{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:G733ZGC7OAU7TFMARFNKPDDCUA","short_pith_number":"pith:G733ZGC7","canonical_record":{"source":{"id":"1809.07936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-21T04:02:51Z","cross_cats_sorted":[],"title_canon_sha256":"844e36f24b08313cf8bb20767d5b046a23ef6e99cd376488b38ac0db26f6e016","abstract_canon_sha256":"e5f9e948951c9e9db161bf3e0413f68ab4c582722ed75799d6d50d7e75098d6e"},"schema_version":"1.0"},"canonical_sha256":"37f7bc985f7029f99580895aa78c62a01f4fe7ea414acbe152b2f0a6e210a8dd","source":{"kind":"arxiv","id":"1809.07936","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07936","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07936v1","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07936","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"pith_short_12","alias_value":"G733ZGC7OAU7","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G733ZGC7OAU7TFMA","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G733ZGC7","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:G733ZGC7OAU7TFMARFNKPDDCUA","target":"record","payload":{"canonical_record":{"source":{"id":"1809.07936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-21T04:02:51Z","cross_cats_sorted":[],"title_canon_sha256":"844e36f24b08313cf8bb20767d5b046a23ef6e99cd376488b38ac0db26f6e016","abstract_canon_sha256":"e5f9e948951c9e9db161bf3e0413f68ab4c582722ed75799d6d50d7e75098d6e"},"schema_version":"1.0"},"canonical_sha256":"37f7bc985f7029f99580895aa78c62a01f4fe7ea414acbe152b2f0a6e210a8dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:10.859725Z","signature_b64":"oLm7GxVh+FvOxmPE2JBZ1jWGcXotE6VM5zNwWgTbabSyZQ9WdYzYU4IhszVna4E+kCW7JOWGe3EguGRcqW82Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37f7bc985f7029f99580895aa78c62a01f4fe7ea414acbe152b2f0a6e210a8dd","last_reissued_at":"2026-05-18T00:05:10.859239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:10.859239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.07936","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":"2026-05-18T00:05:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5yVjcqHLGCSkiNFYVWRfwkwEopv/hN16KFodwnq6zt7V4yrQw78bu5a95Fv2oEWUP1ZqmMjIIlhEXfWfzEIbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:21:41.696658Z"},"content_sha256":"45b1362230102775cbefafe4eb65ee989d18fd9597256f890df93180780db262","schema_version":"1.0","event_id":"sha256:45b1362230102775cbefafe4eb65ee989d18fd9597256f890df93180780db262"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:G733ZGC7OAU7TFMARFNKPDDCUA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computational modelling of cardiac ischaemia using a variable-order fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ian W. Turner, Kevin Burrage, Megan E. Farquhar, Qianqian Yang, Timothy J. Moroney","submitted_at":"2018-09-21T04:02:51Z","abstract_excerpt":"Heart failure is one of the most common causes of death in the western world. Many heart problems are linked to disturbances in cardiac electrical activity, such as wave re-entry caused by ischaemia. In terms of mathematical modelling, the monodomain equation is widely used to model electrical activity in the heart. Recently, Bueno-Orovio et al. [J. R. Soc. Interface 11: 20140352, 2014] pioneered the use of a fractional Laplacian operator in the monodomain equation to account for the complex heterogeneous structures in heart tissue. In this work we consider how to extend this approach to apply"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07936","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":"2026-05-18T00:05:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J0UW+32THzxh1Pmn+bp/ADvVcFiNJVfOsWTfmJOl12V4g9Tgt4mfxfQPxODAfb1Imb9QeDiW3jb4jBQcPVv8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:21:41.697001Z"},"content_sha256":"c48e7367e715819db48bb772048b9991118ff47e40f8a4eb82c5027110416ca3","schema_version":"1.0","event_id":"sha256:c48e7367e715819db48bb772048b9991118ff47e40f8a4eb82c5027110416ca3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G733ZGC7OAU7TFMARFNKPDDCUA/bundle.json","state_url":"https://pith.science/pith/G733ZGC7OAU7TFMARFNKPDDCUA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G733ZGC7OAU7TFMARFNKPDDCUA/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":"2026-06-01T15:21:41Z","links":{"resolver":"https://pith.science/pith/G733ZGC7OAU7TFMARFNKPDDCUA","bundle":"https://pith.science/pith/G733ZGC7OAU7TFMARFNKPDDCUA/bundle.json","state":"https://pith.science/pith/G733ZGC7OAU7TFMARFNKPDDCUA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G733ZGC7OAU7TFMARFNKPDDCUA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G733ZGC7OAU7TFMARFNKPDDCUA","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":"e5f9e948951c9e9db161bf3e0413f68ab4c582722ed75799d6d50d7e75098d6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-21T04:02:51Z","title_canon_sha256":"844e36f24b08313cf8bb20767d5b046a23ef6e99cd376488b38ac0db26f6e016"},"schema_version":"1.0","source":{"id":"1809.07936","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07936","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07936v1","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07936","created_at":"2026-05-18T00:05:10Z"},{"alias_kind":"pith_short_12","alias_value":"G733ZGC7OAU7","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G733ZGC7OAU7TFMA","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G733ZGC7","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:c48e7367e715819db48bb772048b9991118ff47e40f8a4eb82c5027110416ca3","target":"graph","created_at":"2026-05-18T00:05:10Z","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":"Heart failure is one of the most common causes of death in the western world. Many heart problems are linked to disturbances in cardiac electrical activity, such as wave re-entry caused by ischaemia. In terms of mathematical modelling, the monodomain equation is widely used to model electrical activity in the heart. Recently, Bueno-Orovio et al. [J. R. Soc. Interface 11: 20140352, 2014] pioneered the use of a fractional Laplacian operator in the monodomain equation to account for the complex heterogeneous structures in heart tissue. In this work we consider how to extend this approach to apply","authors_text":"Ian W. Turner, Kevin Burrage, Megan E. Farquhar, Qianqian Yang, Timothy J. Moroney","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-21T04:02:51Z","title":"Computational modelling of cardiac ischaemia using a variable-order fractional Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07936","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":"sha256:45b1362230102775cbefafe4eb65ee989d18fd9597256f890df93180780db262","target":"record","created_at":"2026-05-18T00:05:10Z","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":"e5f9e948951c9e9db161bf3e0413f68ab4c582722ed75799d6d50d7e75098d6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-21T04:02:51Z","title_canon_sha256":"844e36f24b08313cf8bb20767d5b046a23ef6e99cd376488b38ac0db26f6e016"},"schema_version":"1.0","source":{"id":"1809.07936","kind":"arxiv","version":1}},"canonical_sha256":"37f7bc985f7029f99580895aa78c62a01f4fe7ea414acbe152b2f0a6e210a8dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37f7bc985f7029f99580895aa78c62a01f4fe7ea414acbe152b2f0a6e210a8dd","first_computed_at":"2026-05-18T00:05:10.859239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:10.859239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oLm7GxVh+FvOxmPE2JBZ1jWGcXotE6VM5zNwWgTbabSyZQ9WdYzYU4IhszVna4E+kCW7JOWGe3EguGRcqW82Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:10.859725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.07936","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45b1362230102775cbefafe4eb65ee989d18fd9597256f890df93180780db262","sha256:c48e7367e715819db48bb772048b9991118ff47e40f8a4eb82c5027110416ca3"],"state_sha256":"789b18d48f2abfe4e36a69bd6798fccd6e6fe0e4891040ec3ba51ea8829808fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vx8HfbjLxbgSufPGI2tFBAQ5JKgZK8VrRT7k2xPcyiHL+RwtSXl+tGRzDWbY4F/RacFforwasz6TeOuGrh8WDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:21:41.698969Z","bundle_sha256":"120f2f67857655e46f074e356608a6231bcd7deb1bc576822b3c37ed2ed9c990"}}