{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:GARXAVGFABTRFNYQ66GO3EVFBP","short_pith_number":"pith:GARXAVGF","canonical_record":{"source":{"id":"2502.06357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-10T11:17:56Z","cross_cats_sorted":[],"title_canon_sha256":"60850a71bb642ca90993578871816b3551f11610a65daa2618d90ab33b2658ed","abstract_canon_sha256":"7f2e505bc8f284ab08ce5e47a1c7ec38a1e45570b01f62026e11db9b553e12f7"},"schema_version":"1.0"},"canonical_sha256":"30237054c5006712b710f78ced92a50bed892ba355e64072345d858048379506","source":{"kind":"arxiv","id":"2502.06357","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.06357","created_at":"2026-07-05T11:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"2502.06357v2","created_at":"2026-07-05T11:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06357","created_at":"2026-07-05T11:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"GARXAVGFABTR","created_at":"2026-07-05T11:36:27Z"},{"alias_kind":"pith_short_16","alias_value":"GARXAVGFABTRFNYQ","created_at":"2026-07-05T11:36:27Z"},{"alias_kind":"pith_short_8","alias_value":"GARXAVGF","created_at":"2026-07-05T11:36:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:GARXAVGFABTRFNYQ66GO3EVFBP","target":"record","payload":{"canonical_record":{"source":{"id":"2502.06357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-10T11:17:56Z","cross_cats_sorted":[],"title_canon_sha256":"60850a71bb642ca90993578871816b3551f11610a65daa2618d90ab33b2658ed","abstract_canon_sha256":"7f2e505bc8f284ab08ce5e47a1c7ec38a1e45570b01f62026e11db9b553e12f7"},"schema_version":"1.0"},"canonical_sha256":"30237054c5006712b710f78ced92a50bed892ba355e64072345d858048379506","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:27.912129Z","signature_b64":"AmAczPoKaaF7Kk+u8xJ7yurHL7k/tvICk8qTntOU/x7vDz6VxXIGabaJ/mAabL1sIl6weOkzYh0qD7ZqROSqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30237054c5006712b710f78ced92a50bed892ba355e64072345d858048379506","last_reissued_at":"2026-07-05T11:36:27.911638Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:27.911638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.06357","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":"2026-07-05T11:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BLuMf/vVTT682PjOyTz7+CO301menWBkvSJ66VQSW7bw+m6VL55tkOvSko5HzfIRxf5RsA9MP1wiJVSd5uujDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:51:01.445659Z"},"content_sha256":"a068e294f9c2f4118a6cddbd68d6a33ed5637bb7d1e56a4b721029ca8cd043a9","schema_version":"1.0","event_id":"sha256:a068e294f9c2f4118a6cddbd68d6a33ed5637bb7d1e56a4b721029ca8cd043a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:GARXAVGFABTRFNYQ66GO3EVFBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong ill-posedness and non-existence in Sobolev spaces for generalized-SQG","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diego C\\'ordoba, Jos\\'e Lucas-Manch\\'on, Luis Mart\\'inez-Zoroa","submitted_at":"2025-02-10T11:17:56Z","abstract_excerpt":"The general surface quasi-geostrophic equation is the scalar transport equation defined by \\begin{equation*}\n  \\frac{\\partial \\theta}{\\partial t}+v^\\gamma_1 \\frac{\\partial \\theta}{\\partial x_1}+v^\\gamma_2 \\frac{\\partial \\theta}{\\partial x_2} =0 ,\n  \\end{equation*} where the velocity comes defined by\n  \\begin{equation*}\n  v^\\gamma=\\nabla^{\\perp} \\psi_\\gamma=\\left(\\partial_{2} \\psi_\\gamma,-\\partial_{1} \\psi_\\gamma \\right), \\quad \\psi_\\gamma=-\\Lambda^{-1+\\gamma} \\theta,\n  \\end{equation*} and $\\theta(\\cdot,0)=\\theta_0(\\cdot)$ is the initial condition. We consider the parameter $\\gamma \\in (-1,1)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06357","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/2502.06357/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":"2026-07-05T11:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nbJXEA3TY/C9x/DfGWbwtn2UEQCbuixRmk5r05lBuI2R54gc5tJz93cswuz++TAw81+2edy31K/kzO9PFbYBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T06:51:01.446224Z"},"content_sha256":"42bbfab493e76e147b786736b8595f7eb4233114b4289f91c668710784be6bf3","schema_version":"1.0","event_id":"sha256:42bbfab493e76e147b786736b8595f7eb4233114b4289f91c668710784be6bf3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP/bundle.json","state_url":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GARXAVGFABTRFNYQ66GO3EVFBP/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":"2026-08-09T06:51:01Z","links":{"resolver":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP","bundle":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP/bundle.json","state":"https://pith.science/pith/GARXAVGFABTRFNYQ66GO3EVFBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GARXAVGFABTRFNYQ66GO3EVFBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GARXAVGFABTRFNYQ66GO3EVFBP","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":"7f2e505bc8f284ab08ce5e47a1c7ec38a1e45570b01f62026e11db9b553e12f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-10T11:17:56Z","title_canon_sha256":"60850a71bb642ca90993578871816b3551f11610a65daa2618d90ab33b2658ed"},"schema_version":"1.0","source":{"id":"2502.06357","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.06357","created_at":"2026-07-05T11:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"2502.06357v2","created_at":"2026-07-05T11:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06357","created_at":"2026-07-05T11:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"GARXAVGFABTR","created_at":"2026-07-05T11:36:27Z"},{"alias_kind":"pith_short_16","alias_value":"GARXAVGFABTRFNYQ","created_at":"2026-07-05T11:36:27Z"},{"alias_kind":"pith_short_8","alias_value":"GARXAVGF","created_at":"2026-07-05T11:36:27Z"}],"graph_snapshots":[{"event_id":"sha256:42bbfab493e76e147b786736b8595f7eb4233114b4289f91c668710784be6bf3","target":"graph","created_at":"2026-07-05T11:36:27Z","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/2502.06357/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The general surface quasi-geostrophic equation is the scalar transport equation defined by \\begin{equation*}\n  \\frac{\\partial \\theta}{\\partial t}+v^\\gamma_1 \\frac{\\partial \\theta}{\\partial x_1}+v^\\gamma_2 \\frac{\\partial \\theta}{\\partial x_2} =0 ,\n  \\end{equation*} where the velocity comes defined by\n  \\begin{equation*}\n  v^\\gamma=\\nabla^{\\perp} \\psi_\\gamma=\\left(\\partial_{2} \\psi_\\gamma,-\\partial_{1} \\psi_\\gamma \\right), \\quad \\psi_\\gamma=-\\Lambda^{-1+\\gamma} \\theta,\n  \\end{equation*} and $\\theta(\\cdot,0)=\\theta_0(\\cdot)$ is the initial condition. We consider the parameter $\\gamma \\in (-1,1)$ ","authors_text":"Diego C\\'ordoba, Jos\\'e Lucas-Manch\\'on, Luis Mart\\'inez-Zoroa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-10T11:17:56Z","title":"Strong ill-posedness and non-existence in Sobolev spaces for generalized-SQG"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06357","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:a068e294f9c2f4118a6cddbd68d6a33ed5637bb7d1e56a4b721029ca8cd043a9","target":"record","created_at":"2026-07-05T11:36:27Z","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":"7f2e505bc8f284ab08ce5e47a1c7ec38a1e45570b01f62026e11db9b553e12f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-10T11:17:56Z","title_canon_sha256":"60850a71bb642ca90993578871816b3551f11610a65daa2618d90ab33b2658ed"},"schema_version":"1.0","source":{"id":"2502.06357","kind":"arxiv","version":2}},"canonical_sha256":"30237054c5006712b710f78ced92a50bed892ba355e64072345d858048379506","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30237054c5006712b710f78ced92a50bed892ba355e64072345d858048379506","first_computed_at":"2026-07-05T11:36:27.911638Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:36:27.911638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AmAczPoKaaF7Kk+u8xJ7yurHL7k/tvICk8qTntOU/x7vDz6VxXIGabaJ/mAabL1sIl6weOkzYh0qD7ZqROSqDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:36:27.912129Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.06357","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a068e294f9c2f4118a6cddbd68d6a33ed5637bb7d1e56a4b721029ca8cd043a9","sha256:42bbfab493e76e147b786736b8595f7eb4233114b4289f91c668710784be6bf3"],"state_sha256":"d56ff0f5a83ee5ffd46f81eae41d5d7e75bcc9cf6f4ac56d7355c2690ba18862"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fq3EZZtAUkIIanGms3qxtwNTM0BKfdjEXKyr01Fp4asDbtKtYD9gy0WAjXaf2/OVOlA4p/3+s1/s8G+VXNYnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T06:51:01.452534Z","bundle_sha256":"083dc590c1b5e2816c1904fd3feac99740e17a3763131c608bf272bb95e21ef0"}}