{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FNL6S52PL25R6VII3BCWQFKMBK","short_pith_number":"pith:FNL6S52P","canonical_record":{"source":{"id":"1808.07595","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-23T00:22:10Z","cross_cats_sorted":[],"title_canon_sha256":"cf2f4f44637f23baaff3622054146c589abbbb8877fff5a65ff11a06157d9283","abstract_canon_sha256":"c5c9c50814de03d32238f83e27f0bcecd39a955dc5f815a235f1b76e8a6b3fee"},"schema_version":"1.0"},"canonical_sha256":"2b57e9774f5ebb1f5508d84568154c0ab0bff95108e1d792b797747348bbf50f","source":{"kind":"arxiv","id":"1808.07595","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07595","created_at":"2026-07-05T00:55:26Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07595v3","created_at":"2026-07-05T00:55:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07595","created_at":"2026-07-05T00:55:26Z"},{"alias_kind":"pith_short_12","alias_value":"FNL6S52PL25R","created_at":"2026-07-05T00:55:26Z"},{"alias_kind":"pith_short_16","alias_value":"FNL6S52PL25R6VII","created_at":"2026-07-05T00:55:26Z"},{"alias_kind":"pith_short_8","alias_value":"FNL6S52P","created_at":"2026-07-05T00:55:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FNL6S52PL25R6VII3BCWQFKMBK","target":"record","payload":{"canonical_record":{"source":{"id":"1808.07595","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-23T00:22:10Z","cross_cats_sorted":[],"title_canon_sha256":"cf2f4f44637f23baaff3622054146c589abbbb8877fff5a65ff11a06157d9283","abstract_canon_sha256":"c5c9c50814de03d32238f83e27f0bcecd39a955dc5f815a235f1b76e8a6b3fee"},"schema_version":"1.0"},"canonical_sha256":"2b57e9774f5ebb1f5508d84568154c0ab0bff95108e1d792b797747348bbf50f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:55:26.867079Z","signature_b64":"qv+hEJmjdXmtIJp5ic3ezcbxeOVvCXKn3USaGWurr++hGJ0lHx3Osj6mWbvjKPdGrngD8Y0SzxIJfESu0aWOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b57e9774f5ebb1f5508d84568154c0ab0bff95108e1d792b797747348bbf50f","last_reissued_at":"2026-07-05T00:55:26.866667Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:55:26.866667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.07595","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:55:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u5w7i1veAnGjj/QNJf2PrdmJ4YldjQzivDWohN768DX8jk18Nr5mqH/zbJ7Z0dtz6je1sQdBkOGDx53rrze3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T03:43:44.000713Z"},"content_sha256":"79d69ab03e612d8f0e8ac648b78faeda260f0840cc215314d009ea1612fc58fe","schema_version":"1.0","event_id":"sha256:79d69ab03e612d8f0e8ac648b78faeda260f0840cc215314d009ea1612fc58fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FNL6S52PL25R6VII3BCWQFKMBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-uniqueness of Weak Solutions to Hyperviscous Navier-Stokes Equations -- On Sharpness of J.-L. Lions Exponent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Edriss S. Titi, Tianwen Luo","submitted_at":"2018-08-23T00:22:10Z","abstract_excerpt":"Using the convex integration technique for the three-dimensional Navier-Stokes equations introduced by T. Buckmaster and V. Vicol, it is shown the existence of non-unique weak solutions for the 3D Navier-Stokes equations with fractional hyperviscosity $(-\\Delta)^{\\theta}$, whenever the exponent $\\theta$ is less than J.-L. Lions' exponent $5/4$, i.e., when $\\theta < 5/4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07595","kind":"arxiv","version":3},"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/1808.07595/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":"2026-07-05T00:55:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4q5H6pX+7Mj9LmDss8BgfcxshgZ4o0duWikC7BlHa+Ez2/C9ihh2xyOnEfuY0f1cc1fXLhZRrzL48YyRfvbMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T03:43:44.001226Z"},"content_sha256":"6a216270b43963f6d58efe5d9302eac367847ea774224d8d6bc6430ab324618a","schema_version":"1.0","event_id":"sha256:6a216270b43963f6d58efe5d9302eac367847ea774224d8d6bc6430ab324618a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FNL6S52PL25R6VII3BCWQFKMBK/bundle.json","state_url":"https://pith.science/pith/FNL6S52PL25R6VII3BCWQFKMBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FNL6S52PL25R6VII3BCWQFKMBK/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":"2026-08-17T03:43:44Z","links":{"resolver":"https://pith.science/pith/FNL6S52PL25R6VII3BCWQFKMBK","bundle":"https://pith.science/pith/FNL6S52PL25R6VII3BCWQFKMBK/bundle.json","state":"https://pith.science/pith/FNL6S52PL25R6VII3BCWQFKMBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FNL6S52PL25R6VII3BCWQFKMBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FNL6S52PL25R6VII3BCWQFKMBK","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":"c5c9c50814de03d32238f83e27f0bcecd39a955dc5f815a235f1b76e8a6b3fee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-23T00:22:10Z","title_canon_sha256":"cf2f4f44637f23baaff3622054146c589abbbb8877fff5a65ff11a06157d9283"},"schema_version":"1.0","source":{"id":"1808.07595","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07595","created_at":"2026-07-05T00:55:26Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07595v3","created_at":"2026-07-05T00:55:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07595","created_at":"2026-07-05T00:55:26Z"},{"alias_kind":"pith_short_12","alias_value":"FNL6S52PL25R","created_at":"2026-07-05T00:55:26Z"},{"alias_kind":"pith_short_16","alias_value":"FNL6S52PL25R6VII","created_at":"2026-07-05T00:55:26Z"},{"alias_kind":"pith_short_8","alias_value":"FNL6S52P","created_at":"2026-07-05T00:55:26Z"}],"graph_snapshots":[{"event_id":"sha256:6a216270b43963f6d58efe5d9302eac367847ea774224d8d6bc6430ab324618a","target":"graph","created_at":"2026-07-05T00:55:26Z","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/1808.07595/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using the convex integration technique for the three-dimensional Navier-Stokes equations introduced by T. Buckmaster and V. Vicol, it is shown the existence of non-unique weak solutions for the 3D Navier-Stokes equations with fractional hyperviscosity $(-\\Delta)^{\\theta}$, whenever the exponent $\\theta$ is less than J.-L. Lions' exponent $5/4$, i.e., when $\\theta < 5/4$.","authors_text":"Edriss S. Titi, Tianwen Luo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-23T00:22:10Z","title":"Non-uniqueness of Weak Solutions to Hyperviscous Navier-Stokes Equations -- On Sharpness of J.-L. Lions Exponent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07595","kind":"arxiv","version":3},"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":"sha256:79d69ab03e612d8f0e8ac648b78faeda260f0840cc215314d009ea1612fc58fe","target":"record","created_at":"2026-07-05T00:55:26Z","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":"c5c9c50814de03d32238f83e27f0bcecd39a955dc5f815a235f1b76e8a6b3fee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-08-23T00:22:10Z","title_canon_sha256":"cf2f4f44637f23baaff3622054146c589abbbb8877fff5a65ff11a06157d9283"},"schema_version":"1.0","source":{"id":"1808.07595","kind":"arxiv","version":3}},"canonical_sha256":"2b57e9774f5ebb1f5508d84568154c0ab0bff95108e1d792b797747348bbf50f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b57e9774f5ebb1f5508d84568154c0ab0bff95108e1d792b797747348bbf50f","first_computed_at":"2026-07-05T00:55:26.866667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:55:26.866667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qv+hEJmjdXmtIJp5ic3ezcbxeOVvCXKn3USaGWurr++hGJ0lHx3Osj6mWbvjKPdGrngD8Y0SzxIJfESu0aWOCg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:55:26.867079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.07595","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79d69ab03e612d8f0e8ac648b78faeda260f0840cc215314d009ea1612fc58fe","sha256:6a216270b43963f6d58efe5d9302eac367847ea774224d8d6bc6430ab324618a"],"state_sha256":"6d147d6d3a237d6dfd2b14273b4afc76d5da492b41ae1b19f69bf19439df3909"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RgliaGjc48USYLWT3424QnFR/h2zKKSX1fJrGizZ8ogVKJ30LU2oGZTSJWAkup4Xd8MFZmrgh27XF6rnMnGuDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T03:43:44.005895Z","bundle_sha256":"30d26d3d48474c02fa092baaef0558c3ee36e4d2cfff8000866e3624ec25104e"}}