{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TO23G7YINKF2QRHS6TWB2XKWWE","short_pith_number":"pith:TO23G7YI","canonical_record":{"source":{"id":"2408.11678","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-08-21T14:57:53Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"1e6c254708f6a65cece6984dc77f4f5fcbd6f7e5e6d1042ce151b5e864260f5d","abstract_canon_sha256":"18a4f47bfe0356126cef6fa73b0a38f621b5377e2595a02e4e64620b4979abd0"},"schema_version":"1.0"},"canonical_sha256":"9bb5b37f086a8ba844f2f4ec1d5d56b10a92bbaf820f36ad8d47cef2a8adf3fb","source":{"kind":"arxiv","id":"2408.11678","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.11678","created_at":"2026-07-05T08:57:47Z"},{"alias_kind":"arxiv_version","alias_value":"2408.11678v1","created_at":"2026-07-05T08:57:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.11678","created_at":"2026-07-05T08:57:47Z"},{"alias_kind":"pith_short_12","alias_value":"TO23G7YINKF2","created_at":"2026-07-05T08:57:47Z"},{"alias_kind":"pith_short_16","alias_value":"TO23G7YINKF2QRHS","created_at":"2026-07-05T08:57:47Z"},{"alias_kind":"pith_short_8","alias_value":"TO23G7YI","created_at":"2026-07-05T08:57:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TO23G7YINKF2QRHS6TWB2XKWWE","target":"record","payload":{"canonical_record":{"source":{"id":"2408.11678","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-08-21T14:57:53Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"1e6c254708f6a65cece6984dc77f4f5fcbd6f7e5e6d1042ce151b5e864260f5d","abstract_canon_sha256":"18a4f47bfe0356126cef6fa73b0a38f621b5377e2595a02e4e64620b4979abd0"},"schema_version":"1.0"},"canonical_sha256":"9bb5b37f086a8ba844f2f4ec1d5d56b10a92bbaf820f36ad8d47cef2a8adf3fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:57:47.263942Z","signature_b64":"mdTv3abZpn+/WgMfLSMBW6BEVHDqWJpU01/1TnGtbaYKLBMsYTd5g6auVlgSthwEIoJie9JS8jqcrQ+nWlzKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bb5b37f086a8ba844f2f4ec1d5d56b10a92bbaf820f36ad8d47cef2a8adf3fb","last_reissued_at":"2026-07-05T08:57:47.263518Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:57:47.263518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.11678","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":"2026-07-05T08:57:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RO/2WMbnyKBOB4zwkMV8NiWQ8sZLg9/kHRT8BQeV9yjKUVSOPSGeXOrRVIjLq8xTY5f59BeH3RGBfK07OOyTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T08:48:18.106965Z"},"content_sha256":"dfbb980f872b5bc7b99a1e87aa78c7277b97e37611a3b0ea297cde4490156ef1","schema_version":"1.0","event_id":"sha256:dfbb980f872b5bc7b99a1e87aa78c7277b97e37611a3b0ea297cde4490156ef1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TO23G7YINKF2QRHS6TWB2XKWWE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Daniel Goodair","submitted_at":"2024-08-21T14:57:53Z","abstract_excerpt":"We extend recent existence and uniqueness results for maximal solutions of SPDEs through an improved blow-up criterion. Whilst the maximal time of existence is typically characterised by blow-up in the energy norm of solutions, we show instead that solutions exist until blow-up in the larger spaces of the variational framework. The result is applied to show that solutions of 2D and 3D Stochastic Navier-Stokes Equations retain the higher order regularity of the initial condition on their time of existence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.11678","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.11678/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":"2026-07-05T08:57:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eegBOAzScLi9Ofu7Pal6OOfFtYivVJVb/ZFrYCFkMd0qT1cpKphH9VdB+QAn/ZvGxfWP2XpDwny6pX9kEGYRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T08:48:18.107478Z"},"content_sha256":"ef216ee62f440ef4d0060ef53f01f00f057ff9608c1d4d5840ee6e5f656a57d3","schema_version":"1.0","event_id":"sha256:ef216ee62f440ef4d0060ef53f01f00f057ff9608c1d4d5840ee6e5f656a57d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TO23G7YINKF2QRHS6TWB2XKWWE/bundle.json","state_url":"https://pith.science/pith/TO23G7YINKF2QRHS6TWB2XKWWE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TO23G7YINKF2QRHS6TWB2XKWWE/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":"2026-08-10T08:48:18Z","links":{"resolver":"https://pith.science/pith/TO23G7YINKF2QRHS6TWB2XKWWE","bundle":"https://pith.science/pith/TO23G7YINKF2QRHS6TWB2XKWWE/bundle.json","state":"https://pith.science/pith/TO23G7YINKF2QRHS6TWB2XKWWE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TO23G7YINKF2QRHS6TWB2XKWWE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TO23G7YINKF2QRHS6TWB2XKWWE","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":"18a4f47bfe0356126cef6fa73b0a38f621b5377e2595a02e4e64620b4979abd0","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-08-21T14:57:53Z","title_canon_sha256":"1e6c254708f6a65cece6984dc77f4f5fcbd6f7e5e6d1042ce151b5e864260f5d"},"schema_version":"1.0","source":{"id":"2408.11678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.11678","created_at":"2026-07-05T08:57:47Z"},{"alias_kind":"arxiv_version","alias_value":"2408.11678v1","created_at":"2026-07-05T08:57:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.11678","created_at":"2026-07-05T08:57:47Z"},{"alias_kind":"pith_short_12","alias_value":"TO23G7YINKF2","created_at":"2026-07-05T08:57:47Z"},{"alias_kind":"pith_short_16","alias_value":"TO23G7YINKF2QRHS","created_at":"2026-07-05T08:57:47Z"},{"alias_kind":"pith_short_8","alias_value":"TO23G7YI","created_at":"2026-07-05T08:57:47Z"}],"graph_snapshots":[{"event_id":"sha256:ef216ee62f440ef4d0060ef53f01f00f057ff9608c1d4d5840ee6e5f656a57d3","target":"graph","created_at":"2026-07-05T08:57:47Z","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/2408.11678/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend recent existence and uniqueness results for maximal solutions of SPDEs through an improved blow-up criterion. Whilst the maximal time of existence is typically characterised by blow-up in the energy norm of solutions, we show instead that solutions exist until blow-up in the larger spaces of the variational framework. The result is applied to show that solutions of 2D and 3D Stochastic Navier-Stokes Equations retain the higher order regularity of the initial condition on their time of existence.","authors_text":"Daniel Goodair","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-08-21T14:57:53Z","title":"Improved Blow-Up Criterion in a Variational Framework for Nonlinear SPDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.11678","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:dfbb980f872b5bc7b99a1e87aa78c7277b97e37611a3b0ea297cde4490156ef1","target":"record","created_at":"2026-07-05T08:57:47Z","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":"18a4f47bfe0356126cef6fa73b0a38f621b5377e2595a02e4e64620b4979abd0","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-08-21T14:57:53Z","title_canon_sha256":"1e6c254708f6a65cece6984dc77f4f5fcbd6f7e5e6d1042ce151b5e864260f5d"},"schema_version":"1.0","source":{"id":"2408.11678","kind":"arxiv","version":1}},"canonical_sha256":"9bb5b37f086a8ba844f2f4ec1d5d56b10a92bbaf820f36ad8d47cef2a8adf3fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bb5b37f086a8ba844f2f4ec1d5d56b10a92bbaf820f36ad8d47cef2a8adf3fb","first_computed_at":"2026-07-05T08:57:47.263518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:57:47.263518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mdTv3abZpn+/WgMfLSMBW6BEVHDqWJpU01/1TnGtbaYKLBMsYTd5g6auVlgSthwEIoJie9JS8jqcrQ+nWlzKCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:57:47.263942Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.11678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfbb980f872b5bc7b99a1e87aa78c7277b97e37611a3b0ea297cde4490156ef1","sha256:ef216ee62f440ef4d0060ef53f01f00f057ff9608c1d4d5840ee6e5f656a57d3"],"state_sha256":"5fae5b91e7e1a03a348482936995e37401a4e0b5a421cdc45371ca63072738e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2/epPPBDQXVekGTg6YBsGqwROmi6ABO2U9zUbxrsSJ2+rHjlOzNA1ONI4UeHaSSvkka/9h41Jme1qAO5XjN1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T08:48:18.112582Z","bundle_sha256":"dc8d68f08ef0ed6e87404d2e33773c46424a7aec0985f35689f173472f1c2f26"}}