{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:4ROY67GKIATJDFIJNWSABEZYRX","short_pith_number":"pith:4ROY67GK","schema_version":"1.0","canonical_sha256":"e45d8f7cca40269195096da40093388dee4e77b00cf438b3037af2c6a451e7e9","source":{"kind":"arxiv","id":"1909.02948","version":1},"attestation_state":"computed","paper":{"title":"Elliptic solutions of Boussinesq type lattice equations and the elliptic Nth root of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Da-jun Zhang, Frank W Nijhoff, Ying-ying Sun","submitted_at":"2019-09-06T14:57:25Z","abstract_excerpt":"We establish an infinite family of solutions in terms of elliptic functions of the lattice Boussinesq systems by setting up a direct linearisation scheme, which provides the solution structure for those equations in the elliptic case. The latter, which contains as main structural element a Cauchy kernel on the torus, is obtained from a dimensional reduction of the elliptic direct linearisation scheme of the lattice Kadomtsev-Petviashvili equation, which requires the introduction of a novel technical concept, namely the \"elliptic cube root of unity\". Thus, in order to implement the reduction we"},"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":"1909.02948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2019-09-06T14:57:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d8de9fb678b1c4a481dc38ae73adaabb74a8951521b2d1f2fc1729d0acdc7daa","abstract_canon_sha256":"eba15fa6c5f58a02137685929051aa99604207a5b575b42f9e8ce75ae1c3c484"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:02:44.681458Z","signature_b64":"DlLOsddiZNQysopNWPztnjLRU1Lc81aiga0pfcophIkIG8SI0L+hmlcR4rGEslD8zWxzVM2/1HoQuANzgrw3AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e45d8f7cca40269195096da40093388dee4e77b00cf438b3037af2c6a451e7e9","last_reissued_at":"2026-07-05T00:02:44.680996Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:02:44.680996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elliptic solutions of Boussinesq type lattice equations and the elliptic Nth root of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Da-jun Zhang, Frank W Nijhoff, Ying-ying Sun","submitted_at":"2019-09-06T14:57:25Z","abstract_excerpt":"We establish an infinite family of solutions in terms of elliptic functions of the lattice Boussinesq systems by setting up a direct linearisation scheme, which provides the solution structure for those equations in the elliptic case. The latter, which contains as main structural element a Cauchy kernel on the torus, is obtained from a dimensional reduction of the elliptic direct linearisation scheme of the lattice Kadomtsev-Petviashvili equation, which requires the introduction of a novel technical concept, namely the \"elliptic cube root of unity\". Thus, in order to implement the reduction we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.02948","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/1909.02948/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":"1909.02948","created_at":"2026-07-05T00:02:44.681062+00:00"},{"alias_kind":"arxiv_version","alias_value":"1909.02948v1","created_at":"2026-07-05T00:02:44.681062+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.02948","created_at":"2026-07-05T00:02:44.681062+00:00"},{"alias_kind":"pith_short_12","alias_value":"4ROY67GKIATJ","created_at":"2026-07-05T00:02:44.681062+00:00"},{"alias_kind":"pith_short_16","alias_value":"4ROY67GKIATJDFIJ","created_at":"2026-07-05T00:02:44.681062+00:00"},{"alias_kind":"pith_short_8","alias_value":"4ROY67GK","created_at":"2026-07-05T00:02:44.681062+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/4ROY67GKIATJDFIJNWSABEZYRX","json":"https://pith.science/pith/4ROY67GKIATJDFIJNWSABEZYRX.json","graph_json":"https://pith.science/api/pith-number/4ROY67GKIATJDFIJNWSABEZYRX/graph.json","events_json":"https://pith.science/api/pith-number/4ROY67GKIATJDFIJNWSABEZYRX/events.json","paper":"https://pith.science/paper/4ROY67GK"},"agent_actions":{"view_html":"https://pith.science/pith/4ROY67GKIATJDFIJNWSABEZYRX","download_json":"https://pith.science/pith/4ROY67GKIATJDFIJNWSABEZYRX.json","view_paper":"https://pith.science/paper/4ROY67GK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1909.02948&json=true","fetch_graph":"https://pith.science/api/pith-number/4ROY67GKIATJDFIJNWSABEZYRX/graph.json","fetch_events":"https://pith.science/api/pith-number/4ROY67GKIATJDFIJNWSABEZYRX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4ROY67GKIATJDFIJNWSABEZYRX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4ROY67GKIATJDFIJNWSABEZYRX/action/storage_attestation","attest_author":"https://pith.science/pith/4ROY67GKIATJDFIJNWSABEZYRX/action/author_attestation","sign_citation":"https://pith.science/pith/4ROY67GKIATJDFIJNWSABEZYRX/action/citation_signature","submit_replication":"https://pith.science/pith/4ROY67GKIATJDFIJNWSABEZYRX/action/replication_record"}},"created_at":"2026-07-05T00:02:44.681062+00:00","updated_at":"2026-07-05T00:02:44.681062+00:00"}