{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PYUJYTTLS7S3HJYEDTKV2M4WFB","short_pith_number":"pith:PYUJYTTL","canonical_record":{"source":{"id":"1501.05782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-23T12:10:15Z","cross_cats_sorted":[],"title_canon_sha256":"706a4edf30b03a6dd234bc3eb48157042efc6d72f33496a51b6470d5ee776a9a","abstract_canon_sha256":"f24bc69d4be03d7f80943e856dfb2c2e894035f46e1f52f0beb4ac9756512309"},"schema_version":"1.0"},"canonical_sha256":"7e289c4e6b97e5b3a7041cd55d33962847826b79b6c2ce79cff1a5aa60f15080","source":{"kind":"arxiv","id":"1501.05782","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05782","created_at":"2026-05-18T02:28:49Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05782v1","created_at":"2026-05-18T02:28:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05782","created_at":"2026-05-18T02:28:49Z"},{"alias_kind":"pith_short_12","alias_value":"PYUJYTTLS7S3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PYUJYTTLS7S3HJYE","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PYUJYTTL","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PYUJYTTLS7S3HJYEDTKV2M4WFB","target":"record","payload":{"canonical_record":{"source":{"id":"1501.05782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-23T12:10:15Z","cross_cats_sorted":[],"title_canon_sha256":"706a4edf30b03a6dd234bc3eb48157042efc6d72f33496a51b6470d5ee776a9a","abstract_canon_sha256":"f24bc69d4be03d7f80943e856dfb2c2e894035f46e1f52f0beb4ac9756512309"},"schema_version":"1.0"},"canonical_sha256":"7e289c4e6b97e5b3a7041cd55d33962847826b79b6c2ce79cff1a5aa60f15080","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:49.010609Z","signature_b64":"fZgIyU/dKxqrJjGIG8Q6FtbxPxXZIrc2ucnVqUE/Ul3b4+AUMuQuwFSUMBziH7HsSo35LVfaeutJpwDCTMsgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e289c4e6b97e5b3a7041cd55d33962847826b79b6c2ce79cff1a5aa60f15080","last_reissued_at":"2026-05-18T02:28:49.010239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:49.010239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.05782","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":"2026-05-18T02:28:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LAtVFGYbfOunkikDTePX7uqe6Vkkwhty1w9P91PsKRKedFp9tce7kkcCjEqdGNkfB7rt/VXn/U+zs2tm90+LAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:22:57.301617Z"},"content_sha256":"70652925be7e8241933c2fd9d245099a7760f617b4be03b2f3e9d45d6924897a","schema_version":"1.0","event_id":"sha256:70652925be7e8241933c2fd9d245099a7760f617b4be03b2f3e9d45d6924897a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PYUJYTTLS7S3HJYEDTKV2M4WFB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fully implicit time-stepping schemes and non-linear solvers for systems of reaction-diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andy H.W. Chung, Anotida Madzvamuse","submitted_at":"2015-01-23T12:10:15Z","abstract_excerpt":"In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications of reaction-diffusion systems is abundant in the literature, from modelling pattern formation in developmental biology to cancer research, wound healing, tissue and bone regeneration and cell motility. Therefore, it is crucial that modellers, analysts and biologists are able to solve accurately and efficiently systems of highly nonlinear parabolic partial differential equations on complex stationary and sometimes cont"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05782","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":"2026-05-18T02:28:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zKHF4AVDQ+v02w1QlKhDQvJn2+RbIyL+G25cjmFhX7uZ/ySXCAURX2ojJ789g04TsH2NovkoIv/pRIrcI/BfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:22:57.301962Z"},"content_sha256":"0225213c3cd3ffc2de2c5b344e3683b50eb25c183e2a1399ce0156966cef769d","schema_version":"1.0","event_id":"sha256:0225213c3cd3ffc2de2c5b344e3683b50eb25c183e2a1399ce0156966cef769d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PYUJYTTLS7S3HJYEDTKV2M4WFB/bundle.json","state_url":"https://pith.science/pith/PYUJYTTLS7S3HJYEDTKV2M4WFB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PYUJYTTLS7S3HJYEDTKV2M4WFB/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":"2026-06-21T22:22:57Z","links":{"resolver":"https://pith.science/pith/PYUJYTTLS7S3HJYEDTKV2M4WFB","bundle":"https://pith.science/pith/PYUJYTTLS7S3HJYEDTKV2M4WFB/bundle.json","state":"https://pith.science/pith/PYUJYTTLS7S3HJYEDTKV2M4WFB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PYUJYTTLS7S3HJYEDTKV2M4WFB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PYUJYTTLS7S3HJYEDTKV2M4WFB","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":"f24bc69d4be03d7f80943e856dfb2c2e894035f46e1f52f0beb4ac9756512309","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-23T12:10:15Z","title_canon_sha256":"706a4edf30b03a6dd234bc3eb48157042efc6d72f33496a51b6470d5ee776a9a"},"schema_version":"1.0","source":{"id":"1501.05782","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05782","created_at":"2026-05-18T02:28:49Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05782v1","created_at":"2026-05-18T02:28:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05782","created_at":"2026-05-18T02:28:49Z"},{"alias_kind":"pith_short_12","alias_value":"PYUJYTTLS7S3","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PYUJYTTLS7S3HJYE","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PYUJYTTL","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:0225213c3cd3ffc2de2c5b344e3683b50eb25c183e2a1399ce0156966cef769d","target":"graph","created_at":"2026-05-18T02:28:49Z","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":"In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications of reaction-diffusion systems is abundant in the literature, from modelling pattern formation in developmental biology to cancer research, wound healing, tissue and bone regeneration and cell motility. Therefore, it is crucial that modellers, analysts and biologists are able to solve accurately and efficiently systems of highly nonlinear parabolic partial differential equations on complex stationary and sometimes cont","authors_text":"Andy H.W. Chung, Anotida Madzvamuse","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-23T12:10:15Z","title":"Fully implicit time-stepping schemes and non-linear solvers for systems of reaction-diffusion equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05782","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":"sha256:70652925be7e8241933c2fd9d245099a7760f617b4be03b2f3e9d45d6924897a","target":"record","created_at":"2026-05-18T02:28:49Z","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":"f24bc69d4be03d7f80943e856dfb2c2e894035f46e1f52f0beb4ac9756512309","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-23T12:10:15Z","title_canon_sha256":"706a4edf30b03a6dd234bc3eb48157042efc6d72f33496a51b6470d5ee776a9a"},"schema_version":"1.0","source":{"id":"1501.05782","kind":"arxiv","version":1}},"canonical_sha256":"7e289c4e6b97e5b3a7041cd55d33962847826b79b6c2ce79cff1a5aa60f15080","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e289c4e6b97e5b3a7041cd55d33962847826b79b6c2ce79cff1a5aa60f15080","first_computed_at":"2026-05-18T02:28:49.010239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:49.010239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fZgIyU/dKxqrJjGIG8Q6FtbxPxXZIrc2ucnVqUE/Ul3b4+AUMuQuwFSUMBziH7HsSo35LVfaeutJpwDCTMsgBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:49.010609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05782","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70652925be7e8241933c2fd9d245099a7760f617b4be03b2f3e9d45d6924897a","sha256:0225213c3cd3ffc2de2c5b344e3683b50eb25c183e2a1399ce0156966cef769d"],"state_sha256":"07d9d64aa92ce5db23cbab3b3c897c3299f586a58e334e2e1a6ebbbffc174fdd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ou4g6/37/bmQeD0pn6gprrja0Fqx84Wp6Jnc5CzugvuOvBtYEiELbeXIOXIQK7kvXhW0NFV1wUxdpwwSeg6DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:22:57.303863Z","bundle_sha256":"0120ac82d298e2495284d00d03c596e17ac595067a508e858a1767e67a1e9567"}}