136386ebcea9ad3ef98b7abb70bdc29","target":"record","created_at":"2026-07-05T03:04:09Z","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":"79db50235326c9a7f52e84fffc01f1dd023353e79928d9dd419b107423d5c577","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2021-08-08T21:23:48Z","title_canon_sha256":"6c6616ab3e2842e0dffd63863ce8d20c7b4a8ab55b0509fb915592c97c5f67de"},"schema_version":"1.0","source":{"id":"2108.03737","kind":"arxiv","version":1}},"canonical_sha256":"3dce85fe214f315a1b70d156ba5aadd13a2da2fc3e77aff09d0e43008503739d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dce85fe214f315a1b70d156ba5aadd13a2da2fc3e77aff09d0e43008503739d","first_computed_at":"2026-07-05T03:04:09.042079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:04:09.042079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7t1uhkMsHQKAXxGD/HeTgWvWjDM0Za4W34YlJozJPAOsIH5rO6rbmCzRbFTJ/BvqaSXDb+XEeTZM5sllE2M4DA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:04:09.042420Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.03737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8237126ab02a1be8e93b10501b2796197136386ebcea9ad3ef98b7abb70bdc29","sha256:aeb5b1e5f76391b3cf06bd4d4d60dd956a07ea0b5bc61afaf024eb2f2f878146"],"state_sha256":"920b8ac30e73ded97c96852c13bc0be8e4c29ee21be4a65dbbb928db7bfe3584"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j2/3eEHYt+g9B2XA7JVYGNAyXyWA9QdChG+U1ztu1SiBUnPHRieL4uFeTdiy+kmEr3UjUe2dUVdsEzJHzpGJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-17T04:27:29.041312Z","bundle_sha256":"a0a4433c0706dc1ce23ce8cbe89640c68fa2955ef7c7f0c7448183c8a3d24d62"}}