{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GFVD4PTEDN3YXDMFZ5PGE6JL4F","short_pith_number":"pith:GFVD4PTE","schema_version":"1.0","canonical_sha256":"316a3e3e641b778b8d85cf5e62792be162cb2de7663a89e5619e4f5327e8fcd1","source":{"kind":"arxiv","id":"2506.14171","version":1},"attestation_state":"computed","paper":{"title":"Coordinate-energy transformation and the one-point function for the Heisenberg-Ising XXZ spin-1/2 chain on the ring","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Axel Saenz, Eric I. Corwin, Nikolaus Elsaesser","submitted_at":"2025-06-17T04:26:52Z","abstract_excerpt":"We provide a basis transformation that inverts the coordinate Bethe Ansatz. It is widely believed that the Bethe Ansatz is complete, based on numerical evidence and combinatorial arguments. We present a constructive and comprehensive approach to show that the Bethe Ansatz is complete. The transformation formula is verified numerically with excellent accuracy for non-zero anisotropy parameters and rings of odd length. Additionally, assuming the Bethe Ansatz is complete, we derive a novel exact formula for the one-point function systems through special identities for the Izergin-Korepin determin"},"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":"2506.14171","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-06-17T04:26:52Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"a80c01ff36ffd49c3775470f8946f93826f4cdefc6c14fb848883b1907295792","abstract_canon_sha256":"15ccdc7937044e1fd10122e2d50b9bce96e9fb914b10e25db4b7fefbbf73be65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:50.287382Z","signature_b64":"uT4XjN4XSzGPd5iT4hCLctxQwO2N37fgZ21pt9uxs9FCoyjd+Q1JoZgZ+EsBV58VB+O1XFcfccQnDefLFhyKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"316a3e3e641b778b8d85cf5e62792be162cb2de7663a89e5619e4f5327e8fcd1","last_reissued_at":"2026-07-05T11:22:50.286976Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:50.286976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Coordinate-energy transformation and the one-point function for the Heisenberg-Ising XXZ spin-1/2 chain on the ring","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Axel Saenz, Eric I. Corwin, Nikolaus Elsaesser","submitted_at":"2025-06-17T04:26:52Z","abstract_excerpt":"We provide a basis transformation that inverts the coordinate Bethe Ansatz. It is widely believed that the Bethe Ansatz is complete, based on numerical evidence and combinatorial arguments. We present a constructive and comprehensive approach to show that the Bethe Ansatz is complete. The transformation formula is verified numerically with excellent accuracy for non-zero anisotropy parameters and rings of odd length. Additionally, assuming the Bethe Ansatz is complete, we derive a novel exact formula for the one-point function systems through special identities for the Izergin-Korepin determin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.14171","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/2506.14171/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":"2506.14171","created_at":"2026-07-05T11:22:50.287030+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.14171v1","created_at":"2026-07-05T11:22:50.287030+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.14171","created_at":"2026-07-05T11:22:50.287030+00:00"},{"alias_kind":"pith_short_12","alias_value":"GFVD4PTEDN3Y","created_at":"2026-07-05T11:22:50.287030+00:00"},{"alias_kind":"pith_short_16","alias_value":"GFVD4PTEDN3YXDMF","created_at":"2026-07-05T11:22:50.287030+00:00"},{"alias_kind":"pith_short_8","alias_value":"GFVD4PTE","created_at":"2026-07-05T11:22:50.287030+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/GFVD4PTEDN3YXDMFZ5PGE6JL4F","json":"https://pith.science/pith/GFVD4PTEDN3YXDMFZ5PGE6JL4F.json","graph_json":"https://pith.science/api/pith-number/GFVD4PTEDN3YXDMFZ5PGE6JL4F/graph.json","events_json":"https://pith.science/api/pith-number/GFVD4PTEDN3YXDMFZ5PGE6JL4F/events.json","paper":"https://pith.science/paper/GFVD4PTE"},"agent_actions":{"view_html":"https://pith.science/pith/GFVD4PTEDN3YXDMFZ5PGE6JL4F","download_json":"https://pith.science/pith/GFVD4PTEDN3YXDMFZ5PGE6JL4F.json","view_paper":"https://pith.science/paper/GFVD4PTE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.14171&json=true","fetch_graph":"https://pith.science/api/pith-number/GFVD4PTEDN3YXDMFZ5PGE6JL4F/graph.json","fetch_events":"https://pith.science/api/pith-number/GFVD4PTEDN3YXDMFZ5PGE6JL4F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GFVD4PTEDN3YXDMFZ5PGE6JL4F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GFVD4PTEDN3YXDMFZ5PGE6JL4F/action/storage_attestation","attest_author":"https://pith.science/pith/GFVD4PTEDN3YXDMFZ5PGE6JL4F/action/author_attestation","sign_citation":"https://pith.science/pith/GFVD4PTEDN3YXDMFZ5PGE6JL4F/action/citation_signature","submit_replication":"https://pith.science/pith/GFVD4PTEDN3YXDMFZ5PGE6JL4F/action/replication_record"}},"created_at":"2026-07-05T11:22:50.287030+00:00","updated_at":"2026-07-05T11:22:50.287030+00:00"}