{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:QTRFV7SX72DUU3LHYC7VBNO4NE","short_pith_number":"pith:QTRFV7SX","schema_version":"1.0","canonical_sha256":"84e25afe57fe874a6d67c0bf50b5dc6905c9916083a53fc1f5a19713ad3f4cfb","source":{"kind":"arxiv","id":"2207.07548","version":1},"attestation_state":"computed","paper":{"title":"Global existence and singularity formation for the generalized Constantin-Lax-Majda equation with dissipation: The real line vs. periodic domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.PS","nlin.SI"],"primary_cat":"math.AP","authors_text":"David M. Ambrose, Denis A. Silantyev, Michael Siegel, Pavel M. Lushnikov","submitted_at":"2022-07-15T15:42:46Z","abstract_excerpt":"The question of global existence versus finite-time singularity formation is considered for the generalized Constantin-Lax-Majda equation with dissipation $-\\Lambda^\\sigma$, where $\\widehat {{\\Lambda}^\\sigma}=|k|^\\sigma$, both for the problem on the circle $x \\in [-\\pi,\\pi]$ and the real line. In the periodic geometry, two complementary approaches are used to prove global-in-time existence of solutions for $\\sigma \\geq 1$ and all real values of an advection parameter $a$ when the data is small. We also derive new analytical solutions in both geometries when $a=0$, and on the real line when $a="},"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":"2207.07548","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-07-15T15:42:46Z","cross_cats_sorted":["nlin.PS","nlin.SI"],"title_canon_sha256":"5b381a8acf73b895adb42337525b742953c0734589cc6157fb47894dca2a534d","abstract_canon_sha256":"47bdb173c20b8f7f5f29ccc1619312577ddeba518bf0d560f9b85efcf0ae6378"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:40:33.662273Z","signature_b64":"wbGprkqAEQDLp2JbHOCe0KAqwnUA241eR/NvjkzNTwJAa40zjQT+u7oNWn4TB/wicFUqofPtym28hvUeEeiuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84e25afe57fe874a6d67c0bf50b5dc6905c9916083a53fc1f5a19713ad3f4cfb","last_reissued_at":"2026-07-05T04:40:33.661928Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:40:33.661928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global existence and singularity formation for the generalized Constantin-Lax-Majda equation with dissipation: The real line vs. periodic domains","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.PS","nlin.SI"],"primary_cat":"math.AP","authors_text":"David M. Ambrose, Denis A. Silantyev, Michael Siegel, Pavel M. Lushnikov","submitted_at":"2022-07-15T15:42:46Z","abstract_excerpt":"The question of global existence versus finite-time singularity formation is considered for the generalized Constantin-Lax-Majda equation with dissipation $-\\Lambda^\\sigma$, where $\\widehat {{\\Lambda}^\\sigma}=|k|^\\sigma$, both for the problem on the circle $x \\in [-\\pi,\\pi]$ and the real line. In the periodic geometry, two complementary approaches are used to prove global-in-time existence of solutions for $\\sigma \\geq 1$ and all real values of an advection parameter $a$ when the data is small. We also derive new analytical solutions in both geometries when $a=0$, and on the real line when $a="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.07548","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/2207.07548/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2207.07548","created_at":"2026-07-05T04:40:33.661986+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.07548v1","created_at":"2026-07-05T04:40:33.661986+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.07548","created_at":"2026-07-05T04:40:33.661986+00:00"},{"alias_kind":"pith_short_12","alias_value":"QTRFV7SX72DU","created_at":"2026-07-05T04:40:33.661986+00:00"},{"alias_kind":"pith_short_16","alias_value":"QTRFV7SX72DUU3LH","created_at":"2026-07-05T04:40:33.661986+00:00"},{"alias_kind":"pith_short_8","alias_value":"QTRFV7SX","created_at":"2026-07-05T04:40:33.661986+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/QTRFV7SX72DUU3LHYC7VBNO4NE","json":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE.json","graph_json":"https://pith.science/api/pith-number/QTRFV7SX72DUU3LHYC7VBNO4NE/graph.json","events_json":"https://pith.science/api/pith-number/QTRFV7SX72DUU3LHYC7VBNO4NE/events.json","paper":"https://pith.science/paper/QTRFV7SX"},"agent_actions":{"view_html":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE","download_json":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE.json","view_paper":"https://pith.science/paper/QTRFV7SX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.07548&json=true","fetch_graph":"https://pith.science/api/pith-number/QTRFV7SX72DUU3LHYC7VBNO4NE/graph.json","fetch_events":"https://pith.science/api/pith-number/QTRFV7SX72DUU3LHYC7VBNO4NE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE/action/storage_attestation","attest_author":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE/action/author_attestation","sign_citation":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE/action/citation_signature","submit_replication":"https://pith.science/pith/QTRFV7SX72DUU3LHYC7VBNO4NE/action/replication_record"}},"created_at":"2026-07-05T04:40:33.661986+00:00","updated_at":"2026-07-05T04:40:33.661986+00:00"}