{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:GKMSJAQ6SYIA6RRJTI47YHIZM2","short_pith_number":"pith:GKMSJAQ6","canonical_record":{"source":{"id":"2502.10274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-14T16:32:20Z","cross_cats_sorted":[],"title_canon_sha256":"8001ebc9991c392ef998b9e03fa97a8564df337aba86c68f980c876ebf81dcf7","abstract_canon_sha256":"7be566da1b33d4f9abfdaf5b08051789bcc6e2809a319dffe881ef805412521e"},"schema_version":"1.0"},"canonical_sha256":"329924821e96100f46299a39fc1d1966b02874b8a2008b36646741624f3b75b7","source":{"kind":"arxiv","id":"2502.10274","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.10274","created_at":"2026-07-05T10:14:30Z"},{"alias_kind":"arxiv_version","alias_value":"2502.10274v1","created_at":"2026-07-05T10:14:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.10274","created_at":"2026-07-05T10:14:30Z"},{"alias_kind":"pith_short_12","alias_value":"GKMSJAQ6SYIA","created_at":"2026-07-05T10:14:30Z"},{"alias_kind":"pith_short_16","alias_value":"GKMSJAQ6SYIA6RRJ","created_at":"2026-07-05T10:14:30Z"},{"alias_kind":"pith_short_8","alias_value":"GKMSJAQ6","created_at":"2026-07-05T10:14:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:GKMSJAQ6SYIA6RRJTI47YHIZM2","target":"record","payload":{"canonical_record":{"source":{"id":"2502.10274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-14T16:32:20Z","cross_cats_sorted":[],"title_canon_sha256":"8001ebc9991c392ef998b9e03fa97a8564df337aba86c68f980c876ebf81dcf7","abstract_canon_sha256":"7be566da1b33d4f9abfdaf5b08051789bcc6e2809a319dffe881ef805412521e"},"schema_version":"1.0"},"canonical_sha256":"329924821e96100f46299a39fc1d1966b02874b8a2008b36646741624f3b75b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:14:30.863494Z","signature_b64":"ucgMY4vQwCcN6cmoQzOULvDw72c2sZFKpul7iFiY3MjNSrc/QyEMMN6ddhH55pOhQcj7XqpYaxYxZrfzaZnsDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"329924821e96100f46299a39fc1d1966b02874b8a2008b36646741624f3b75b7","last_reissued_at":"2026-07-05T10:14:30.862954Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:14:30.862954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.10274","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":"2026-07-05T10:14:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qGiyYfcC1GsjsbZE16CV2CqZVa/D+I68hIzAzWi2i707HHa69m2Qq0Ct5CEfP3PDk70wcIVuvrU30pSQhjiGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:49:14.610039Z"},"content_sha256":"930d6fd3c51600c35ae663a971b836875857d0abd48de47a4d7086646a694919","schema_version":"1.0","event_id":"sha256:930d6fd3c51600c35ae663a971b836875857d0abd48de47a4d7086646a694919"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:GKMSJAQ6SYIA6RRJTI47YHIZM2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unstable vortices, sharp non-uniqueness with forcing, and global smooth solutions for the SQG equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"\\'Angel Castro, Daniel Faraco, Francisco Mengual, Marcos Solera","submitted_at":"2025-02-14T16:32:20Z","abstract_excerpt":"We prove non-uniqueness of weak solutions to the forced $\\alpha$-SQG equation with Sobolev regularity $W^{s,p}$ in the supercritical regime $s < \\alpha + \\frac{2}{p}$, covering the 2D Euler equation ($\\alpha = 0$), the Surface Quasi-Geostrophic equation ($\\alpha = 1$), and the intermediate cases. A key step is the construction of smooth, compactly supported vortices that exhibit non-linear instability. As a by-product, we show existence of global smooth solutions to the (unforced) $\\alpha$-SQG equation that are neither rotating nor traveling."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10274","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.10274/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":"2026-07-05T10:14:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H29UXlEQKk80ONVs0lRDNB9bL/nXW9Vg/YeCirm3iDzk94jypO6+UpMexwUXsg6JupFIt4epfm0+38FTESZsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:49:14.610536Z"},"content_sha256":"63425d0b3a4425a2ea135e44ba0bdf93e28a1d644e0cedc491a6ad82c146aaba","schema_version":"1.0","event_id":"sha256:63425d0b3a4425a2ea135e44ba0bdf93e28a1d644e0cedc491a6ad82c146aaba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKMSJAQ6SYIA6RRJTI47YHIZM2/bundle.json","state_url":"https://pith.science/pith/GKMSJAQ6SYIA6RRJTI47YHIZM2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKMSJAQ6SYIA6RRJTI47YHIZM2/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":"2026-08-09T09:49:14Z","links":{"resolver":"https://pith.science/pith/GKMSJAQ6SYIA6RRJTI47YHIZM2","bundle":"https://pith.science/pith/GKMSJAQ6SYIA6RRJTI47YHIZM2/bundle.json","state":"https://pith.science/pith/GKMSJAQ6SYIA6RRJTI47YHIZM2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKMSJAQ6SYIA6RRJTI47YHIZM2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GKMSJAQ6SYIA6RRJTI47YHIZM2","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":"7be566da1b33d4f9abfdaf5b08051789bcc6e2809a319dffe881ef805412521e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-14T16:32:20Z","title_canon_sha256":"8001ebc9991c392ef998b9e03fa97a8564df337aba86c68f980c876ebf81dcf7"},"schema_version":"1.0","source":{"id":"2502.10274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.10274","created_at":"2026-07-05T10:14:30Z"},{"alias_kind":"arxiv_version","alias_value":"2502.10274v1","created_at":"2026-07-05T10:14:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.10274","created_at":"2026-07-05T10:14:30Z"},{"alias_kind":"pith_short_12","alias_value":"GKMSJAQ6SYIA","created_at":"2026-07-05T10:14:30Z"},{"alias_kind":"pith_short_16","alias_value":"GKMSJAQ6SYIA6RRJ","created_at":"2026-07-05T10:14:30Z"},{"alias_kind":"pith_short_8","alias_value":"GKMSJAQ6","created_at":"2026-07-05T10:14:30Z"}],"graph_snapshots":[{"event_id":"sha256:63425d0b3a4425a2ea135e44ba0bdf93e28a1d644e0cedc491a6ad82c146aaba","target":"graph","created_at":"2026-07-05T10:14:30Z","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/2502.10274/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove non-uniqueness of weak solutions to the forced $\\alpha$-SQG equation with Sobolev regularity $W^{s,p}$ in the supercritical regime $s < \\alpha + \\frac{2}{p}$, covering the 2D Euler equation ($\\alpha = 0$), the Surface Quasi-Geostrophic equation ($\\alpha = 1$), and the intermediate cases. A key step is the construction of smooth, compactly supported vortices that exhibit non-linear instability. As a by-product, we show existence of global smooth solutions to the (unforced) $\\alpha$-SQG equation that are neither rotating nor traveling.","authors_text":"\\'Angel Castro, Daniel Faraco, Francisco Mengual, Marcos Solera","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-14T16:32:20Z","title":"Unstable vortices, sharp non-uniqueness with forcing, and global smooth solutions for the SQG equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10274","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":"sha256:930d6fd3c51600c35ae663a971b836875857d0abd48de47a4d7086646a694919","target":"record","created_at":"2026-07-05T10:14:30Z","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":"7be566da1b33d4f9abfdaf5b08051789bcc6e2809a319dffe881ef805412521e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-14T16:32:20Z","title_canon_sha256":"8001ebc9991c392ef998b9e03fa97a8564df337aba86c68f980c876ebf81dcf7"},"schema_version":"1.0","source":{"id":"2502.10274","kind":"arxiv","version":1}},"canonical_sha256":"329924821e96100f46299a39fc1d1966b02874b8a2008b36646741624f3b75b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"329924821e96100f46299a39fc1d1966b02874b8a2008b36646741624f3b75b7","first_computed_at":"2026-07-05T10:14:30.862954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:14:30.862954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ucgMY4vQwCcN6cmoQzOULvDw72c2sZFKpul7iFiY3MjNSrc/QyEMMN6ddhH55pOhQcj7XqpYaxYxZrfzaZnsDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:14:30.863494Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.10274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:930d6fd3c51600c35ae663a971b836875857d0abd48de47a4d7086646a694919","sha256:63425d0b3a4425a2ea135e44ba0bdf93e28a1d644e0cedc491a6ad82c146aaba"],"state_sha256":"74ba305feb78c010997ff5f2f9b69272790b058d6dc0bbfc1619888529d55cff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NhZ6HqIbSSk1YUiXGMbdy8l/IUF1WVx3jbVjkV9dfd5hUVrVXDecWhVtpwHxZygoKL2wQZZcAr6ePlPJZXyBCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T09:49:14.614337Z","bundle_sha256":"cca12b16a6c3453580bdf0947941211ae51144f550df56fbfb2050ea49c56cb3"}}