{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ILOFN52YJ7O4JTDMQEF2NKNN5I","short_pith_number":"pith:ILOFN52Y","canonical_record":{"source":{"id":"2502.00189","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-31T22:07:53Z","cross_cats_sorted":[],"title_canon_sha256":"a4843f8c2bc27e82c2f3e413ef9768c7b0acd061147dff1fe463b619d2d8186b","abstract_canon_sha256":"98612adae904bb4894df92c3059c364dc7b4fcd40bea4354db7b58061a32ea78"},"schema_version":"1.0"},"canonical_sha256":"42dc56f7584fddc4cc6c810ba6a9adea0b62ae88f7d91b962cc16849bcdffd54","source":{"kind":"arxiv","id":"2502.00189","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.00189","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"arxiv_version","alias_value":"2502.00189v4","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.00189","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"pith_short_12","alias_value":"ILOFN52YJ7O4","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"pith_short_16","alias_value":"ILOFN52YJ7O4JTDM","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"pith_short_8","alias_value":"ILOFN52Y","created_at":"2026-06-23T01:12:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ILOFN52YJ7O4JTDMQEF2NKNN5I","target":"record","payload":{"canonical_record":{"source":{"id":"2502.00189","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-31T22:07:53Z","cross_cats_sorted":[],"title_canon_sha256":"a4843f8c2bc27e82c2f3e413ef9768c7b0acd061147dff1fe463b619d2d8186b","abstract_canon_sha256":"98612adae904bb4894df92c3059c364dc7b4fcd40bea4354db7b58061a32ea78"},"schema_version":"1.0"},"canonical_sha256":"42dc56f7584fddc4cc6c810ba6a9adea0b62ae88f7d91b962cc16849bcdffd54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:44.971681Z","signature_b64":"J9bvgEKlSjcJ/ozAAXnz28BWQTMnflnQi1uMkUlBGKWl6Ob7odST57YD2oFnjodSbEynmLIzF/el1tbjpkEwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42dc56f7584fddc4cc6c810ba6a9adea0b62ae88f7d91b962cc16849bcdffd54","last_reissued_at":"2026-06-23T01:12:44.971022Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:44.971022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.00189","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":"2026-06-23T01:12:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1fxhARE/6nI+JF3SOi+uKPanjaxj+6RCSqCdxd0bJBLLM7A2kRIKFK3vSyDuPqRbMVFSIbJoVTCl3HJUXLZPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:23:31.118243Z"},"content_sha256":"968ee6a8f7dec4998e44d125ec4274fc4f03ba5c1bdd490de9ab51e0ca2cae90","schema_version":"1.0","event_id":"sha256:968ee6a8f7dec4998e44d125ec4274fc4f03ba5c1bdd490de9ab51e0ca2cae90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ILOFN52YJ7O4JTDMQEF2NKNN5I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Yamada-Watanabe-Engelbert theorem for SPDEs in Banach spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Esm\\'ee Theewis","submitted_at":"2025-01-31T22:07:53Z","abstract_excerpt":"We give a unified proof of the Yamada-Watanabe-Engelbert theorem for various notions of solutions for SPDEs in Banach spaces with cylindrical Wiener noise. We use Kurtz' generalization of the theorems of Yamada, Watanabe and Engelbert. In addition, we deduce the classical Yamada-Watanabe theorem for SPDEs, with a slightly different notion of `unique strong solution' than that corresponding to the result of Kurtz. Our setting includes analytically strong solutions, analytically weak solutions and mild solutions. Moreover, our approach offers flexibility with regard to the function spaces and in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.00189","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/2502.00189/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":"2026-06-23T01:12:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dR3eit53GOSOoEYKpSjjf2iRNDwrc/2KWkEyyeHAkMuj24pWadbiXpJ1ach3RIfjeLHbWGkG3d59pktu8Py6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T08:23:31.118785Z"},"content_sha256":"5843e95dc9633d24512f24b8e3488054c9aefefd1e4083ed63391df5c637982d","schema_version":"1.0","event_id":"sha256:5843e95dc9633d24512f24b8e3488054c9aefefd1e4083ed63391df5c637982d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ILOFN52YJ7O4JTDMQEF2NKNN5I/bundle.json","state_url":"https://pith.science/pith/ILOFN52YJ7O4JTDMQEF2NKNN5I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ILOFN52YJ7O4JTDMQEF2NKNN5I/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":"2026-08-11T08:23:31Z","links":{"resolver":"https://pith.science/pith/ILOFN52YJ7O4JTDMQEF2NKNN5I","bundle":"https://pith.science/pith/ILOFN52YJ7O4JTDMQEF2NKNN5I/bundle.json","state":"https://pith.science/pith/ILOFN52YJ7O4JTDMQEF2NKNN5I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ILOFN52YJ7O4JTDMQEF2NKNN5I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ILOFN52YJ7O4JTDMQEF2NKNN5I","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":"98612adae904bb4894df92c3059c364dc7b4fcd40bea4354db7b58061a32ea78","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-31T22:07:53Z","title_canon_sha256":"a4843f8c2bc27e82c2f3e413ef9768c7b0acd061147dff1fe463b619d2d8186b"},"schema_version":"1.0","source":{"id":"2502.00189","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.00189","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"arxiv_version","alias_value":"2502.00189v4","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.00189","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"pith_short_12","alias_value":"ILOFN52YJ7O4","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"pith_short_16","alias_value":"ILOFN52YJ7O4JTDM","created_at":"2026-06-23T01:12:44Z"},{"alias_kind":"pith_short_8","alias_value":"ILOFN52Y","created_at":"2026-06-23T01:12:44Z"}],"graph_snapshots":[{"event_id":"sha256:5843e95dc9633d24512f24b8e3488054c9aefefd1e4083ed63391df5c637982d","target":"graph","created_at":"2026-06-23T01:12:44Z","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/2502.00189/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a unified proof of the Yamada-Watanabe-Engelbert theorem for various notions of solutions for SPDEs in Banach spaces with cylindrical Wiener noise. We use Kurtz' generalization of the theorems of Yamada, Watanabe and Engelbert. In addition, we deduce the classical Yamada-Watanabe theorem for SPDEs, with a slightly different notion of `unique strong solution' than that corresponding to the result of Kurtz. Our setting includes analytically strong solutions, analytically weak solutions and mild solutions. Moreover, our approach offers flexibility with regard to the function spaces and in","authors_text":"Esm\\'ee Theewis","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-31T22:07:53Z","title":"The Yamada-Watanabe-Engelbert theorem for SPDEs in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.00189","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":"sha256:968ee6a8f7dec4998e44d125ec4274fc4f03ba5c1bdd490de9ab51e0ca2cae90","target":"record","created_at":"2026-06-23T01:12:44Z","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":"98612adae904bb4894df92c3059c364dc7b4fcd40bea4354db7b58061a32ea78","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-31T22:07:53Z","title_canon_sha256":"a4843f8c2bc27e82c2f3e413ef9768c7b0acd061147dff1fe463b619d2d8186b"},"schema_version":"1.0","source":{"id":"2502.00189","kind":"arxiv","version":4}},"canonical_sha256":"42dc56f7584fddc4cc6c810ba6a9adea0b62ae88f7d91b962cc16849bcdffd54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42dc56f7584fddc4cc6c810ba6a9adea0b62ae88f7d91b962cc16849bcdffd54","first_computed_at":"2026-06-23T01:12:44.971022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T01:12:44.971022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J9bvgEKlSjcJ/ozAAXnz28BWQTMnflnQi1uMkUlBGKWl6Ob7odST57YD2oFnjodSbEynmLIzF/el1tbjpkEwBw==","signature_status":"signed_v1","signed_at":"2026-06-23T01:12:44.971681Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.00189","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:968ee6a8f7dec4998e44d125ec4274fc4f03ba5c1bdd490de9ab51e0ca2cae90","sha256:5843e95dc9633d24512f24b8e3488054c9aefefd1e4083ed63391df5c637982d"],"state_sha256":"10412a2487eb8978e692f5c9528073cd9f5f0e0354f2fce6030d685cbf026e8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a/jS49klZs7FZhYHobMnQEqFSyywHTC/hJbQet5Bc3GTMlMjwUn4HjQUdsW1y237/F0PIDNObmbqVAWeJrLUBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T08:23:31.125823Z","bundle_sha256":"b137c9bb33e76ec5156bb418f202c061dca485653683f8eb1b06c70d8cfeee7b"}}