{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VFC3O4YGIZ4PEHE7EMUH6NBWID","short_pith_number":"pith:VFC3O4YG","canonical_record":{"source":{"id":"1805.07109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-05-18T09:25:54Z","cross_cats_sorted":[],"title_canon_sha256":"574645a4b5850d659a7f394e1fe544a835619f466e336ea3312a25dedbe72b42","abstract_canon_sha256":"18e05320c16ebe35eba2ff01570db9e9a6ca2ad044c22ed663839cc91ae4bfce"},"schema_version":"1.0"},"canonical_sha256":"a945b773064678f21c9f23287f343640f6314d5324f549b79b4d66bdb175bc85","source":{"kind":"arxiv","id":"1805.07109","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07109","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07109v2","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07109","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"pith_short_12","alias_value":"VFC3O4YGIZ4P","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VFC3O4YGIZ4PEHE7","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VFC3O4YG","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VFC3O4YGIZ4PEHE7EMUH6NBWID","target":"record","payload":{"canonical_record":{"source":{"id":"1805.07109","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-05-18T09:25:54Z","cross_cats_sorted":[],"title_canon_sha256":"574645a4b5850d659a7f394e1fe544a835619f466e336ea3312a25dedbe72b42","abstract_canon_sha256":"18e05320c16ebe35eba2ff01570db9e9a6ca2ad044c22ed663839cc91ae4bfce"},"schema_version":"1.0"},"canonical_sha256":"a945b773064678f21c9f23287f343640f6314d5324f549b79b4d66bdb175bc85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:27.333127Z","signature_b64":"BYCd+eDWg3pEfwWqzgu1uddw3yfXpJUop7YRCG58WU81/yBDCqpfGAWs3nrbd6MeT23aYUdQGNat/JdYwF+9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a945b773064678f21c9f23287f343640f6314d5324f549b79b4d66bdb175bc85","last_reissued_at":"2026-05-18T00:15:27.332346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:27.332346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.07109","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z9XBa6woEXr1vj2vk2U169bVEl51935kLmLAuPVgDoyggrBI/YCamoI2YM95VgfnWk6vL1DqU+RYLpHxXs8bAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:29:50.181476Z"},"content_sha256":"f5d58fc0e09b4cde14264b77959d14983b1e29769ebbe415d85eee4176f89f20","schema_version":"1.0","event_id":"sha256:f5d58fc0e09b4cde14264b77959d14983b1e29769ebbe415d85eee4176f89f20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VFC3O4YGIZ4PEHE7EMUH6NBWID","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Bayesian Solution of Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Chris Oates, Jon Cockayne, Junyang Wang","submitted_at":"2018-05-18T09:25:54Z","abstract_excerpt":"The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators allows for formal statistical quantification of the error due to discretisation in the numerical context. Competing statistical paradigms can be considered and Bayesian probabilistic numerical methods (PNMs) are obtained when Bayesian statistical principles are deployed. Bayesian PNM are closed under composition, such that uncertainty due to different sources of discretisation can be jointly modelled and rigorously propagated. However, we argue that no strictly Bayesian PN"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07109","kind":"arxiv","version":2},"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":"2026-05-18T00:15:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2iYyXTMO73x1p+ssXTed7SHRVCEjXOkvwolaEzX5N+X6k0DIQ1C3FGW0voKspvkzaHi+kShmd6drRlLD8neyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:29:50.181879Z"},"content_sha256":"8cd7651cb2232d4ad61dd8f69218d5677ba7b6dc45af3da071e6b3535fdebe4d","schema_version":"1.0","event_id":"sha256:8cd7651cb2232d4ad61dd8f69218d5677ba7b6dc45af3da071e6b3535fdebe4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VFC3O4YGIZ4PEHE7EMUH6NBWID/bundle.json","state_url":"https://pith.science/pith/VFC3O4YGIZ4PEHE7EMUH6NBWID/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VFC3O4YGIZ4PEHE7EMUH6NBWID/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":"2026-05-27T04:29:50Z","links":{"resolver":"https://pith.science/pith/VFC3O4YGIZ4PEHE7EMUH6NBWID","bundle":"https://pith.science/pith/VFC3O4YGIZ4PEHE7EMUH6NBWID/bundle.json","state":"https://pith.science/pith/VFC3O4YGIZ4PEHE7EMUH6NBWID/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VFC3O4YGIZ4PEHE7EMUH6NBWID/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VFC3O4YGIZ4PEHE7EMUH6NBWID","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":"18e05320c16ebe35eba2ff01570db9e9a6ca2ad044c22ed663839cc91ae4bfce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-05-18T09:25:54Z","title_canon_sha256":"574645a4b5850d659a7f394e1fe544a835619f466e336ea3312a25dedbe72b42"},"schema_version":"1.0","source":{"id":"1805.07109","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07109","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07109v2","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07109","created_at":"2026-05-18T00:15:27Z"},{"alias_kind":"pith_short_12","alias_value":"VFC3O4YGIZ4P","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VFC3O4YGIZ4PEHE7","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VFC3O4YG","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:8cd7651cb2232d4ad61dd8f69218d5677ba7b6dc45af3da071e6b3535fdebe4d","target":"graph","created_at":"2026-05-18T00:15:27Z","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":"The interpretation of numerical methods, such as finite difference methods for differential equations, as point estimators allows for formal statistical quantification of the error due to discretisation in the numerical context. Competing statistical paradigms can be considered and Bayesian probabilistic numerical methods (PNMs) are obtained when Bayesian statistical principles are deployed. Bayesian PNM are closed under composition, such that uncertainty due to different sources of discretisation can be jointly modelled and rigorously propagated. However, we argue that no strictly Bayesian PN","authors_text":"Chris Oates, Jon Cockayne, Junyang Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-05-18T09:25:54Z","title":"On the Bayesian Solution of Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07109","kind":"arxiv","version":2},"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:f5d58fc0e09b4cde14264b77959d14983b1e29769ebbe415d85eee4176f89f20","target":"record","created_at":"2026-05-18T00:15:27Z","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":"18e05320c16ebe35eba2ff01570db9e9a6ca2ad044c22ed663839cc91ae4bfce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-05-18T09:25:54Z","title_canon_sha256":"574645a4b5850d659a7f394e1fe544a835619f466e336ea3312a25dedbe72b42"},"schema_version":"1.0","source":{"id":"1805.07109","kind":"arxiv","version":2}},"canonical_sha256":"a945b773064678f21c9f23287f343640f6314d5324f549b79b4d66bdb175bc85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a945b773064678f21c9f23287f343640f6314d5324f549b79b4d66bdb175bc85","first_computed_at":"2026-05-18T00:15:27.332346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:27.332346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BYCd+eDWg3pEfwWqzgu1uddw3yfXpJUop7YRCG58WU81/yBDCqpfGAWs3nrbd6MeT23aYUdQGNat/JdYwF+9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:27.333127Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07109","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5d58fc0e09b4cde14264b77959d14983b1e29769ebbe415d85eee4176f89f20","sha256:8cd7651cb2232d4ad61dd8f69218d5677ba7b6dc45af3da071e6b3535fdebe4d"],"state_sha256":"08570bf2303ab7f0934d5bdda5f4949c613dbdd8c7f85401d99c6ffb3bb9c0ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dZrrzrfFVdBl81mMijCGj3mn6k7uklR+KwgeWfr1LppQNRgOLoiUoxJ9Ul8wn9HTGySAGlxqa6LTpRafRPfgAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:29:50.184544Z","bundle_sha256":"943995fc133265f5bd151e6c17b9c9808ee7e203203c9a5df29e528a88523a39"}}