{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:O23R33RRI3XHF4QETLGQPK5BBU","short_pith_number":"pith:O23R33RR","canonical_record":{"source":{"id":"1806.10430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-27T12:15:04Z","cross_cats_sorted":[],"title_canon_sha256":"add2f11cea926ad08ae1f1e3cb7e87fdc9bafa0c518785a88928486099295222","abstract_canon_sha256":"314176e2d5b7e35bbc69511bd0f299ee589565124b982cdca67c78258151beae"},"schema_version":"1.0"},"canonical_sha256":"76b71dee3146ee72f2049acd07aba10d2efa430214eabace93c5408c47c0d770","source":{"kind":"arxiv","id":"1806.10430","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10430","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10430v2","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10430","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"O23R33RRI3XH","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O23R33RRI3XHF4QE","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O23R33RR","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:O23R33RRI3XHF4QETLGQPK5BBU","target":"record","payload":{"canonical_record":{"source":{"id":"1806.10430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-27T12:15:04Z","cross_cats_sorted":[],"title_canon_sha256":"add2f11cea926ad08ae1f1e3cb7e87fdc9bafa0c518785a88928486099295222","abstract_canon_sha256":"314176e2d5b7e35bbc69511bd0f299ee589565124b982cdca67c78258151beae"},"schema_version":"1.0"},"canonical_sha256":"76b71dee3146ee72f2049acd07aba10d2efa430214eabace93c5408c47c0d770","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:56.462802Z","signature_b64":"JVDOPPY+N3dNLJM8POS11IxQMIaOhXBOkeKxQFEZpwQjoV3KEaJacYplqC9msbQ5D2dCCN3HApp+eP4n0+E4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76b71dee3146ee72f2049acd07aba10d2efa430214eabace93c5408c47c0d770","last_reissued_at":"2026-05-18T00:11:56.462149Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:56.462149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.10430","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":"2026-05-18T00:11:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FuWxfrlFPtvw9tthrtJ6/7wzaG799lo1UK+5dWZ8ORP+3FAH8sBeFr33/y8LMG1Ye0Lt83S5dmRYcoZ9K9fTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:49:20.747450Z"},"content_sha256":"16a011a9c7d3e8484d7f6a313b1f24db40d58001b4ebf8ec4895b637c476d928","schema_version":"1.0","event_id":"sha256:16a011a9c7d3e8484d7f6a313b1f24db40d58001b4ebf8ec4895b637c476d928"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:O23R33RRI3XHF4QETLGQPK5BBU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deterministics descriptions of the turbulence in the Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diego Chamorro (LaMME), Isabelle Gallagher (IMJ), Lorenzo Brandolese (ICJ), Oscar Jarrin (LaMME), Pierre Gilles (DCM), Roger Lewandowski (IRMAR)","submitted_at":"2018-06-27T12:15:04Z","abstract_excerpt":"This PhD thesis is devoted to deterministic study of the turbulence in the Navier- Stokes equations. The thesis is divided in four independent chapters.The first chapter involves a rigorous discussion about the energy's dissipation law, proposed by theory of the turbulence K41, in the deterministic setting of the homogeneous and incompressible Navier-Stokes equations, with a stationary external force (the force only depends of the spatial variable) and on the whole space R3. The energy's dissipation law, also called the Kolmogorov's dissipation law, characterizes the energy's dissipation rate "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10430","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":"2026-05-18T00:11:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gDAqOy5RbPWQ40IPmVaa0RXnkK6FTP2lfE0o8FZ4S3B5UlP6YuaOUsFq1ZTaTT9YG9sOLs+UYuW3QIqvdL82BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:49:20.747805Z"},"content_sha256":"609721c12884164aeb14c662283059bdabf3aaf91169fb5a3343226ca0ba4a23","schema_version":"1.0","event_id":"sha256:609721c12884164aeb14c662283059bdabf3aaf91169fb5a3343226ca0ba4a23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O23R33RRI3XHF4QETLGQPK5BBU/bundle.json","state_url":"https://pith.science/pith/O23R33RRI3XHF4QETLGQPK5BBU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O23R33RRI3XHF4QETLGQPK5BBU/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":"2026-06-24T22:49:20Z","links":{"resolver":"https://pith.science/pith/O23R33RRI3XHF4QETLGQPK5BBU","bundle":"https://pith.science/pith/O23R33RRI3XHF4QETLGQPK5BBU/bundle.json","state":"https://pith.science/pith/O23R33RRI3XHF4QETLGQPK5BBU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O23R33RRI3XHF4QETLGQPK5BBU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O23R33RRI3XHF4QETLGQPK5BBU","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":"314176e2d5b7e35bbc69511bd0f299ee589565124b982cdca67c78258151beae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-27T12:15:04Z","title_canon_sha256":"add2f11cea926ad08ae1f1e3cb7e87fdc9bafa0c518785a88928486099295222"},"schema_version":"1.0","source":{"id":"1806.10430","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10430","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10430v2","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10430","created_at":"2026-05-18T00:11:56Z"},{"alias_kind":"pith_short_12","alias_value":"O23R33RRI3XH","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O23R33RRI3XHF4QE","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O23R33RR","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:609721c12884164aeb14c662283059bdabf3aaf91169fb5a3343226ca0ba4a23","target":"graph","created_at":"2026-05-18T00:11:56Z","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":"This PhD thesis is devoted to deterministic study of the turbulence in the Navier- Stokes equations. The thesis is divided in four independent chapters.The first chapter involves a rigorous discussion about the energy's dissipation law, proposed by theory of the turbulence K41, in the deterministic setting of the homogeneous and incompressible Navier-Stokes equations, with a stationary external force (the force only depends of the spatial variable) and on the whole space R3. The energy's dissipation law, also called the Kolmogorov's dissipation law, characterizes the energy's dissipation rate ","authors_text":"Diego Chamorro (LaMME), Isabelle Gallagher (IMJ), Lorenzo Brandolese (ICJ), Oscar Jarrin (LaMME), Pierre Gilles (DCM), Roger Lewandowski (IRMAR)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-27T12:15:04Z","title":"Deterministics descriptions of the turbulence in the Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10430","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":"sha256:16a011a9c7d3e8484d7f6a313b1f24db40d58001b4ebf8ec4895b637c476d928","target":"record","created_at":"2026-05-18T00:11:56Z","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":"314176e2d5b7e35bbc69511bd0f299ee589565124b982cdca67c78258151beae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-27T12:15:04Z","title_canon_sha256":"add2f11cea926ad08ae1f1e3cb7e87fdc9bafa0c518785a88928486099295222"},"schema_version":"1.0","source":{"id":"1806.10430","kind":"arxiv","version":2}},"canonical_sha256":"76b71dee3146ee72f2049acd07aba10d2efa430214eabace93c5408c47c0d770","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76b71dee3146ee72f2049acd07aba10d2efa430214eabace93c5408c47c0d770","first_computed_at":"2026-05-18T00:11:56.462149Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:56.462149Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JVDOPPY+N3dNLJM8POS11IxQMIaOhXBOkeKxQFEZpwQjoV3KEaJacYplqC9msbQ5D2dCCN3HApp+eP4n0+E4Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:56.462802Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10430","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16a011a9c7d3e8484d7f6a313b1f24db40d58001b4ebf8ec4895b637c476d928","sha256:609721c12884164aeb14c662283059bdabf3aaf91169fb5a3343226ca0ba4a23"],"state_sha256":"ab46c84a34bc1f5ea21a7be40a5dfbe644d9996740a9ffab1744764264ade9d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5e5qKX+9jTnb+NUVb70/7GEaNlkl1srE1q+Hpi/q1a8/Ua5VJrhNTrilK8VrD52hzadGTF4T553R7QjiYFqMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:49:20.749815Z","bundle_sha256":"ad10e3122667df502cef8460f34ba147818140b90d1e2685e2a1c8469308d09c"}}