{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3GF2TGELGDCAUQDEEP4ZCAPQST","short_pith_number":"pith:3GF2TGEL","canonical_record":{"source":{"id":"1201.6326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-30T19:21:26Z","cross_cats_sorted":[],"title_canon_sha256":"8cbeaedbb776a20c3d1547bb272f2a79e3982a20202706aedf4acefd524e5ec7","abstract_canon_sha256":"5c04fadc8b64afc0fae8f888a25e9f94508a6a889ec2b1b24f5d9cdaa48301fa"},"schema_version":"1.0"},"canonical_sha256":"d98ba9988b30c40a406423f99101f094de71f7468aa702bcf9a9c5cb18b7195b","source":{"kind":"arxiv","id":"1201.6326","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6326","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6326v1","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6326","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"3GF2TGELGDCA","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3GF2TGELGDCAUQDE","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3GF2TGEL","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3GF2TGELGDCAUQDEEP4ZCAPQST","target":"record","payload":{"canonical_record":{"source":{"id":"1201.6326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-30T19:21:26Z","cross_cats_sorted":[],"title_canon_sha256":"8cbeaedbb776a20c3d1547bb272f2a79e3982a20202706aedf4acefd524e5ec7","abstract_canon_sha256":"5c04fadc8b64afc0fae8f888a25e9f94508a6a889ec2b1b24f5d9cdaa48301fa"},"schema_version":"1.0"},"canonical_sha256":"d98ba9988b30c40a406423f99101f094de71f7468aa702bcf9a9c5cb18b7195b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:16.428167Z","signature_b64":"df/NSUgcgina6RULpb9QKk5a3i8E05g+lUnsZt1aIP5mwlspKNrZ5KKPWuUlsGO7Q7fRoq2PO761ix7hV7U6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d98ba9988b30c40a406423f99101f094de71f7468aa702bcf9a9c5cb18b7195b","last_reissued_at":"2026-05-18T03:29:16.427367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:16.427367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.6326","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":"2026-05-18T03:29:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vkM/4dhelEuJ67a483pG05Vn+AhqyL6bkb44TUQFSRk31zWiic8pTXqN6GZsNywXm6r0w9wAiFNV7MqZ2XIvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:12:44.521283Z"},"content_sha256":"ec9eb5bf2f0d400625f83df63a4df1c4379ed7019e23df2de6ea7363619f3820","schema_version":"1.0","event_id":"sha256:ec9eb5bf2f0d400625f83df63a4df1c4379ed7019e23df2de6ea7363619f3820"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3GF2TGELGDCAUQDEEP4ZCAPQST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rapha\\\"el Danchin (LAMA)","submitted_at":"2012-01-30T19:21:26Z","abstract_excerpt":"We give lower bounds for the lifespan of a solution to the inviscid Boussinesq system. In dimension two, we point out that it tends to infinity when the initial (relative) temperature tends to zero. This is, to the best of our knowledge, the first result of this kind for the inviscid Boussinesq system. In passing, we provide continuation criteria (of independent interest) in the $N$-dimensional case. In the second part of the paper, our method is adapted to handle the axisymmetric incompressible Euler equations with swirl."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6326","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":"2026-05-18T03:29:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dtPGOSk1jUMowdspuQ41WhUFxQcPqJodGho2T9uq8fE/1JplALzePIVUGy/vsKgawnBinmE63LHpWPJNi2+bDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:12:44.521656Z"},"content_sha256":"e056eb696ec39ba5c1eb606e3255145c43f1e70dc4691a140a909d2c09e0b5c8","schema_version":"1.0","event_id":"sha256:e056eb696ec39ba5c1eb606e3255145c43f1e70dc4691a140a909d2c09e0b5c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3GF2TGELGDCAUQDEEP4ZCAPQST/bundle.json","state_url":"https://pith.science/pith/3GF2TGELGDCAUQDEEP4ZCAPQST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3GF2TGELGDCAUQDEEP4ZCAPQST/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":"2026-06-26T02:12:44Z","links":{"resolver":"https://pith.science/pith/3GF2TGELGDCAUQDEEP4ZCAPQST","bundle":"https://pith.science/pith/3GF2TGELGDCAUQDEEP4ZCAPQST/bundle.json","state":"https://pith.science/pith/3GF2TGELGDCAUQDEEP4ZCAPQST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3GF2TGELGDCAUQDEEP4ZCAPQST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3GF2TGELGDCAUQDEEP4ZCAPQST","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":"5c04fadc8b64afc0fae8f888a25e9f94508a6a889ec2b1b24f5d9cdaa48301fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-30T19:21:26Z","title_canon_sha256":"8cbeaedbb776a20c3d1547bb272f2a79e3982a20202706aedf4acefd524e5ec7"},"schema_version":"1.0","source":{"id":"1201.6326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6326","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6326v1","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6326","created_at":"2026-05-18T03:29:16Z"},{"alias_kind":"pith_short_12","alias_value":"3GF2TGELGDCA","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3GF2TGELGDCAUQDE","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3GF2TGEL","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:e056eb696ec39ba5c1eb606e3255145c43f1e70dc4691a140a909d2c09e0b5c8","target":"graph","created_at":"2026-05-18T03:29:16Z","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":"We give lower bounds for the lifespan of a solution to the inviscid Boussinesq system. In dimension two, we point out that it tends to infinity when the initial (relative) temperature tends to zero. This is, to the best of our knowledge, the first result of this kind for the inviscid Boussinesq system. In passing, we provide continuation criteria (of independent interest) in the $N$-dimensional case. In the second part of the paper, our method is adapted to handle the axisymmetric incompressible Euler equations with swirl.","authors_text":"Rapha\\\"el Danchin (LAMA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-30T19:21:26Z","title":"Remarks on the lifespan of the solutions to some models of incompressible fluid mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6326","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:ec9eb5bf2f0d400625f83df63a4df1c4379ed7019e23df2de6ea7363619f3820","target":"record","created_at":"2026-05-18T03:29:16Z","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":"5c04fadc8b64afc0fae8f888a25e9f94508a6a889ec2b1b24f5d9cdaa48301fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-01-30T19:21:26Z","title_canon_sha256":"8cbeaedbb776a20c3d1547bb272f2a79e3982a20202706aedf4acefd524e5ec7"},"schema_version":"1.0","source":{"id":"1201.6326","kind":"arxiv","version":1}},"canonical_sha256":"d98ba9988b30c40a406423f99101f094de71f7468aa702bcf9a9c5cb18b7195b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d98ba9988b30c40a406423f99101f094de71f7468aa702bcf9a9c5cb18b7195b","first_computed_at":"2026-05-18T03:29:16.427367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:16.427367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"df/NSUgcgina6RULpb9QKk5a3i8E05g+lUnsZt1aIP5mwlspKNrZ5KKPWuUlsGO7Q7fRoq2PO761ix7hV7U6AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:16.428167Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec9eb5bf2f0d400625f83df63a4df1c4379ed7019e23df2de6ea7363619f3820","sha256:e056eb696ec39ba5c1eb606e3255145c43f1e70dc4691a140a909d2c09e0b5c8"],"state_sha256":"76ccb6db6e36873f690b6b4a91ea773dfee6384d4351a6d704d3edcfcba25daf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYB3v7+LIV9zpKWeUAM/5mXlJNBfAnHJNt0Q4RQEHIsnW2CyGdlZ/jKedkriUnfwdf57+riqRFWbeG7epDEFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T02:12:44.523645Z","bundle_sha256":"8b8eeb9e0165df4fc37c0a6792f75bd7b4da0cb1d5c2d1287e05910d13d6987e"}}