{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KSVUL4YL7YWJYNHZGK3BYQDVN2","short_pith_number":"pith:KSVUL4YL","schema_version":"1.0","canonical_sha256":"54ab45f30bfe2c9c34f932b61c40756eb26a67bbdfaa8d4db02320836c19f87f","source":{"kind":"arxiv","id":"1708.03440","version":1},"attestation_state":"computed","paper":{"title":"Degeneration of Trigonal Curves and Solutions of the KP-Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.QA"],"primary_cat":"nlin.SI","authors_text":"Atsushi Nakayashiki","submitted_at":"2017-08-11T05:48:16Z","abstract_excerpt":"It is known that soliton solutions of the KP-hierarchy corresponds to singular rational curves with only ordinary double points. In this paper we study the degeneration of theta function solutions corresponding to certain trigonal curves. We show that, when the curves degenerate to singular rational curves with only ordinary triple points, the solutions tend to some intermediate solutions between solitons and rational solutions. They are considered as cerain limits of solitons. The Sato Grassmannian is extensively used here to study the degeneration of solutions, since it directly connects sol"},"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":"1708.03440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2017-08-11T05:48:16Z","cross_cats_sorted":["math-ph","math.AG","math.MP","math.QA"],"title_canon_sha256":"29a09b5706fa9845a5fc20697c032bb4dbeca4516dc8979ae1e0e588cdddf495","abstract_canon_sha256":"7345c41418d8b7b64918b3c9dbd27864691382545b08684b01efe8ad950a5725"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:30.913699Z","signature_b64":"8ifcSyru4h21NdpoZmf57OR6/GrF+93grYZvGjy6aGHDTSGdwfhNwg4SG1iySlIlyBOY1B9pib7W1FU6hH4gBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54ab45f30bfe2c9c34f932b61c40756eb26a67bbdfaa8d4db02320836c19f87f","last_reissued_at":"2026-05-18T00:09:30.912978Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:30.912978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Degeneration of Trigonal Curves and Solutions of the KP-Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.QA"],"primary_cat":"nlin.SI","authors_text":"Atsushi Nakayashiki","submitted_at":"2017-08-11T05:48:16Z","abstract_excerpt":"It is known that soliton solutions of the KP-hierarchy corresponds to singular rational curves with only ordinary double points. In this paper we study the degeneration of theta function solutions corresponding to certain trigonal curves. We show that, when the curves degenerate to singular rational curves with only ordinary triple points, the solutions tend to some intermediate solutions between solitons and rational solutions. They are considered as cerain limits of solitons. The Sato Grassmannian is extensively used here to study the degeneration of solutions, since it directly connects sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03440","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":"1708.03440","created_at":"2026-05-18T00:09:30.913089+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.03440v1","created_at":"2026-05-18T00:09:30.913089+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03440","created_at":"2026-05-18T00:09:30.913089+00:00"},{"alias_kind":"pith_short_12","alias_value":"KSVUL4YL7YWJ","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"KSVUL4YL7YWJYNHZ","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"KSVUL4YL","created_at":"2026-05-18T12:31:28.150371+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/KSVUL4YL7YWJYNHZGK3BYQDVN2","json":"https://pith.science/pith/KSVUL4YL7YWJYNHZGK3BYQDVN2.json","graph_json":"https://pith.science/api/pith-number/KSVUL4YL7YWJYNHZGK3BYQDVN2/graph.json","events_json":"https://pith.science/api/pith-number/KSVUL4YL7YWJYNHZGK3BYQDVN2/events.json","paper":"https://pith.science/paper/KSVUL4YL"},"agent_actions":{"view_html":"https://pith.science/pith/KSVUL4YL7YWJYNHZGK3BYQDVN2","download_json":"https://pith.science/pith/KSVUL4YL7YWJYNHZGK3BYQDVN2.json","view_paper":"https://pith.science/paper/KSVUL4YL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.03440&json=true","fetch_graph":"https://pith.science/api/pith-number/KSVUL4YL7YWJYNHZGK3BYQDVN2/graph.json","fetch_events":"https://pith.science/api/pith-number/KSVUL4YL7YWJYNHZGK3BYQDVN2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KSVUL4YL7YWJYNHZGK3BYQDVN2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KSVUL4YL7YWJYNHZGK3BYQDVN2/action/storage_attestation","attest_author":"https://pith.science/pith/KSVUL4YL7YWJYNHZGK3BYQDVN2/action/author_attestation","sign_citation":"https://pith.science/pith/KSVUL4YL7YWJYNHZGK3BYQDVN2/action/citation_signature","submit_replication":"https://pith.science/pith/KSVUL4YL7YWJYNHZGK3BYQDVN2/action/replication_record"}},"created_at":"2026-05-18T00:09:30.913089+00:00","updated_at":"2026-05-18T00:09:30.913089+00:00"}