{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YYEA3UG3LRGPPAVZOADMWSODUN","short_pith_number":"pith:YYEA3UG3","canonical_record":{"source":{"id":"2603.03666","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-03-04T02:46:48Z","cross_cats_sorted":[],"title_canon_sha256":"63e661309cd5861504fb76c62ffe5ceb31c1ae8cc82db061772d9c99972ca9d3","abstract_canon_sha256":"bde75033369d152f88d3e633beacf8bc7b6386065c2f3a9c55bdd8dfbb423b8d"},"schema_version":"1.0"},"canonical_sha256":"c6080dd0db5c4cf782b97006cb49c3a353e975fa1186e3cc93ce1678ebc5bedf","source":{"kind":"arxiv","id":"2603.03666","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.03666","created_at":"2026-06-12T01:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"2603.03666v2","created_at":"2026-06-12T01:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.03666","created_at":"2026-06-12T01:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"YYEA3UG3LRGP","created_at":"2026-06-12T01:09:24Z"},{"alias_kind":"pith_short_16","alias_value":"YYEA3UG3LRGPPAVZ","created_at":"2026-06-12T01:09:24Z"},{"alias_kind":"pith_short_8","alias_value":"YYEA3UG3","created_at":"2026-06-12T01:09:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YYEA3UG3LRGPPAVZOADMWSODUN","target":"record","payload":{"canonical_record":{"source":{"id":"2603.03666","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-03-04T02:46:48Z","cross_cats_sorted":[],"title_canon_sha256":"63e661309cd5861504fb76c62ffe5ceb31c1ae8cc82db061772d9c99972ca9d3","abstract_canon_sha256":"bde75033369d152f88d3e633beacf8bc7b6386065c2f3a9c55bdd8dfbb423b8d"},"schema_version":"1.0"},"canonical_sha256":"c6080dd0db5c4cf782b97006cb49c3a353e975fa1186e3cc93ce1678ebc5bedf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T01:09:24.441402Z","signature_b64":"AAw/pIwyzNrAXm0IH3U9TSzry+mYMeC5UKqYXVAreigyPJdbNDx3VLlBW6oztphzQATpdYnYC0JGiAnkVzWdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6080dd0db5c4cf782b97006cb49c3a353e975fa1186e3cc93ce1678ebc5bedf","last_reissued_at":"2026-06-12T01:09:24.440928Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T01:09:24.440928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.03666","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":"2026-06-12T01:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AZPBha3BWHwI+FAz+FM1JMj6aiQeVH2g+5XrFmOe9aeoOnEKBEUxHBG0n9nkWcOw+j80yNKHvCyNywNOg+ZYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:49:21.356022Z"},"content_sha256":"fe8db7d1ae5cfaba7432f18a921ae5846d2aa88daa442f4220f589e67d68580b","schema_version":"1.0","event_id":"sha256:fe8db7d1ae5cfaba7432f18a921ae5846d2aa88daa442f4220f589e67d68580b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YYEA3UG3LRGPPAVZOADMWSODUN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexey Cheskidov, Hedong Hou","submitted_at":"2026-03-04T02:46:48Z","abstract_excerpt":"We prove that the unconditional uniqueness of mild solutions to the Navier-Stokes equations fails in all the Besov spaces with negative regularity index, by constructing non-trivial stationary singular solutions via convex integration. We also establish uniqueness of stationary weak solutions in an endpoint critical space. Similar results are proved for the fractional Navier-Stokes equations with arbitrarily large power of the Laplacian in both Lebesgue and Besov spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.03666","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.03666/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":"2026-06-12T01:09:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ODg76LKc9/RrwunuDA7QA+3gbJKxWrgHUksIBiqYeKc+XdxdfxtEKHHYibLDxG/7HocnYW+jFRGRXb9dbzKOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T08:49:21.356674Z"},"content_sha256":"7833678b0ac374fd88e0d55b6b839993c653e284105af39a48d7a4a747c1190a","schema_version":"1.0","event_id":"sha256:7833678b0ac374fd88e0d55b6b839993c653e284105af39a48d7a4a747c1190a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYEA3UG3LRGPPAVZOADMWSODUN/bundle.json","state_url":"https://pith.science/pith/YYEA3UG3LRGPPAVZOADMWSODUN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYEA3UG3LRGPPAVZOADMWSODUN/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":"2026-08-08T08:49:21Z","links":{"resolver":"https://pith.science/pith/YYEA3UG3LRGPPAVZOADMWSODUN","bundle":"https://pith.science/pith/YYEA3UG3LRGPPAVZOADMWSODUN/bundle.json","state":"https://pith.science/pith/YYEA3UG3LRGPPAVZOADMWSODUN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYEA3UG3LRGPPAVZOADMWSODUN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YYEA3UG3LRGPPAVZOADMWSODUN","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":"bde75033369d152f88d3e633beacf8bc7b6386065c2f3a9c55bdd8dfbb423b8d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-03-04T02:46:48Z","title_canon_sha256":"63e661309cd5861504fb76c62ffe5ceb31c1ae8cc82db061772d9c99972ca9d3"},"schema_version":"1.0","source":{"id":"2603.03666","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.03666","created_at":"2026-06-12T01:09:24Z"},{"alias_kind":"arxiv_version","alias_value":"2603.03666v2","created_at":"2026-06-12T01:09:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.03666","created_at":"2026-06-12T01:09:24Z"},{"alias_kind":"pith_short_12","alias_value":"YYEA3UG3LRGP","created_at":"2026-06-12T01:09:24Z"},{"alias_kind":"pith_short_16","alias_value":"YYEA3UG3LRGPPAVZ","created_at":"2026-06-12T01:09:24Z"},{"alias_kind":"pith_short_8","alias_value":"YYEA3UG3","created_at":"2026-06-12T01:09:24Z"}],"graph_snapshots":[{"event_id":"sha256:7833678b0ac374fd88e0d55b6b839993c653e284105af39a48d7a4a747c1190a","target":"graph","created_at":"2026-06-12T01:09:24Z","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/2603.03666/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the unconditional uniqueness of mild solutions to the Navier-Stokes equations fails in all the Besov spaces with negative regularity index, by constructing non-trivial stationary singular solutions via convex integration. We also establish uniqueness of stationary weak solutions in an endpoint critical space. Similar results are proved for the fractional Navier-Stokes equations with arbitrarily large power of the Laplacian in both Lebesgue and Besov spaces.","authors_text":"Alexey Cheskidov, Hedong Hou","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-03-04T02:46:48Z","title":"On non-uniqueness of mild solutions and stationary singular solutions to the Navier-Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.03666","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:fe8db7d1ae5cfaba7432f18a921ae5846d2aa88daa442f4220f589e67d68580b","target":"record","created_at":"2026-06-12T01:09:24Z","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":"bde75033369d152f88d3e633beacf8bc7b6386065c2f3a9c55bdd8dfbb423b8d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-03-04T02:46:48Z","title_canon_sha256":"63e661309cd5861504fb76c62ffe5ceb31c1ae8cc82db061772d9c99972ca9d3"},"schema_version":"1.0","source":{"id":"2603.03666","kind":"arxiv","version":2}},"canonical_sha256":"c6080dd0db5c4cf782b97006cb49c3a353e975fa1186e3cc93ce1678ebc5bedf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6080dd0db5c4cf782b97006cb49c3a353e975fa1186e3cc93ce1678ebc5bedf","first_computed_at":"2026-06-12T01:09:24.440928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T01:09:24.440928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AAw/pIwyzNrAXm0IH3U9TSzry+mYMeC5UKqYXVAreigyPJdbNDx3VLlBW6oztphzQATpdYnYC0JGiAnkVzWdDA==","signature_status":"signed_v1","signed_at":"2026-06-12T01:09:24.441402Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.03666","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe8db7d1ae5cfaba7432f18a921ae5846d2aa88daa442f4220f589e67d68580b","sha256:7833678b0ac374fd88e0d55b6b839993c653e284105af39a48d7a4a747c1190a"],"state_sha256":"974c56b81c291ed0b31b5b7b9f7ede8adc5451e27b589a3fd36bdcb46e52b7ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VhPKG1sn6sXXLarw3I3iX7XWvAzdIbd5zvBOQGO1Gbf0yA5mbl7nOD3ODBIGWyHE2yDJ0HlEWHGXPohT/pdTCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T08:49:21.360925Z","bundle_sha256":"8e3a38bb1abaf3d2eb581bf6918e80183ad60848c74da7824498650980b08791"}}