{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:D6ELJM55FJKENKYGNUHDOR34U5","short_pith_number":"pith:D6ELJM55","schema_version":"1.0","canonical_sha256":"1f88b4b3bd2a5446ab066d0e37477ca77a362e7f3ccde742e63fc1c7c1ffc6b1","source":{"kind":"arxiv","id":"1305.2487","version":2},"attestation_state":"computed","paper":{"title":"A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"nlin.SI","authors_text":"Gerald Teschl, Jonathan Eckhardt","submitted_at":"2013-05-11T09:46:01Z","abstract_excerpt":"We propose a novel technique for analyzing the long-time asymptotics of integrable wave equations in the case when the underlying isospectral problem has purely discrete spectrum. To this end, we introduce a natural coupling problem for entire functions, which serves as a replacement for the usual Riemann-Hilbert problem, which does not apply in these cases. As a prototypical example, we investigate the long-time asymptotics of the dispersionless Camassa-Holm equation."},"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":"1305.2487","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-05-11T09:46:01Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"ef3f0bb80feb6db3befd7ef8ddb056567144b1eace505f0afe27f3b731e2e567","abstract_canon_sha256":"68c6d05069deb92b3fa7931e6ac913940fa03eb3593bdd72deb217dc0a7566e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:20.072278Z","signature_b64":"7KqiDgHmTlwkE6g3tR8i1Vc8rBwyu7lOymv706w1rzN4oqBZsQQN9Uuci66bNRC7YNE0CWJLg+a41DTZHnOLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f88b4b3bd2a5446ab066d0e37477ca77a362e7f3ccde742e63fc1c7c1ffc6b1","last_reissued_at":"2026-05-18T01:21:20.071775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:20.071775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A coupling problem for entire functions and its application to the long-time asymptotics of integrable wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"nlin.SI","authors_text":"Gerald Teschl, Jonathan Eckhardt","submitted_at":"2013-05-11T09:46:01Z","abstract_excerpt":"We propose a novel technique for analyzing the long-time asymptotics of integrable wave equations in the case when the underlying isospectral problem has purely discrete spectrum. To this end, we introduce a natural coupling problem for entire functions, which serves as a replacement for the usual Riemann-Hilbert problem, which does not apply in these cases. As a prototypical example, we investigate the long-time asymptotics of the dispersionless Camassa-Holm equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2487","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":""},"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":"1305.2487","created_at":"2026-05-18T01:21:20.071847+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.2487v2","created_at":"2026-05-18T01:21:20.071847+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2487","created_at":"2026-05-18T01:21:20.071847+00:00"},{"alias_kind":"pith_short_12","alias_value":"D6ELJM55FJKE","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"D6ELJM55FJKENKYG","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"D6ELJM55","created_at":"2026-05-18T12:27:40.988391+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/D6ELJM55FJKENKYGNUHDOR34U5","json":"https://pith.science/pith/D6ELJM55FJKENKYGNUHDOR34U5.json","graph_json":"https://pith.science/api/pith-number/D6ELJM55FJKENKYGNUHDOR34U5/graph.json","events_json":"https://pith.science/api/pith-number/D6ELJM55FJKENKYGNUHDOR34U5/events.json","paper":"https://pith.science/paper/D6ELJM55"},"agent_actions":{"view_html":"https://pith.science/pith/D6ELJM55FJKENKYGNUHDOR34U5","download_json":"https://pith.science/pith/D6ELJM55FJKENKYGNUHDOR34U5.json","view_paper":"https://pith.science/paper/D6ELJM55","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.2487&json=true","fetch_graph":"https://pith.science/api/pith-number/D6ELJM55FJKENKYGNUHDOR34U5/graph.json","fetch_events":"https://pith.science/api/pith-number/D6ELJM55FJKENKYGNUHDOR34U5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D6ELJM55FJKENKYGNUHDOR34U5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D6ELJM55FJKENKYGNUHDOR34U5/action/storage_attestation","attest_author":"https://pith.science/pith/D6ELJM55FJKENKYGNUHDOR34U5/action/author_attestation","sign_citation":"https://pith.science/pith/D6ELJM55FJKENKYGNUHDOR34U5/action/citation_signature","submit_replication":"https://pith.science/pith/D6ELJM55FJKENKYGNUHDOR34U5/action/replication_record"}},"created_at":"2026-05-18T01:21:20.071847+00:00","updated_at":"2026-05-18T01:21:20.071847+00:00"}