{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:AITN5B3KJL2O5MK5TN7LRF3F7Z","short_pith_number":"pith:AITN5B3K","schema_version":"1.0","canonical_sha256":"0226de876a4af4eeb15d9b7eb89765fe782e22c29ecaedaaf464644680d4b15e","source":{"kind":"arxiv","id":"1212.4203","version":1},"attestation_state":"computed","paper":{"title":"On the Euler-Poincar\\'e equation with non-zero dispersion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Dong Li, Xinwei Yu, Zhichun Zhai","submitted_at":"2012-12-18T00:37:54Z","abstract_excerpt":"We consider the Euler-Poincar\\'e equation on $\\mathbb R^d$, $d\\ge 2$. For a large class of smooth initial data we prove that the corresponding solution blows up in finite time. This settles an open problem raised by Chae and Liu \\cite{Chae Liu}. Our analysis exhibits some new concentration mechanism and hidden monotonicity formula associated with the Euler-Poincar\\'e flow. In particular we show the abundance of blowups emanating from smooth initial data with certain sign properties. No size restrictions are imposed on the data. We also showcase a class of initial data for which the correspondi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1212.4203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-18T00:37:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"db9c0a6565c4519f24c893284ee0fbfac19467ae48554c2e40b1fa9036d01934","abstract_canon_sha256":"e6a54d63c25b8a2cd4383ac8e629b33539dfd6ada34bc8cf70428a8cb6627584"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:31.227687Z","signature_b64":"S4GW9uYPG1wLrgKpP8u8jbVbbaIpMx97JAoYtjgUmjDuxNmGEr1l+N/EmyrJWb5n+LkC2FtuBPRloNDko/wcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0226de876a4af4eeb15d9b7eb89765fe782e22c29ecaedaaf464644680d4b15e","last_reissued_at":"2026-05-18T01:52:31.227005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:31.227005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Euler-Poincar\\'e equation with non-zero dispersion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Dong Li, Xinwei Yu, Zhichun Zhai","submitted_at":"2012-12-18T00:37:54Z","abstract_excerpt":"We consider the Euler-Poincar\\'e equation on $\\mathbb R^d$, $d\\ge 2$. For a large class of smooth initial data we prove that the corresponding solution blows up in finite time. This settles an open problem raised by Chae and Liu \\cite{Chae Liu}. Our analysis exhibits some new concentration mechanism and hidden monotonicity formula associated with the Euler-Poincar\\'e flow. In particular we show the abundance of blowups emanating from smooth initial data with certain sign properties. No size restrictions are imposed on the data. We also showcase a class of initial data for which the correspondi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4203","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.4203","created_at":"2026-05-18T01:52:31.227081+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.4203v1","created_at":"2026-05-18T01:52:31.227081+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4203","created_at":"2026-05-18T01:52:31.227081+00:00"},{"alias_kind":"pith_short_12","alias_value":"AITN5B3KJL2O","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"AITN5B3KJL2O5MK5","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"AITN5B3K","created_at":"2026-05-18T12:26:58.693483+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AITN5B3KJL2O5MK5TN7LRF3F7Z","json":"https://pith.science/pith/AITN5B3KJL2O5MK5TN7LRF3F7Z.json","graph_json":"https://pith.science/api/pith-number/AITN5B3KJL2O5MK5TN7LRF3F7Z/graph.json","events_json":"https://pith.science/api/pith-number/AITN5B3KJL2O5MK5TN7LRF3F7Z/events.json","paper":"https://pith.science/paper/AITN5B3K"},"agent_actions":{"view_html":"https://pith.science/pith/AITN5B3KJL2O5MK5TN7LRF3F7Z","download_json":"https://pith.science/pith/AITN5B3KJL2O5MK5TN7LRF3F7Z.json","view_paper":"https://pith.science/paper/AITN5B3K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.4203&json=true","fetch_graph":"https://pith.science/api/pith-number/AITN5B3KJL2O5MK5TN7LRF3F7Z/graph.json","fetch_events":"https://pith.science/api/pith-number/AITN5B3KJL2O5MK5TN7LRF3F7Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AITN5B3KJL2O5MK5TN7LRF3F7Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AITN5B3KJL2O5MK5TN7LRF3F7Z/action/storage_attestation","attest_author":"https://pith.science/pith/AITN5B3KJL2O5MK5TN7LRF3F7Z/action/author_attestation","sign_citation":"https://pith.science/pith/AITN5B3KJL2O5MK5TN7LRF3F7Z/action/citation_signature","submit_replication":"https://pith.science/pith/AITN5B3KJL2O5MK5TN7LRF3F7Z/action/replication_record"}},"created_at":"2026-05-18T01:52:31.227081+00:00","updated_at":"2026-05-18T01:52:31.227081+00:00"}