{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:Y4LVGNZO3FGLEE4UFNUFC4IR77","short_pith_number":"pith:Y4LVGNZO","canonical_record":{"source":{"id":"1001.2751","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-01-15T19:03:59Z","cross_cats_sorted":["cs.NA","math.AP","math.PR"],"title_canon_sha256":"5d0654d5065a8757f3db9ae80e2a1dfe783e23ab5c989f22dc7fe85c0505e756","abstract_canon_sha256":"dde50976e8bdf46bba20cdf4d8e01e48515e9d05450e1970bfef03119803d3c2"},"schema_version":"1.0"},"canonical_sha256":"c71753372ed94cb213942b68517111fffc971d119c1637cb275b4c25e7909870","source":{"kind":"arxiv","id":"1001.2751","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2751","created_at":"2026-06-03T23:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2751v4","created_at":"2026-06-03T23:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2751","created_at":"2026-06-03T23:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"Y4LVGNZO3FGL","created_at":"2026-06-03T23:06:32Z"},{"alias_kind":"pith_short_16","alias_value":"Y4LVGNZO3FGLEE4U","created_at":"2026-06-03T23:06:32Z"},{"alias_kind":"pith_short_8","alias_value":"Y4LVGNZO","created_at":"2026-06-03T23:06:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:Y4LVGNZO3FGLEE4UFNUFC4IR77","target":"record","payload":{"canonical_record":{"source":{"id":"1001.2751","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-01-15T19:03:59Z","cross_cats_sorted":["cs.NA","math.AP","math.PR"],"title_canon_sha256":"5d0654d5065a8757f3db9ae80e2a1dfe783e23ab5c989f22dc7fe85c0505e756","abstract_canon_sha256":"dde50976e8bdf46bba20cdf4d8e01e48515e9d05450e1970bfef03119803d3c2"},"schema_version":"1.0"},"canonical_sha256":"c71753372ed94cb213942b68517111fffc971d119c1637cb275b4c25e7909870","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:32.709979Z","signature_b64":"pz54F2zTVa2izy+v/kmXd+1lNgJPJDbQ9oFAgJ9KgAzLDZ57V/DzFOd8gGoMH/ZP3Fv+7rxIJtWnspNcf/0GDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c71753372ed94cb213942b68517111fffc971d119c1637cb275b4c25e7909870","last_reissued_at":"2026-06-03T23:06:32.709511Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:32.709511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.2751","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-03T23:06:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mLSeSGrB74kqivBX/tvTQQNHLg+aVbjfyDuFbm7fSHxebEo42aTLidvBhp/w5Vj6/sJv/NPimCMZnqndAIlmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T08:01:04.636487Z"},"content_sha256":"8e999a56deea9da1c616321cddaf8100ce3befd9246937e16c15fc1941a08111","schema_version":"1.0","event_id":"sha256:8e999a56deea9da1c616321cddaf8100ce3befd9246937e16c15fc1941a08111"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:Y4LVGNZO3FGLEE4UFNUFC4IR77","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Milstein scheme for SPDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.PR"],"primary_cat":"math.NA","authors_text":"Arnulf Jentzen, Michael Roeckner","submitted_at":"2010-01-15T19:03:59Z","abstract_excerpt":"This article studies an infinite dimensional analog of Milstein's scheme for finite dimensional stochastic ordinary differential equations (SODEs). The Milstein scheme is known to be impressively efficient for SODEs which fulfill a certain commutativity type condition. This article introduces the infinite dimensional analog of this commutativity type condition and observes that a certain class of semilinear stochastic partial differential equation (SPDEs) with multiplicative trace class noise naturally fulfills the resulting infinite dimensional commutativity condition. In particular, a suitab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2751","kind":"arxiv","version":4},"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/1001.2751/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":"2026-06-03T23:06:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Io7AscBR7Z3F3JbAvZmb7mVwP/0Iw9ZJ7YmsarVEvFgIaxmXNKe6XbXZC3Uqf5e4iLGbAx61LNFIMP1FoyGaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T08:01:04.636860Z"},"content_sha256":"16b630189b5ba0339b6d86abd1f7380fcd9aa9522524b4f2c530403077ca6c12","schema_version":"1.0","event_id":"sha256:16b630189b5ba0339b6d86abd1f7380fcd9aa9522524b4f2c530403077ca6c12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y4LVGNZO3FGLEE4UFNUFC4IR77/bundle.json","state_url":"https://pith.science/pith/Y4LVGNZO3FGLEE4UFNUFC4IR77/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y4LVGNZO3FGLEE4UFNUFC4IR77/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":"2026-06-22T08:01:04Z","links":{"resolver":"https://pith.science/pith/Y4LVGNZO3FGLEE4UFNUFC4IR77","bundle":"https://pith.science/pith/Y4LVGNZO3FGLEE4UFNUFC4IR77/bundle.json","state":"https://pith.science/pith/Y4LVGNZO3FGLEE4UFNUFC4IR77/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y4LVGNZO3FGLEE4UFNUFC4IR77/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:Y4LVGNZO3FGLEE4UFNUFC4IR77","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":"dde50976e8bdf46bba20cdf4d8e01e48515e9d05450e1970bfef03119803d3c2","cross_cats_sorted":["cs.NA","math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-01-15T19:03:59Z","title_canon_sha256":"5d0654d5065a8757f3db9ae80e2a1dfe783e23ab5c989f22dc7fe85c0505e756"},"schema_version":"1.0","source":{"id":"1001.2751","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2751","created_at":"2026-06-03T23:06:32Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2751v4","created_at":"2026-06-03T23:06:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2751","created_at":"2026-06-03T23:06:32Z"},{"alias_kind":"pith_short_12","alias_value":"Y4LVGNZO3FGL","created_at":"2026-06-03T23:06:32Z"},{"alias_kind":"pith_short_16","alias_value":"Y4LVGNZO3FGLEE4U","created_at":"2026-06-03T23:06:32Z"},{"alias_kind":"pith_short_8","alias_value":"Y4LVGNZO","created_at":"2026-06-03T23:06:32Z"}],"graph_snapshots":[{"event_id":"sha256:16b630189b5ba0339b6d86abd1f7380fcd9aa9522524b4f2c530403077ca6c12","target":"graph","created_at":"2026-06-03T23:06:32Z","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/1001.2751/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article studies an infinite dimensional analog of Milstein's scheme for finite dimensional stochastic ordinary differential equations (SODEs). The Milstein scheme is known to be impressively efficient for SODEs which fulfill a certain commutativity type condition. This article introduces the infinite dimensional analog of this commutativity type condition and observes that a certain class of semilinear stochastic partial differential equation (SPDEs) with multiplicative trace class noise naturally fulfills the resulting infinite dimensional commutativity condition. In particular, a suitab","authors_text":"Arnulf Jentzen, Michael Roeckner","cross_cats":["cs.NA","math.AP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-01-15T19:03:59Z","title":"A Milstein scheme for SPDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2751","kind":"arxiv","version":4},"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":"sha256:8e999a56deea9da1c616321cddaf8100ce3befd9246937e16c15fc1941a08111","target":"record","created_at":"2026-06-03T23:06:32Z","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":"dde50976e8bdf46bba20cdf4d8e01e48515e9d05450e1970bfef03119803d3c2","cross_cats_sorted":["cs.NA","math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2010-01-15T19:03:59Z","title_canon_sha256":"5d0654d5065a8757f3db9ae80e2a1dfe783e23ab5c989f22dc7fe85c0505e756"},"schema_version":"1.0","source":{"id":"1001.2751","kind":"arxiv","version":4}},"canonical_sha256":"c71753372ed94cb213942b68517111fffc971d119c1637cb275b4c25e7909870","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c71753372ed94cb213942b68517111fffc971d119c1637cb275b4c25e7909870","first_computed_at":"2026-06-03T23:06:32.709511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:32.709511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pz54F2zTVa2izy+v/kmXd+1lNgJPJDbQ9oFAgJ9KgAzLDZ57V/DzFOd8gGoMH/ZP3Fv+7rxIJtWnspNcf/0GDw==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:32.709979Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.2751","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e999a56deea9da1c616321cddaf8100ce3befd9246937e16c15fc1941a08111","sha256:16b630189b5ba0339b6d86abd1f7380fcd9aa9522524b4f2c530403077ca6c12"],"state_sha256":"ec7077e87b0f149ffe6631fd863aa08d5dda5fbaf389f37d7645772e1fa984a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8WdFNSZ6lszo8c4A2bsbOc8h62Nxcl7AGfL61ThWTJk0z0cSYQbMAHWOjsa0YXhqtjQ/m8kdHJJvG/Swm8zNDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T08:01:04.638984Z","bundle_sha256":"f88696a4971dc55547d3dfbcd45b03450e1105aec2593894dd13598850f864f0"}}