{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:STO26IQ56H2EBEBHWGPANZ4Q3C","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":"b3468c5dd27d98df91244fc299440b5ff7ed6b374f924bc8f04885ee1e0774bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-09T11:47:27Z","title_canon_sha256":"8870f3bea9e7afd30e8f7fc5290eb2567b7fe1d1b1a68463ae56d1c71e564522"},"schema_version":"1.0","source":{"id":"2407.06776","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.06776","created_at":"2026-07-05T08:51:54Z"},{"alias_kind":"arxiv_version","alias_value":"2407.06776v2","created_at":"2026-07-05T08:51:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.06776","created_at":"2026-07-05T08:51:54Z"},{"alias_kind":"pith_short_12","alias_value":"STO26IQ56H2E","created_at":"2026-07-05T08:51:54Z"},{"alias_kind":"pith_short_16","alias_value":"STO26IQ56H2EBEBH","created_at":"2026-07-05T08:51:54Z"},{"alias_kind":"pith_short_8","alias_value":"STO26IQ5","created_at":"2026-07-05T08:51:54Z"}],"graph_snapshots":[{"event_id":"sha256:504d893d6bad9fd09f7b618401019e058a401bdd3851d862b7d88a5f89b1ae72","target":"graph","created_at":"2026-07-05T08:51:54Z","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/2407.06776/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work we establish the formation of singularities of classical solutions with finite energy of the forced fractional Navier Stokes equations where the dissipative term is given by $|\\nabla|^{\\alpha}$ for any $\\alpha\\in [0, \\alpha_0)$ ($\\alpha_0 = \\frac{22-8\\sqrt7}{9} > 0$). We construct solutions in $\\mathbb{R}^3\\times [0,T]$ with a finite $T>0$ and with an external forcing which is in $L^1_t([0, T]) C_x^{1,\\epsilon}\\cap L^{\\infty}_{t}L_{x}^2$, such that on the time interval $0 \\le t < T$, the velocity $u$ is in the space $C^\\infty\\cap L^2$ and such that as the time $t$ approaches the b","authors_text":"Diego C\\'ordoba, Fan Zheng, Luis Mart\\'inez-Zoroa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-09T11:47:27Z","title":"Finite time blow-up for the hypodissipative Navier Stokes equations with a force in $L^1_t C_x^{1,\\epsilon}\\cap L^{\\infty}_{t}L_{x}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.06776","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":"sha256:3f862092cb92dac9b89fa21374629cce541031862c97b79c0c2bd753686e3a12","target":"record","created_at":"2026-07-05T08:51:54Z","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":"b3468c5dd27d98df91244fc299440b5ff7ed6b374f924bc8f04885ee1e0774bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-07-09T11:47:27Z","title_canon_sha256":"8870f3bea9e7afd30e8f7fc5290eb2567b7fe1d1b1a68463ae56d1c71e564522"},"schema_version":"1.0","source":{"id":"2407.06776","kind":"arxiv","version":2}},"canonical_sha256":"94ddaf221df1f4409027b19e06e790d89e54da5ad7710b2d7a5e0d9621b8ef62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94ddaf221df1f4409027b19e06e790d89e54da5ad7710b2d7a5e0d9621b8ef62","first_computed_at":"2026-07-05T08:51:54.454341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:51:54.454341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UIlxTXoVFHiqPr7lnbaVbHpTmjki6SCiBNG64TkQIWATK139oL0uBDkZeb9+ghjKB+Qv2fo5IF1mX3TpBFlYBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:51:54.454891Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.06776","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f862092cb92dac9b89fa21374629cce541031862c97b79c0c2bd753686e3a12","sha256:504d893d6bad9fd09f7b618401019e058a401bdd3851d862b7d88a5f89b1ae72"],"state_sha256":"95d71c2a606270d561bf65d57510263ac20244bce369d685e1f4952afa8c3dfa"}