{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VVOE2QKIMLYP23TQ3HHKOMIFII","short_pith_number":"pith:VVOE2QKI","schema_version":"1.0","canonical_sha256":"ad5c4d414862f0fd6e70d9cea731054219922eb6163b025d7f1004753814d2c8","source":{"kind":"arxiv","id":"1507.05476","version":1},"attestation_state":"computed","paper":{"title":"The Sylvester equation and the elliptic Korteweg-de Vries system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Da-jun Zhang, Frank W. Nijhoff, Ying-ying Sun","submitted_at":"2015-07-20T12:55:12Z","abstract_excerpt":"The elliptic Korteweg-de Vries (KdV) system is a multi-component generalization of the lattice potential KdV equation, whose soliton solutions are associated with an elliptic Cauchy kernel (i.e., a Cauchy kernel on the torus). In this paper we generalize the class of solutions by using a Sylvester type matrix equation and rederiving the system from the associated Cauchy matrix. Our starting point is the Sylvester equation in the form of $~\\boldsymbol{k} \\boldsymbol{M}+ \\boldsymbol{M} \\boldsymbol{k} = \\boldsymbol{r} {\\boldsymbol{c}}^{T}-g\\boldsymbol{K}^{-1} \\boldsymbol{r} {\\boldsymbol{c}}^{T} \\"},"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":"1507.05476","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2015-07-20T12:55:12Z","cross_cats_sorted":[],"title_canon_sha256":"5fa38e96d51bd5a0b2b9de954e44a7a58dbaa94ccf569322043792432c9a5859","abstract_canon_sha256":"50e4ae492e779af25968b8e228784ff6665b22ac0219ca2257d89a222d586e52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:36.702719Z","signature_b64":"t8P0rPeYNKUKmuWmpf1rV2sPI29eiH1zEHrXlec7nCBE/5dduaAJ4WXXODSmzV8wPB/zP6K1sknFrW+Faq82BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad5c4d414862f0fd6e70d9cea731054219922eb6163b025d7f1004753814d2c8","last_reissued_at":"2026-05-18T01:36:36.702141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:36.702141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Sylvester equation and the elliptic Korteweg-de Vries system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Da-jun Zhang, Frank W. Nijhoff, Ying-ying Sun","submitted_at":"2015-07-20T12:55:12Z","abstract_excerpt":"The elliptic Korteweg-de Vries (KdV) system is a multi-component generalization of the lattice potential KdV equation, whose soliton solutions are associated with an elliptic Cauchy kernel (i.e., a Cauchy kernel on the torus). In this paper we generalize the class of solutions by using a Sylvester type matrix equation and rederiving the system from the associated Cauchy matrix. Our starting point is the Sylvester equation in the form of $~\\boldsymbol{k} \\boldsymbol{M}+ \\boldsymbol{M} \\boldsymbol{k} = \\boldsymbol{r} {\\boldsymbol{c}}^{T}-g\\boldsymbol{K}^{-1} \\boldsymbol{r} {\\boldsymbol{c}}^{T} \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05476","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":"1507.05476","created_at":"2026-05-18T01:36:36.702217+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.05476v1","created_at":"2026-05-18T01:36:36.702217+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05476","created_at":"2026-05-18T01:36:36.702217+00:00"},{"alias_kind":"pith_short_12","alias_value":"VVOE2QKIMLYP","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"VVOE2QKIMLYP23TQ","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"VVOE2QKI","created_at":"2026-05-18T12:29:47.479230+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/VVOE2QKIMLYP23TQ3HHKOMIFII","json":"https://pith.science/pith/VVOE2QKIMLYP23TQ3HHKOMIFII.json","graph_json":"https://pith.science/api/pith-number/VVOE2QKIMLYP23TQ3HHKOMIFII/graph.json","events_json":"https://pith.science/api/pith-number/VVOE2QKIMLYP23TQ3HHKOMIFII/events.json","paper":"https://pith.science/paper/VVOE2QKI"},"agent_actions":{"view_html":"https://pith.science/pith/VVOE2QKIMLYP23TQ3HHKOMIFII","download_json":"https://pith.science/pith/VVOE2QKIMLYP23TQ3HHKOMIFII.json","view_paper":"https://pith.science/paper/VVOE2QKI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.05476&json=true","fetch_graph":"https://pith.science/api/pith-number/VVOE2QKIMLYP23TQ3HHKOMIFII/graph.json","fetch_events":"https://pith.science/api/pith-number/VVOE2QKIMLYP23TQ3HHKOMIFII/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VVOE2QKIMLYP23TQ3HHKOMIFII/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VVOE2QKIMLYP23TQ3HHKOMIFII/action/storage_attestation","attest_author":"https://pith.science/pith/VVOE2QKIMLYP23TQ3HHKOMIFII/action/author_attestation","sign_citation":"https://pith.science/pith/VVOE2QKIMLYP23TQ3HHKOMIFII/action/citation_signature","submit_replication":"https://pith.science/pith/VVOE2QKIMLYP23TQ3HHKOMIFII/action/replication_record"}},"created_at":"2026-05-18T01:36:36.702217+00:00","updated_at":"2026-05-18T01:36:36.702217+00:00"}