{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:UCRS2E2LMASZTEA2RGYA5PAZAQ","short_pith_number":"pith:UCRS2E2L","schema_version":"1.0","canonical_sha256":"a0a32d134b602599901a89b00ebc19042472564764526c7784ab6074c577312f","source":{"kind":"arxiv","id":"2607.01493","version":1},"attestation_state":"computed","paper":{"title":"Learning Lax Pairs: Revisiting the Classical Paradigm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Gino Biondini, Jimmie Adriazola, Panayotis G. Kevrekidis, Wei Zhu","submitted_at":"2026-07-01T21:43:13Z","abstract_excerpt":"A Lax pair $(L,P)$ is sometimes thought of as a structural certificate, in that the spatial operator $L$ carries the spectral data of an integrable system, and its isospectral evolution under $\\partial_t L = [L,P]$ encodes the nonlinear dynamics. Yet, experience shows that the correspondence between equations and Lax pairs is much more nuanced than this picture suggests. Equations can admit Lax pairs that fail to encode the expected integrable structure. This paper probes that anomalous corner of the Lax pair landscape through five case studies (the Euler top, the free Schr\\\"odinger 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":"2607.01493","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.SI","submitted_at":"2026-07-01T21:43:13Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"02e303b594d592bf03e5ea387c16a6fbc2211a367151c11005c146921212bbf1","abstract_canon_sha256":"5c36bb4718e7e9ab3f779bf5323e4b76a44e56302c49cc6e5ef736937ad34952"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T00:17:02.291885Z","signature_b64":"oef+ceG16oT3F8aL5TN21BRqU/3oz9VjiK0qdioSK/lELfJVYXtEL6jpsY1P2rjSBGMmET1D1ZZi1aHZlQZYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0a32d134b602599901a89b00ebc19042472564764526c7784ab6074c577312f","last_reissued_at":"2026-07-03T00:17:02.291495Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T00:17:02.291495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning Lax Pairs: Revisiting the Classical Paradigm","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Gino Biondini, Jimmie Adriazola, Panayotis G. Kevrekidis, Wei Zhu","submitted_at":"2026-07-01T21:43:13Z","abstract_excerpt":"A Lax pair $(L,P)$ is sometimes thought of as a structural certificate, in that the spatial operator $L$ carries the spectral data of an integrable system, and its isospectral evolution under $\\partial_t L = [L,P]$ encodes the nonlinear dynamics. Yet, experience shows that the correspondence between equations and Lax pairs is much more nuanced than this picture suggests. Equations can admit Lax pairs that fail to encode the expected integrable structure. This paper probes that anomalous corner of the Lax pair landscape through five case studies (the Euler top, the free Schr\\\"odinger equation, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01493","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/2607.01493/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":"2607.01493","created_at":"2026-07-03T00:17:02.291549+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.01493v1","created_at":"2026-07-03T00:17:02.291549+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.01493","created_at":"2026-07-03T00:17:02.291549+00:00"},{"alias_kind":"pith_short_12","alias_value":"UCRS2E2LMASZ","created_at":"2026-07-03T00:17:02.291549+00:00"},{"alias_kind":"pith_short_16","alias_value":"UCRS2E2LMASZTEA2","created_at":"2026-07-03T00:17:02.291549+00:00"},{"alias_kind":"pith_short_8","alias_value":"UCRS2E2L","created_at":"2026-07-03T00:17:02.291549+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.05146","citing_title":"Machine-Learning Search for Lax Connections","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UCRS2E2LMASZTEA2RGYA5PAZAQ","json":"https://pith.science/pith/UCRS2E2LMASZTEA2RGYA5PAZAQ.json","graph_json":"https://pith.science/api/pith-number/UCRS2E2LMASZTEA2RGYA5PAZAQ/graph.json","events_json":"https://pith.science/api/pith-number/UCRS2E2LMASZTEA2RGYA5PAZAQ/events.json","paper":"https://pith.science/paper/UCRS2E2L"},"agent_actions":{"view_html":"https://pith.science/pith/UCRS2E2LMASZTEA2RGYA5PAZAQ","download_json":"https://pith.science/pith/UCRS2E2LMASZTEA2RGYA5PAZAQ.json","view_paper":"https://pith.science/paper/UCRS2E2L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.01493&json=true","fetch_graph":"https://pith.science/api/pith-number/UCRS2E2LMASZTEA2RGYA5PAZAQ/graph.json","fetch_events":"https://pith.science/api/pith-number/UCRS2E2LMASZTEA2RGYA5PAZAQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UCRS2E2LMASZTEA2RGYA5PAZAQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UCRS2E2LMASZTEA2RGYA5PAZAQ/action/storage_attestation","attest_author":"https://pith.science/pith/UCRS2E2LMASZTEA2RGYA5PAZAQ/action/author_attestation","sign_citation":"https://pith.science/pith/UCRS2E2LMASZTEA2RGYA5PAZAQ/action/citation_signature","submit_replication":"https://pith.science/pith/UCRS2E2LMASZTEA2RGYA5PAZAQ/action/replication_record"}},"created_at":"2026-07-03T00:17:02.291549+00:00","updated_at":"2026-07-03T00:17:02.291549+00:00"}