{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OULXHDRPKTZQ4KYSL5EY6PC35T","short_pith_number":"pith:OULXHDRP","canonical_record":{"source":{"id":"1208.5867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-29T09:19:37Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"ffefab8bbe55830f53a742cf5a558a4fbf17afa76757e2714265e0fd21cd282c","abstract_canon_sha256":"b901e62b095bd545311214d5c83ffab427e1e686f1dcb07dd0d431841335fa02"},"schema_version":"1.0"},"canonical_sha256":"7517738e2f54f30e2b125f498f3c5beccfd1e76b09fa6d11478472da9347ef44","source":{"kind":"arxiv","id":"1208.5867","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5867","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5867v1","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5867","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"OULXHDRPKTZQ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OULXHDRPKTZQ4KYS","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OULXHDRP","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OULXHDRPKTZQ4KYSL5EY6PC35T","target":"record","payload":{"canonical_record":{"source":{"id":"1208.5867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-29T09:19:37Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"ffefab8bbe55830f53a742cf5a558a4fbf17afa76757e2714265e0fd21cd282c","abstract_canon_sha256":"b901e62b095bd545311214d5c83ffab427e1e686f1dcb07dd0d431841335fa02"},"schema_version":"1.0"},"canonical_sha256":"7517738e2f54f30e2b125f498f3c5beccfd1e76b09fa6d11478472da9347ef44","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:48.482775Z","signature_b64":"YlDGekFXnc7rAXhVZ1D/Gi4O2vmo5lapK9URan7rc9vgfJ+zfvFEdMl0gIp/fXpL42nszBRvjrTKH1vsWQ2EBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7517738e2f54f30e2b125f498f3c5beccfd1e76b09fa6d11478472da9347ef44","last_reissued_at":"2026-05-18T03:46:48.482074Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:48.482074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.5867","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"49AAPMLQERHlc0FaU2C2sZURsdKCJ9kF9oS0E6wQFYY/rYPbUzyllWJ2+BS7q68GS6sMkFT7Esqhd3OcNVMxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:40:22.904602Z"},"content_sha256":"ef79b8cb62158a92e600ee0c6d2701e040f8c112fb7126c3f2bb827d39d72d45","schema_version":"1.0","event_id":"sha256:ef79b8cb62158a92e600ee0c6d2701e040f8c112fb7126c3f2bb827d39d72d45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OULXHDRPKTZQ4KYSL5EY6PC35T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivation of the Bose-Hubbard model in the multiscale limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Andrea Sacchetti, Reika Fukuizumi","submitted_at":"2012-08-29T09:19:37Z","abstract_excerpt":"In this paper we consider a one-dimensional non-linear Schroedinger equation (NLSE) with a periodic potential. In the semiclassical limit we prove that the stationary solutions of the Bose-Hubbard equation approximate the stationary solutions of the (NLSE). In particular, in the limit of large nonlinearity strength the stationary solutions turn out to be localized on a single lattice site of the periodic potential; as a result the phase transition from superfluid to Mott-insulator phase for Bose-Einstein condensates in a one-dimensional periodic lattice is rigorously proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5867","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:46:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dx2W8bR+soxrFytHMJG32swPlzUo1KmKesJkjHZrXoJLaKKxdXr9BLD/gI1wjo280nK39C2SomUvlfASlTupCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T02:40:22.905212Z"},"content_sha256":"78e735ff4492c20acec4ae9236a7450022a68d2bbc2d85d24b949e47a769a2c0","schema_version":"1.0","event_id":"sha256:78e735ff4492c20acec4ae9236a7450022a68d2bbc2d85d24b949e47a769a2c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OULXHDRPKTZQ4KYSL5EY6PC35T/bundle.json","state_url":"https://pith.science/pith/OULXHDRPKTZQ4KYSL5EY6PC35T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OULXHDRPKTZQ4KYSL5EY6PC35T/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T02:40:22Z","links":{"resolver":"https://pith.science/pith/OULXHDRPKTZQ4KYSL5EY6PC35T","bundle":"https://pith.science/pith/OULXHDRPKTZQ4KYSL5EY6PC35T/bundle.json","state":"https://pith.science/pith/OULXHDRPKTZQ4KYSL5EY6PC35T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OULXHDRPKTZQ4KYSL5EY6PC35T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OULXHDRPKTZQ4KYSL5EY6PC35T","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b901e62b095bd545311214d5c83ffab427e1e686f1dcb07dd0d431841335fa02","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-29T09:19:37Z","title_canon_sha256":"ffefab8bbe55830f53a742cf5a558a4fbf17afa76757e2714265e0fd21cd282c"},"schema_version":"1.0","source":{"id":"1208.5867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5867","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5867v1","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5867","created_at":"2026-05-18T03:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"OULXHDRPKTZQ","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OULXHDRPKTZQ4KYS","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OULXHDRP","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:78e735ff4492c20acec4ae9236a7450022a68d2bbc2d85d24b949e47a769a2c0","target":"graph","created_at":"2026-05-18T03:46:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we consider a one-dimensional non-linear Schroedinger equation (NLSE) with a periodic potential. In the semiclassical limit we prove that the stationary solutions of the Bose-Hubbard equation approximate the stationary solutions of the (NLSE). In particular, in the limit of large nonlinearity strength the stationary solutions turn out to be localized on a single lattice site of the periodic potential; as a result the phase transition from superfluid to Mott-insulator phase for Bose-Einstein condensates in a one-dimensional periodic lattice is rigorously proved.","authors_text":"Andrea Sacchetti, Reika Fukuizumi","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-29T09:19:37Z","title":"Derivation of the Bose-Hubbard model in the multiscale limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5867","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ef79b8cb62158a92e600ee0c6d2701e040f8c112fb7126c3f2bb827d39d72d45","target":"record","created_at":"2026-05-18T03:46:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b901e62b095bd545311214d5c83ffab427e1e686f1dcb07dd0d431841335fa02","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-08-29T09:19:37Z","title_canon_sha256":"ffefab8bbe55830f53a742cf5a558a4fbf17afa76757e2714265e0fd21cd282c"},"schema_version":"1.0","source":{"id":"1208.5867","kind":"arxiv","version":1}},"canonical_sha256":"7517738e2f54f30e2b125f498f3c5beccfd1e76b09fa6d11478472da9347ef44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7517738e2f54f30e2b125f498f3c5beccfd1e76b09fa6d11478472da9347ef44","first_computed_at":"2026-05-18T03:46:48.482074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:48.482074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YlDGekFXnc7rAXhVZ1D/Gi4O2vmo5lapK9URan7rc9vgfJ+zfvFEdMl0gIp/fXpL42nszBRvjrTKH1vsWQ2EBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:48.482775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef79b8cb62158a92e600ee0c6d2701e040f8c112fb7126c3f2bb827d39d72d45","sha256:78e735ff4492c20acec4ae9236a7450022a68d2bbc2d85d24b949e47a769a2c0"],"state_sha256":"161d6233950ebdb5acf8c7f01079db5f40a27ddc2e470b41ee25c0cb1fc5860e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MJsD23+um4mMJ7m+34bqQIh5+DbzWQ8lecl6CGu3uCoGQaDc/tRYipICsEGzH/9ZYWqUUNSZ7mRm/O8W2Hh5CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T02:40:22.907846Z","bundle_sha256":"56fb0be706c1c9d6dbb6b97fce15a46a3964bc40f038c7214c8d392b3828af14"}}