{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:PFJEIT4OJ2LIOEJMB4WE5ZY23Z","short_pith_number":"pith:PFJEIT4O","schema_version":"1.0","canonical_sha256":"7952444f8e4e9687112c0f2c4ee71ade60c4a9599c9c49b05c3c32396b8dd60c","source":{"kind":"arxiv","id":"1508.07581","version":1},"attestation_state":"computed","paper":{"title":"Number of bound states of the Schroedinger operator of a system of three bosons in an optical lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Ahmad M.Khalkhuzhaev, Alimzhan R. Khalmukhamedov, Saidakhmat N. Lakaev","submitted_at":"2015-08-30T14:45:09Z","abstract_excerpt":"We consider the Hamiltonian $\\hat {\\mathrm{H}}_{\\mu}$ of a system of three identical particles(bosons) on the $d-$ dimensional lattice $\\Z^d, d=1,2$ interacting via pairwise zero-range attractive potential $\\mu<0$. We describe precise location and structure of the essential spectrum of the Schr\\\"odinger operator $H_\\mu(K),K\\in \\T^d$ associated to $\\hat {\\mathrm{H}}_\\mu$ and prove the finiteness of the number of bound states of $H_\\mu(K),K\\in \\T^d$ lying below the bottom of the essential spectrum. Moreover, we show that bound states decay exponentially at infinity and eigenvalues and correspond"},"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":"1508.07581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-08-30T14:45:09Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"dae16444ce6dbd346b9c4bc3d0cfa78da65766d29d321c0851524046771cd991","abstract_canon_sha256":"d6fe7fc5d2fa54636520991f6bd34cbc9102eeb98381141f36df3b205c78f631"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:13.049350Z","signature_b64":"BzHLS965AP8KjjD/HzeBIWeeXQSnC7BUzGs6McxNqX1062+/pC85rc2KTrV76P2+Ra0VA03bw9Fg2CqzlwzQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7952444f8e4e9687112c0f2c4ee71ade60c4a9599c9c49b05c3c32396b8dd60c","last_reissued_at":"2026-05-18T01:08:13.048715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:13.048715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Number of bound states of the Schroedinger operator of a system of three bosons in an optical lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Ahmad M.Khalkhuzhaev, Alimzhan R. Khalmukhamedov, Saidakhmat N. Lakaev","submitted_at":"2015-08-30T14:45:09Z","abstract_excerpt":"We consider the Hamiltonian $\\hat {\\mathrm{H}}_{\\mu}$ of a system of three identical particles(bosons) on the $d-$ dimensional lattice $\\Z^d, d=1,2$ interacting via pairwise zero-range attractive potential $\\mu<0$. We describe precise location and structure of the essential spectrum of the Schr\\\"odinger operator $H_\\mu(K),K\\in \\T^d$ associated to $\\hat {\\mathrm{H}}_\\mu$ and prove the finiteness of the number of bound states of $H_\\mu(K),K\\in \\T^d$ lying below the bottom of the essential spectrum. Moreover, we show that bound states decay exponentially at infinity and eigenvalues and correspond"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07581","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":""},"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":"1508.07581","created_at":"2026-05-18T01:08:13.048821+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.07581v1","created_at":"2026-05-18T01:08:13.048821+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07581","created_at":"2026-05-18T01:08:13.048821+00:00"},{"alias_kind":"pith_short_12","alias_value":"PFJEIT4OJ2LI","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_16","alias_value":"PFJEIT4OJ2LIOEJM","created_at":"2026-05-18T12:29:37.295048+00:00"},{"alias_kind":"pith_short_8","alias_value":"PFJEIT4O","created_at":"2026-05-18T12:29:37.295048+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/PFJEIT4OJ2LIOEJMB4WE5ZY23Z","json":"https://pith.science/pith/PFJEIT4OJ2LIOEJMB4WE5ZY23Z.json","graph_json":"https://pith.science/api/pith-number/PFJEIT4OJ2LIOEJMB4WE5ZY23Z/graph.json","events_json":"https://pith.science/api/pith-number/PFJEIT4OJ2LIOEJMB4WE5ZY23Z/events.json","paper":"https://pith.science/paper/PFJEIT4O"},"agent_actions":{"view_html":"https://pith.science/pith/PFJEIT4OJ2LIOEJMB4WE5ZY23Z","download_json":"https://pith.science/pith/PFJEIT4OJ2LIOEJMB4WE5ZY23Z.json","view_paper":"https://pith.science/paper/PFJEIT4O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.07581&json=true","fetch_graph":"https://pith.science/api/pith-number/PFJEIT4OJ2LIOEJMB4WE5ZY23Z/graph.json","fetch_events":"https://pith.science/api/pith-number/PFJEIT4OJ2LIOEJMB4WE5ZY23Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PFJEIT4OJ2LIOEJMB4WE5ZY23Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PFJEIT4OJ2LIOEJMB4WE5ZY23Z/action/storage_attestation","attest_author":"https://pith.science/pith/PFJEIT4OJ2LIOEJMB4WE5ZY23Z/action/author_attestation","sign_citation":"https://pith.science/pith/PFJEIT4OJ2LIOEJMB4WE5ZY23Z/action/citation_signature","submit_replication":"https://pith.science/pith/PFJEIT4OJ2LIOEJMB4WE5ZY23Z/action/replication_record"}},"created_at":"2026-05-18T01:08:13.048821+00:00","updated_at":"2026-05-18T01:08:13.048821+00:00"}