{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:2DWQRZWYI6O5Z37ZJ45QQ7LGNZ","short_pith_number":"pith:2DWQRZWY","canonical_record":{"source":{"id":"2306.09748","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-06-16T10:30:09Z","cross_cats_sorted":[],"title_canon_sha256":"593c1d9779a02cd490baaa00eb4ae22097eec42be8449835ed996fc22062724a","abstract_canon_sha256":"1c9bac4d5ac3023a4243ac35cef4bb124cafc08cfe68949199e48b05e75f5fe5"},"schema_version":"1.0"},"canonical_sha256":"d0ed08e6d8479ddceff94f3b087d666e5dcb3001743b895874e6df1e0698c806","source":{"kind":"arxiv","id":"2306.09748","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.09748","created_at":"2026-07-05T08:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"2306.09748v3","created_at":"2026-07-05T08:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.09748","created_at":"2026-07-05T08:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"2DWQRZWYI6O5","created_at":"2026-07-05T08:34:03Z"},{"alias_kind":"pith_short_16","alias_value":"2DWQRZWYI6O5Z37Z","created_at":"2026-07-05T08:34:03Z"},{"alias_kind":"pith_short_8","alias_value":"2DWQRZWY","created_at":"2026-07-05T08:34:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:2DWQRZWYI6O5Z37ZJ45QQ7LGNZ","target":"record","payload":{"canonical_record":{"source":{"id":"2306.09748","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-06-16T10:30:09Z","cross_cats_sorted":[],"title_canon_sha256":"593c1d9779a02cd490baaa00eb4ae22097eec42be8449835ed996fc22062724a","abstract_canon_sha256":"1c9bac4d5ac3023a4243ac35cef4bb124cafc08cfe68949199e48b05e75f5fe5"},"schema_version":"1.0"},"canonical_sha256":"d0ed08e6d8479ddceff94f3b087d666e5dcb3001743b895874e6df1e0698c806","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:34:03.704093Z","signature_b64":"2n8ITW+8cUwpvHvLIQ7UAwnBzC1UhoM2YgPAn76k2RirWxEsRrspyfRj3baO4CMwc5/5vFYLA3Yde4uQsCSdBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0ed08e6d8479ddceff94f3b087d666e5dcb3001743b895874e6df1e0698c806","last_reissued_at":"2026-07-05T08:34:03.703588Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:34:03.703588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.09748","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fAOdyHRYhLAJxIkjtx5HDciseUaWKZvlw4BCWt7UPzEVtRPcToqJIMjd0YuHIa6w59CI9nyoyg39H5gTjaK6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T16:23:16.151622Z"},"content_sha256":"f2cea818d7dc89900320319f88c822ce82dc8406051805c458297386c75d4bef","schema_version":"1.0","event_id":"sha256:f2cea818d7dc89900320319f88c822ce82dc8406051805c458297386c75d4bef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:2DWQRZWYI6O5Z37ZJ45QQ7LGNZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Liouville comparison theory for blowup of Euler-Arnold equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Justin Valletta, Martin Bauer, Stephen C. Preston","submitted_at":"2023-06-16T10:30:09Z","abstract_excerpt":"In this article we introduce a new blowup criterion for (generalized) Euler-Arnold equations on $\\mathbb R^n$. Our method is based on treating the equation in Lagrangian coordinates, where it is an ODE on the diffeomorphism group, and comparison with the Liouville equation; in contrast to the usual comparison approach at a single point, we apply comparison in an infinite dimensional function space. We thereby show that the Jacobian of the Lagrangian flow map of the solution reaches zero in finite time, which corresponds to $C^1$-blowup of the velocity field solution. We demonstrate the applica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.09748","kind":"arxiv","version":3},"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/2306.09748/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":"2026-07-05T08:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+4gz5bish/z0q8B+xsPigvl3B/Hyy51C8MSUkTzhnsXR0nXtQhQDtxgTh3sT0j7Iz8DQg2mRsuoGhfILWo6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T16:23:16.152599Z"},"content_sha256":"67f12e363dbc908c7f8089f09aeb0c56587f09987759657029769983463685ca","schema_version":"1.0","event_id":"sha256:67f12e363dbc908c7f8089f09aeb0c56587f09987759657029769983463685ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2DWQRZWYI6O5Z37ZJ45QQ7LGNZ/bundle.json","state_url":"https://pith.science/pith/2DWQRZWYI6O5Z37ZJ45QQ7LGNZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2DWQRZWYI6O5Z37ZJ45QQ7LGNZ/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":"2026-08-19T16:23:16Z","links":{"resolver":"https://pith.science/pith/2DWQRZWYI6O5Z37ZJ45QQ7LGNZ","bundle":"https://pith.science/pith/2DWQRZWYI6O5Z37ZJ45QQ7LGNZ/bundle.json","state":"https://pith.science/pith/2DWQRZWYI6O5Z37ZJ45QQ7LGNZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2DWQRZWYI6O5Z37ZJ45QQ7LGNZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2DWQRZWYI6O5Z37ZJ45QQ7LGNZ","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":"1c9bac4d5ac3023a4243ac35cef4bb124cafc08cfe68949199e48b05e75f5fe5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-06-16T10:30:09Z","title_canon_sha256":"593c1d9779a02cd490baaa00eb4ae22097eec42be8449835ed996fc22062724a"},"schema_version":"1.0","source":{"id":"2306.09748","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.09748","created_at":"2026-07-05T08:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"2306.09748v3","created_at":"2026-07-05T08:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.09748","created_at":"2026-07-05T08:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"2DWQRZWYI6O5","created_at":"2026-07-05T08:34:03Z"},{"alias_kind":"pith_short_16","alias_value":"2DWQRZWYI6O5Z37Z","created_at":"2026-07-05T08:34:03Z"},{"alias_kind":"pith_short_8","alias_value":"2DWQRZWY","created_at":"2026-07-05T08:34:03Z"}],"graph_snapshots":[{"event_id":"sha256:67f12e363dbc908c7f8089f09aeb0c56587f09987759657029769983463685ca","target":"graph","created_at":"2026-07-05T08:34:03Z","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/2306.09748/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we introduce a new blowup criterion for (generalized) Euler-Arnold equations on $\\mathbb R^n$. Our method is based on treating the equation in Lagrangian coordinates, where it is an ODE on the diffeomorphism group, and comparison with the Liouville equation; in contrast to the usual comparison approach at a single point, we apply comparison in an infinite dimensional function space. We thereby show that the Jacobian of the Lagrangian flow map of the solution reaches zero in finite time, which corresponds to $C^1$-blowup of the velocity field solution. We demonstrate the applica","authors_text":"Justin Valletta, Martin Bauer, Stephen C. Preston","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-06-16T10:30:09Z","title":"Liouville comparison theory for blowup of Euler-Arnold equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.09748","kind":"arxiv","version":3},"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:f2cea818d7dc89900320319f88c822ce82dc8406051805c458297386c75d4bef","target":"record","created_at":"2026-07-05T08:34:03Z","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":"1c9bac4d5ac3023a4243ac35cef4bb124cafc08cfe68949199e48b05e75f5fe5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-06-16T10:30:09Z","title_canon_sha256":"593c1d9779a02cd490baaa00eb4ae22097eec42be8449835ed996fc22062724a"},"schema_version":"1.0","source":{"id":"2306.09748","kind":"arxiv","version":3}},"canonical_sha256":"d0ed08e6d8479ddceff94f3b087d666e5dcb3001743b895874e6df1e0698c806","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0ed08e6d8479ddceff94f3b087d666e5dcb3001743b895874e6df1e0698c806","first_computed_at":"2026-07-05T08:34:03.703588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:34:03.703588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2n8ITW+8cUwpvHvLIQ7UAwnBzC1UhoM2YgPAn76k2RirWxEsRrspyfRj3baO4CMwc5/5vFYLA3Yde4uQsCSdBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:34:03.704093Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.09748","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2cea818d7dc89900320319f88c822ce82dc8406051805c458297386c75d4bef","sha256:67f12e363dbc908c7f8089f09aeb0c56587f09987759657029769983463685ca"],"state_sha256":"2323b99ef8c0b29dc2bd875f472eecb8d47f80f97d1944920046406fc516fa27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhZ3TOgOoGw2uiA9yyWHMI6kVfLl5pS1SzeBcdF0X4j3WIu49Wm7WaNNMLWquygCD24KomJuN/EkV8canh1rAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T16:23:16.158790Z","bundle_sha256":"9631b22d5f9325a1322c419e3a88668e7eea39beafa208548720595581e3525b"}}