{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZSJWRNM5WEXFJT5MHZ6K5AFBCU","short_pith_number":"pith:ZSJWRNM5","schema_version":"1.0","canonical_sha256":"cc9368b59db12e54cfac3e7cae80a11510e5fce0b5ed45b2d0b8b80d5336202a","source":{"kind":"arxiv","id":"1610.05905","version":2},"attestation_state":"computed","paper":{"title":"Exact solution of the two-axis countertwisting Hamiltonian for the half-integer $J$ case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Feng Pan, Jerry P. Draayer, Yao-Zhong Zhang","submitted_at":"2016-10-19T08:20:27Z","abstract_excerpt":"Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) $J$ are derived based on the Jordan-Schwinger (differential) boson realization of the $SU(2)$ algebra after desired Euler rotations, where $J$ is the total angular momentum quantum number of the system. It is shown that solutions to the Bethe ansatz equations can be obtained as zeros of the extended Heine-Stieltjes polynomials. Two sets of solutions, with solution number being $J+1$ and $J$ respectively when $J$ is an integer and $J+1/2$ each when $J$ is a half-integer, are obtained. Propertie"},"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":"1610.05905","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-10-19T08:20:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5f89bf1de4f1a4c2ba54e7479f2560428c66000b8a74dced1ed534e3cc58efd5","abstract_canon_sha256":"d607c2ca6cc4a28a6e3a72a445b2aba72195b516b8b19da011ffa5a1e2b82fe6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:07.040730Z","signature_b64":"KIhHdYUfXcomqhDhbthbd+6V1xo3GHmyEXNq+sh4W2plRg7k3ZbNDtbmfxkST5tt3l4rZVeAVkfNHuqmzz/yBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc9368b59db12e54cfac3e7cae80a11510e5fce0b5ed45b2d0b8b80d5336202a","last_reissued_at":"2026-05-18T00:51:07.040235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:07.040235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact solution of the two-axis countertwisting Hamiltonian for the half-integer $J$ case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Feng Pan, Jerry P. Draayer, Yao-Zhong Zhang","submitted_at":"2016-10-19T08:20:27Z","abstract_excerpt":"Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) $J$ are derived based on the Jordan-Schwinger (differential) boson realization of the $SU(2)$ algebra after desired Euler rotations, where $J$ is the total angular momentum quantum number of the system. It is shown that solutions to the Bethe ansatz equations can be obtained as zeros of the extended Heine-Stieltjes polynomials. Two sets of solutions, with solution number being $J+1$ and $J$ respectively when $J$ is an integer and $J+1/2$ each when $J$ is a half-integer, are obtained. Propertie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05905","kind":"arxiv","version":2},"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":"1610.05905","created_at":"2026-05-18T00:51:07.040305+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.05905v2","created_at":"2026-05-18T00:51:07.040305+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05905","created_at":"2026-05-18T00:51:07.040305+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZSJWRNM5WEXF","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZSJWRNM5WEXFJT5M","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZSJWRNM5","created_at":"2026-05-18T12:30:55.937587+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/ZSJWRNM5WEXFJT5MHZ6K5AFBCU","json":"https://pith.science/pith/ZSJWRNM5WEXFJT5MHZ6K5AFBCU.json","graph_json":"https://pith.science/api/pith-number/ZSJWRNM5WEXFJT5MHZ6K5AFBCU/graph.json","events_json":"https://pith.science/api/pith-number/ZSJWRNM5WEXFJT5MHZ6K5AFBCU/events.json","paper":"https://pith.science/paper/ZSJWRNM5"},"agent_actions":{"view_html":"https://pith.science/pith/ZSJWRNM5WEXFJT5MHZ6K5AFBCU","download_json":"https://pith.science/pith/ZSJWRNM5WEXFJT5MHZ6K5AFBCU.json","view_paper":"https://pith.science/paper/ZSJWRNM5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.05905&json=true","fetch_graph":"https://pith.science/api/pith-number/ZSJWRNM5WEXFJT5MHZ6K5AFBCU/graph.json","fetch_events":"https://pith.science/api/pith-number/ZSJWRNM5WEXFJT5MHZ6K5AFBCU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZSJWRNM5WEXFJT5MHZ6K5AFBCU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZSJWRNM5WEXFJT5MHZ6K5AFBCU/action/storage_attestation","attest_author":"https://pith.science/pith/ZSJWRNM5WEXFJT5MHZ6K5AFBCU/action/author_attestation","sign_citation":"https://pith.science/pith/ZSJWRNM5WEXFJT5MHZ6K5AFBCU/action/citation_signature","submit_replication":"https://pith.science/pith/ZSJWRNM5WEXFJT5MHZ6K5AFBCU/action/replication_record"}},"created_at":"2026-05-18T00:51:07.040305+00:00","updated_at":"2026-05-18T00:51:07.040305+00:00"}