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We prove for any $\\mu\\ne0$ the existence of bound state of the discrete three-particle Schr\\\"odinger operator $H_{\\mu}(K),\\,K\\in \\T^d$ being the three-particle quasi-momentum, associated to the hamiltonian $\\mathrm{H}_{\\mu}$."},"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":"1602.01571","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-02-04T06:41:45Z","cross_cats_sorted":[],"title_canon_sha256":"95831c1accd6988d1ebfd3cc12c0be3d92223917b8dc51d75df6ed85073b445f","abstract_canon_sha256":"d785e5f6e10b8843c42437eac3b2f5354dc6cdcfc6710cd17998e9df3e6db385"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:03.186236Z","signature_b64":"QsUYMouFY9Qcm9VXNJ6XOYfQuH0H0lVd7fQP+M6VjP0b1qJl2idZE2h/qUGDP1eFxhEpyrQRjOfcp/8EOLptCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7da2f7d9aacd75e0ac4ea815089788ba6b952efd22b22fca68fdc77989fc37df","last_reissued_at":"2026-05-18T00:39:03.185677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:03.185677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The existence of bound states in a system of three particles in an optical lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Saidakhmat N.Lakaev, Shukhrat S.Lakaev","submitted_at":"2016-02-04T06:41:45Z","abstract_excerpt":"We consider the hamiltonian $\\mathrm{H}_{\\mu},\\mu\\in \\R$ of a system of three-particles (two identical fermions and one different particle) moving on the lattice ${\\Z}^d ,\\, d=1,2 $ interacting through repulsive $(\\mu>0)$ or attractive $(\\mu<0)$ zero-range pairwise potential $\\mu V$. 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