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We show that the partition function is an (L-2N)-parameter extension of Slavnov's scalar product of a Bethe eigenstate and a generic state, with N magnons each, on a length-L XXX spin-1/2 chain.\n  Decoupling the extra parameters, we obtain a third determinant expression for the scalar product, where the first is due to Slavnov [1], and the second is due to Kostov and Matsuo [2]. We show that"},"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":"1207.6871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-07-30T09:06:57Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"59a13acbc36aa96ce6c10eed2bf248b1f650299ae4a41d21b19fd9ad88d2bfc4","abstract_canon_sha256":"0d7a4a22b779fe16a213de0628eb303a2fd69a9653f7adcb38b80a644e5bee86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:51.713266Z","signature_b64":"KWnFGQ4TMZ1TQ4lHytjk/VxcDw48DbEhNw7x3mP3Wt7+mtzDrmBq7i9gZZ3UrHxAD+72I39Dcg+nRwgSPJFFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d465df89c47c4a4ff68afa2b934688f2226cfa6cb9189048d33765c3f24ae99c","last_reissued_at":"2026-05-18T01:29:51.712697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:51.712697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Variations on Slavnov's scalar product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"M. Wheeler, O. Foda","submitted_at":"2012-07-30T09:06:57Z","abstract_excerpt":"We consider the rational six-vertex model on an L-by-L lattice with domain wall boundary conditions and restrict N parallel-line rapidities, N < L/2, to satisfy length-L XXX spin-1/2 chain Bethe equations. We show that the partition function is an (L-2N)-parameter extension of Slavnov's scalar product of a Bethe eigenstate and a generic state, with N magnons each, on a length-L XXX spin-1/2 chain.\n  Decoupling the extra parameters, we obtain a third determinant expression for the scalar product, where the first is due to Slavnov [1], and the second is due to Kostov and Matsuo [2]. 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