{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:TEWPLIPKGZKOLKC2SEQMO5DF5F","short_pith_number":"pith:TEWPLIPK","schema_version":"1.0","canonical_sha256":"992cf5a1ea3654e5a85a9120c77465e944bd0fabe95b34478a66c0adfea9b5de","source":{"kind":"arxiv","id":"nlin/0702058","version":3},"attestation_state":"computed","paper":{"title":"The Ablowitz-Ladik Hierarchy Revisited","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Fritz Gesztesy, Gerald Teschl, Helge Holden, Johanna Michor","submitted_at":"2007-02-28T20:23:21Z","abstract_excerpt":"We provide a detailed recursive construction of the Ablowitz-Ladik (AL) hierarchy and its zero-curvature formalism. The two-coefficient AL hierarchy under investigation can be considered a complexified version of the discrete nonlinear Schr\\\"odinger equation and its hierarchy of nonlinear evolution equations.\n  Specifically, we discuss in detail the stationary Ablowitz-Ladik formalism in connection with the underlying hyperelliptic curve and the stationary Baker-Akhiezer function and separately the corresponding time-dependent Ablowitz-Ladik formalism."},"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":"nlin/0702058","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"nlin.SI","submitted_at":"2007-02-28T20:23:21Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"6d340047b7df04ee467b63a1b4ed8432997175c31419a76e93de1bd2ab70ed1d","abstract_canon_sha256":"4697e42dc5521a86771360ec09e00775ca4e29d9c8bf2d3bee45b32411f7022f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:53.748975Z","signature_b64":"J5/neBoT/g148jUxtPZE4QBmxyLRA2K0N9kYw19SgX1XlKpj+jHALoFhFKtXhOTInhGrHPggIzgrQeLDb1sGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"992cf5a1ea3654e5a85a9120c77465e944bd0fabe95b34478a66c0adfea9b5de","last_reissued_at":"2026-05-18T01:31:53.748409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:53.748409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Ablowitz-Ladik Hierarchy Revisited","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Fritz Gesztesy, Gerald Teschl, Helge Holden, Johanna Michor","submitted_at":"2007-02-28T20:23:21Z","abstract_excerpt":"We provide a detailed recursive construction of the Ablowitz-Ladik (AL) hierarchy and its zero-curvature formalism. The two-coefficient AL hierarchy under investigation can be considered a complexified version of the discrete nonlinear Schr\\\"odinger equation and its hierarchy of nonlinear evolution equations.\n  Specifically, we discuss in detail the stationary Ablowitz-Ladik formalism in connection with the underlying hyperelliptic curve and the stationary Baker-Akhiezer function and separately the corresponding time-dependent Ablowitz-Ladik formalism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0702058","kind":"arxiv","version":3},"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":"nlin/0702058","created_at":"2026-05-18T01:31:53.748507+00:00"},{"alias_kind":"arxiv_version","alias_value":"nlin/0702058v3","created_at":"2026-05-18T01:31:53.748507+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0702058","created_at":"2026-05-18T01:31:53.748507+00:00"},{"alias_kind":"pith_short_12","alias_value":"TEWPLIPKGZKO","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"TEWPLIPKGZKOLKC2","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"TEWPLIPK","created_at":"2026-05-18T12:25:56.245647+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/TEWPLIPKGZKOLKC2SEQMO5DF5F","json":"https://pith.science/pith/TEWPLIPKGZKOLKC2SEQMO5DF5F.json","graph_json":"https://pith.science/api/pith-number/TEWPLIPKGZKOLKC2SEQMO5DF5F/graph.json","events_json":"https://pith.science/api/pith-number/TEWPLIPKGZKOLKC2SEQMO5DF5F/events.json","paper":"https://pith.science/paper/TEWPLIPK"},"agent_actions":{"view_html":"https://pith.science/pith/TEWPLIPKGZKOLKC2SEQMO5DF5F","download_json":"https://pith.science/pith/TEWPLIPKGZKOLKC2SEQMO5DF5F.json","view_paper":"https://pith.science/paper/TEWPLIPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=nlin/0702058&json=true","fetch_graph":"https://pith.science/api/pith-number/TEWPLIPKGZKOLKC2SEQMO5DF5F/graph.json","fetch_events":"https://pith.science/api/pith-number/TEWPLIPKGZKOLKC2SEQMO5DF5F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TEWPLIPKGZKOLKC2SEQMO5DF5F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TEWPLIPKGZKOLKC2SEQMO5DF5F/action/storage_attestation","attest_author":"https://pith.science/pith/TEWPLIPKGZKOLKC2SEQMO5DF5F/action/author_attestation","sign_citation":"https://pith.science/pith/TEWPLIPKGZKOLKC2SEQMO5DF5F/action/citation_signature","submit_replication":"https://pith.science/pith/TEWPLIPKGZKOLKC2SEQMO5DF5F/action/replication_record"}},"created_at":"2026-05-18T01:31:53.748507+00:00","updated_at":"2026-05-18T01:31:53.748507+00:00"}