{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:KBUOL4JR5UABNENXFXGOWY4JTE","short_pith_number":"pith:KBUOL4JR","canonical_record":{"source":{"id":"0907.2046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2009-07-12T15:33:08Z","cross_cats_sorted":[],"title_canon_sha256":"ad63612c05f25052078a8150c307b9a399de1b12a68da67d06e6046617dad09e","abstract_canon_sha256":"01780e90c92e3a903840c2c21abdc5e4999275ecaa708210e776d3891584b9ae"},"schema_version":"1.0"},"canonical_sha256":"5068e5f131ed001691b72dcceb638999201885ed964b8bca468d6f8f34d5a524","source":{"kind":"arxiv","id":"0907.2046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2046","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2046v1","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2046","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"pith_short_12","alias_value":"KBUOL4JR5UAB","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KBUOL4JR5UABNENX","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KBUOL4JR","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:KBUOL4JR5UABNENXFXGOWY4JTE","target":"record","payload":{"canonical_record":{"source":{"id":"0907.2046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2009-07-12T15:33:08Z","cross_cats_sorted":[],"title_canon_sha256":"ad63612c05f25052078a8150c307b9a399de1b12a68da67d06e6046617dad09e","abstract_canon_sha256":"01780e90c92e3a903840c2c21abdc5e4999275ecaa708210e776d3891584b9ae"},"schema_version":"1.0"},"canonical_sha256":"5068e5f131ed001691b72dcceb638999201885ed964b8bca468d6f8f34d5a524","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:09.450187Z","signature_b64":"AW4S7ua8jPok6/fVHks39e4Hr9IZDFcJVdPDgUuPpMw8VxUfFZdWI9XgGV5lVmI1CB7evnOwc9XaoMdEbBgSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5068e5f131ed001691b72dcceb638999201885ed964b8bca468d6f8f34d5a524","last_reissued_at":"2026-05-18T03:49:09.449779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:09.449779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.2046","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":"2026-05-18T03:49:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UJfW+iVXy5JRl2MTfLkbn5PAsKSEygCn5ZS/bdavGMoEVr41X9jLBEnGuMVNKQ2uS3uTuOVuAvrI+mvcEcm4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:43:12.344094Z"},"content_sha256":"4c7e794d3b46a1da4277a55f1c321cd4c892155c4f08486bb925a0dcf22ddcb4","schema_version":"1.0","event_id":"sha256:4c7e794d3b46a1da4277a55f1c321cd4c892155c4f08486bb925a0dcf22ddcb4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:KBUOL4JR5UABNENXFXGOWY4JTE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-consistent Single-band Approximation for Interacting Boson Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.quant-gas","authors_text":"Biao Wu, Junren Shi","submitted_at":"2009-07-12T15:33:08Z","abstract_excerpt":"Traditionally, the single-band approximation for interacting many-body systems is done with pre-determined single-particle Wannier functions, ignoring the dependence of the Wannier function on interaction. We show that the single-band approximation has to be done self-consistently to properly account the interaction effect on the Wannier functions. This self-consistent single-band approximation leads to a nonlinear equation for Wannier functions, which can be recast into a set of nonlinear equations for Bloch functions. These equations are simplified for two special cases, the superfluid regim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2046","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":"2026-05-18T03:49:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3ppMuP58XRH2/bP9MEvJGLb/avYskPmopNEM/F9Vp371X3J50VfDc3f2XeKjw26M2P59MG4jDG9GEhQ6Oe30Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:43:12.344465Z"},"content_sha256":"4b54a9628d0c363382cccc6dc7acd38869c63d734fff4452f0f4fcb78a9e9cf6","schema_version":"1.0","event_id":"sha256:4b54a9628d0c363382cccc6dc7acd38869c63d734fff4452f0f4fcb78a9e9cf6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KBUOL4JR5UABNENXFXGOWY4JTE/bundle.json","state_url":"https://pith.science/pith/KBUOL4JR5UABNENXFXGOWY4JTE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KBUOL4JR5UABNENXFXGOWY4JTE/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":"2026-06-03T12:43:12Z","links":{"resolver":"https://pith.science/pith/KBUOL4JR5UABNENXFXGOWY4JTE","bundle":"https://pith.science/pith/KBUOL4JR5UABNENXFXGOWY4JTE/bundle.json","state":"https://pith.science/pith/KBUOL4JR5UABNENXFXGOWY4JTE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KBUOL4JR5UABNENXFXGOWY4JTE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KBUOL4JR5UABNENXFXGOWY4JTE","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":"01780e90c92e3a903840c2c21abdc5e4999275ecaa708210e776d3891584b9ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2009-07-12T15:33:08Z","title_canon_sha256":"ad63612c05f25052078a8150c307b9a399de1b12a68da67d06e6046617dad09e"},"schema_version":"1.0","source":{"id":"0907.2046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.2046","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"arxiv_version","alias_value":"0907.2046v1","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.2046","created_at":"2026-05-18T03:49:09Z"},{"alias_kind":"pith_short_12","alias_value":"KBUOL4JR5UAB","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KBUOL4JR5UABNENX","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KBUOL4JR","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:4b54a9628d0c363382cccc6dc7acd38869c63d734fff4452f0f4fcb78a9e9cf6","target":"graph","created_at":"2026-05-18T03:49:09Z","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":"Traditionally, the single-band approximation for interacting many-body systems is done with pre-determined single-particle Wannier functions, ignoring the dependence of the Wannier function on interaction. We show that the single-band approximation has to be done self-consistently to properly account the interaction effect on the Wannier functions. This self-consistent single-band approximation leads to a nonlinear equation for Wannier functions, which can be recast into a set of nonlinear equations for Bloch functions. These equations are simplified for two special cases, the superfluid regim","authors_text":"Biao Wu, Junren Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2009-07-12T15:33:08Z","title":"Self-consistent Single-band Approximation for Interacting Boson Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.2046","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":"sha256:4c7e794d3b46a1da4277a55f1c321cd4c892155c4f08486bb925a0dcf22ddcb4","target":"record","created_at":"2026-05-18T03:49:09Z","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":"01780e90c92e3a903840c2c21abdc5e4999275ecaa708210e776d3891584b9ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2009-07-12T15:33:08Z","title_canon_sha256":"ad63612c05f25052078a8150c307b9a399de1b12a68da67d06e6046617dad09e"},"schema_version":"1.0","source":{"id":"0907.2046","kind":"arxiv","version":1}},"canonical_sha256":"5068e5f131ed001691b72dcceb638999201885ed964b8bca468d6f8f34d5a524","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5068e5f131ed001691b72dcceb638999201885ed964b8bca468d6f8f34d5a524","first_computed_at":"2026-05-18T03:49:09.449779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:09.449779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AW4S7ua8jPok6/fVHks39e4Hr9IZDFcJVdPDgUuPpMw8VxUfFZdWI9XgGV5lVmI1CB7evnOwc9XaoMdEbBgSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:09.450187Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.2046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c7e794d3b46a1da4277a55f1c321cd4c892155c4f08486bb925a0dcf22ddcb4","sha256:4b54a9628d0c363382cccc6dc7acd38869c63d734fff4452f0f4fcb78a9e9cf6"],"state_sha256":"a122cb5647aaf0ca65ee706fb7633ab3c1b9b308d35a9234508ca8732c491049"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Um+wHbXHooraY7gONipn/tRUx4TmGhS65QRtPgF9JrJ1HQz6hwo8CVR6Nd+pTRaeoIj39zBBPQruDCenoFHzBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T12:43:12.346456Z","bundle_sha256":"a542c448bb2f47d7f911df9793c5e0f29c2455f1f430962fe788bb1ed9a28115"}}