{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YPFG5CPUF3DQAWSRQ6MVFJMWYE","short_pith_number":"pith:YPFG5CPU","canonical_record":{"source":{"id":"1309.1190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-04T21:31:19Z","cross_cats_sorted":[],"title_canon_sha256":"292dca21e061660d2674d49a307c99bb838b79027d46319545b2976850648a68","abstract_canon_sha256":"96e1ce65f395aa433595b254aaa1d4c500c653bac9b7d166ffcb6a163caf2da1"},"schema_version":"1.0"},"canonical_sha256":"c3ca6e89f42ec7005a51879952a596c112e75c6474189aaa3cb6da991889f14f","source":{"kind":"arxiv","id":"1309.1190","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1190","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1190v1","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1190","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"YPFG5CPUF3DQ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YPFG5CPUF3DQAWSR","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YPFG5CPU","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YPFG5CPUF3DQAWSRQ6MVFJMWYE","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-04T21:31:19Z","cross_cats_sorted":[],"title_canon_sha256":"292dca21e061660d2674d49a307c99bb838b79027d46319545b2976850648a68","abstract_canon_sha256":"96e1ce65f395aa433595b254aaa1d4c500c653bac9b7d166ffcb6a163caf2da1"},"schema_version":"1.0"},"canonical_sha256":"c3ca6e89f42ec7005a51879952a596c112e75c6474189aaa3cb6da991889f14f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:08.008651Z","signature_b64":"f+BP3+3cTs/Tqe1HHMDa0LfMGorrP7rTr7kW90wcrrBzRFjUgHi+GT4PgZXQ4sQknLLG3FF/fnZ1Q3QBeaZgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3ca6e89f42ec7005a51879952a596c112e75c6474189aaa3cb6da991889f14f","last_reissued_at":"2026-05-18T03:14:08.008225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:08.008225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1190","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":"2026-05-18T03:14:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MayhWexJQqLs64EfciULF5PT5LpD5df0Mxw0eqheW9m+5TeGVke9gQP5WR0Xg6orke5HhYb14uQycUnmFxiUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T08:33:16.383536Z"},"content_sha256":"e3e4f47c24097e2041f06bdc3375c9e1c03efa7891190b00629ffc1ece69d9fb","schema_version":"1.0","event_id":"sha256:e3e4f47c24097e2041f06bdc3375c9e1c03efa7891190b00629ffc1ece69d9fb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YPFG5CPUF3DQAWSRQ6MVFJMWYE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large deviations for 2D-fractional stochastic Navier-Stokes equation on the torus -Short Proof-","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Latifa Debbi","submitted_at":"2013-09-04T21:31:19Z","abstract_excerpt":"In this note, we prove the large deviation principle for the 2D-fractional stochastic Navier-Stokes equation on the torus under the dissipation order $ \\alpha \\in [\\frac43, 2]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1190","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":"2026-05-18T03:14:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PWa7O7/gfQ8jyYXA96C8ezziBF6EARguZsHh4iWa3eOswKjJA4I4XYUTDCHR0kcUsU63Rq6Z5UdR4OUSupkNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T08:33:16.383873Z"},"content_sha256":"c8108c2a20b935cf23ce22760d1f0ca6d3a4424f72eee3b870d102059f245065","schema_version":"1.0","event_id":"sha256:c8108c2a20b935cf23ce22760d1f0ca6d3a4424f72eee3b870d102059f245065"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YPFG5CPUF3DQAWSRQ6MVFJMWYE/bundle.json","state_url":"https://pith.science/pith/YPFG5CPUF3DQAWSRQ6MVFJMWYE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YPFG5CPUF3DQAWSRQ6MVFJMWYE/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":"2026-06-30T08:33:16Z","links":{"resolver":"https://pith.science/pith/YPFG5CPUF3DQAWSRQ6MVFJMWYE","bundle":"https://pith.science/pith/YPFG5CPUF3DQAWSRQ6MVFJMWYE/bundle.json","state":"https://pith.science/pith/YPFG5CPUF3DQAWSRQ6MVFJMWYE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YPFG5CPUF3DQAWSRQ6MVFJMWYE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YPFG5CPUF3DQAWSRQ6MVFJMWYE","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":"96e1ce65f395aa433595b254aaa1d4c500c653bac9b7d166ffcb6a163caf2da1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-04T21:31:19Z","title_canon_sha256":"292dca21e061660d2674d49a307c99bb838b79027d46319545b2976850648a68"},"schema_version":"1.0","source":{"id":"1309.1190","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1190","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1190v1","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1190","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"YPFG5CPUF3DQ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YPFG5CPUF3DQAWSR","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YPFG5CPU","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:c8108c2a20b935cf23ce22760d1f0ca6d3a4424f72eee3b870d102059f245065","target":"graph","created_at":"2026-05-18T03:14:08Z","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 note, we prove the large deviation principle for the 2D-fractional stochastic Navier-Stokes equation on the torus under the dissipation order $ \\alpha \\in [\\frac43, 2]$.","authors_text":"Latifa Debbi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-04T21:31:19Z","title":"Large deviations for 2D-fractional stochastic Navier-Stokes equation on the torus -Short Proof-"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1190","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:e3e4f47c24097e2041f06bdc3375c9e1c03efa7891190b00629ffc1ece69d9fb","target":"record","created_at":"2026-05-18T03:14:08Z","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":"96e1ce65f395aa433595b254aaa1d4c500c653bac9b7d166ffcb6a163caf2da1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-04T21:31:19Z","title_canon_sha256":"292dca21e061660d2674d49a307c99bb838b79027d46319545b2976850648a68"},"schema_version":"1.0","source":{"id":"1309.1190","kind":"arxiv","version":1}},"canonical_sha256":"c3ca6e89f42ec7005a51879952a596c112e75c6474189aaa3cb6da991889f14f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3ca6e89f42ec7005a51879952a596c112e75c6474189aaa3cb6da991889f14f","first_computed_at":"2026-05-18T03:14:08.008225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:08.008225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f+BP3+3cTs/Tqe1HHMDa0LfMGorrP7rTr7kW90wcrrBzRFjUgHi+GT4PgZXQ4sQknLLG3FF/fnZ1Q3QBeaZgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:08.008651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1190","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3e4f47c24097e2041f06bdc3375c9e1c03efa7891190b00629ffc1ece69d9fb","sha256:c8108c2a20b935cf23ce22760d1f0ca6d3a4424f72eee3b870d102059f245065"],"state_sha256":"9d7cdbe24d06052d8c6f6b3306402de8c495ca902871bc5b26bb01e7595b73d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HAZQig7rVuVvKphIZ7I+h4V73qvpdcg6hCg35jIdrmEGIJ81Tz8oW6vmVrrg9iiWU10+gNJDFnLBc36ryrExAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T08:33:16.385756Z","bundle_sha256":"2c2b0e68788adbb8377d671ee95d0d9c94609cc41a55935688567a30261bf964"}}