{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:B4JCCM6NMOYSZSCNZ7VZZ7YZXY","short_pith_number":"pith:B4JCCM6N","canonical_record":{"source":{"id":"1401.1961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2014-01-09T11:24:24Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"63b93982f8de1e3557f900a3eb9b4c769c6883f4e2b158aacc6b00dd9e1b851b","abstract_canon_sha256":"8ae85cdd2704852e39d7dbd6fc7ce62e15a40fce90cdc2fd5eb0e8b86ab7610e"},"schema_version":"1.0"},"canonical_sha256":"0f122133cd63b12cc84dcfeb9cff19be02930b0b054946915a4ffa089fa358a7","source":{"kind":"arxiv","id":"1401.1961","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1961","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1961v1","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1961","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"pith_short_12","alias_value":"B4JCCM6NMOYS","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B4JCCM6NMOYSZSCN","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B4JCCM6N","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:B4JCCM6NMOYSZSCNZ7VZZ7YZXY","target":"record","payload":{"canonical_record":{"source":{"id":"1401.1961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2014-01-09T11:24:24Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"63b93982f8de1e3557f900a3eb9b4c769c6883f4e2b158aacc6b00dd9e1b851b","abstract_canon_sha256":"8ae85cdd2704852e39d7dbd6fc7ce62e15a40fce90cdc2fd5eb0e8b86ab7610e"},"schema_version":"1.0"},"canonical_sha256":"0f122133cd63b12cc84dcfeb9cff19be02930b0b054946915a4ffa089fa358a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:26.133006Z","signature_b64":"17u3jojprbVbGzklfRJjMxrcDs6BfdzqheGMEOsNq6Q4CCnPj2AQc5y8a+zEJV8RRuQLdmIKi2K8KW/rxi++Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f122133cd63b12cc84dcfeb9cff19be02930b0b054946915a4ffa089fa358a7","last_reissued_at":"2026-05-18T02:43:26.132255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:26.132255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.1961","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":"2026-05-18T02:43:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S6u9ccHOuVYBlAb/wm9A2FT8FO0SFDT3mHkJNSVusIsNg009EXT+EzHOSLKN2Gbof3Byx29H3G2fWooiaBfwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:50:15.019063Z"},"content_sha256":"2478344db7c548f51187316f9cae385bba00e6e40638e6940b4e698efa06c6b3","schema_version":"1.0","event_id":"sha256:2478344db7c548f51187316f9cae385bba00e6e40638e6940b4e698efa06c6b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:B4JCCM6NMOYSZSCNZ7VZZ7YZXY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the effective Dirac equation for ultracold atoms in optical lattices: role of the localization properties of the Wannier functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"cond-mat.quant-gas","authors_text":"Giulio Pettini, Jacopo Sisti, Michele Modugno, Xabier Lopez-Gonzalez","submitted_at":"2014-01-09T11:24:24Z","abstract_excerpt":"We review the derivation of the effective Dirac equation for ultracold atoms in one-dimensional bichromatic optical lattices, following the proposal by Witthaut et al. Phys. Rev. A 84, 033601 (2011). We discuss how such a derivation - based on a suitable rotation of the Bloch basis and on a coarse graining approximation - is affected by the choice of the Wannier functions entering the coarsening procedure. We show that in general the Wannier functions obtained by rotating the maximally localized Wannier functions for the original Bloch bands can be sufficiently localized for justifying the coa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1961","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":"2026-05-18T02:43:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WVLujzPkHKStZu/L1wrhE64wWupZ6oWeUWwJ1Oq2f0QK3lQ6BRqovJHWDZU7T2GeFqNO9a9INwZvAsVOwyKJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:50:15.019421Z"},"content_sha256":"f85466d3e128bff08175e32b015a2eec184c2d14a55427e6e1ee9081e97b9a8d","schema_version":"1.0","event_id":"sha256:f85466d3e128bff08175e32b015a2eec184c2d14a55427e6e1ee9081e97b9a8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B4JCCM6NMOYSZSCNZ7VZZ7YZXY/bundle.json","state_url":"https://pith.science/pith/B4JCCM6NMOYSZSCNZ7VZZ7YZXY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B4JCCM6NMOYSZSCNZ7VZZ7YZXY/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":"2026-06-20T10:50:15Z","links":{"resolver":"https://pith.science/pith/B4JCCM6NMOYSZSCNZ7VZZ7YZXY","bundle":"https://pith.science/pith/B4JCCM6NMOYSZSCNZ7VZZ7YZXY/bundle.json","state":"https://pith.science/pith/B4JCCM6NMOYSZSCNZ7VZZ7YZXY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B4JCCM6NMOYSZSCNZ7VZZ7YZXY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B4JCCM6NMOYSZSCNZ7VZZ7YZXY","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":"8ae85cdd2704852e39d7dbd6fc7ce62e15a40fce90cdc2fd5eb0e8b86ab7610e","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2014-01-09T11:24:24Z","title_canon_sha256":"63b93982f8de1e3557f900a3eb9b4c769c6883f4e2b158aacc6b00dd9e1b851b"},"schema_version":"1.0","source":{"id":"1401.1961","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1961","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1961v1","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1961","created_at":"2026-05-18T02:43:26Z"},{"alias_kind":"pith_short_12","alias_value":"B4JCCM6NMOYS","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B4JCCM6NMOYSZSCN","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B4JCCM6N","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:f85466d3e128bff08175e32b015a2eec184c2d14a55427e6e1ee9081e97b9a8d","target":"graph","created_at":"2026-05-18T02:43:26Z","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":"We review the derivation of the effective Dirac equation for ultracold atoms in one-dimensional bichromatic optical lattices, following the proposal by Witthaut et al. Phys. Rev. A 84, 033601 (2011). We discuss how such a derivation - based on a suitable rotation of the Bloch basis and on a coarse graining approximation - is affected by the choice of the Wannier functions entering the coarsening procedure. We show that in general the Wannier functions obtained by rotating the maximally localized Wannier functions for the original Bloch bands can be sufficiently localized for justifying the coa","authors_text":"Giulio Pettini, Jacopo Sisti, Michele Modugno, Xabier Lopez-Gonzalez","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2014-01-09T11:24:24Z","title":"On the effective Dirac equation for ultracold atoms in optical lattices: role of the localization properties of the Wannier functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1961","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":"sha256:2478344db7c548f51187316f9cae385bba00e6e40638e6940b4e698efa06c6b3","target":"record","created_at":"2026-05-18T02:43:26Z","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":"8ae85cdd2704852e39d7dbd6fc7ce62e15a40fce90cdc2fd5eb0e8b86ab7610e","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.quant-gas","submitted_at":"2014-01-09T11:24:24Z","title_canon_sha256":"63b93982f8de1e3557f900a3eb9b4c769c6883f4e2b158aacc6b00dd9e1b851b"},"schema_version":"1.0","source":{"id":"1401.1961","kind":"arxiv","version":1}},"canonical_sha256":"0f122133cd63b12cc84dcfeb9cff19be02930b0b054946915a4ffa089fa358a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f122133cd63b12cc84dcfeb9cff19be02930b0b054946915a4ffa089fa358a7","first_computed_at":"2026-05-18T02:43:26.132255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:26.132255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"17u3jojprbVbGzklfRJjMxrcDs6BfdzqheGMEOsNq6Q4CCnPj2AQc5y8a+zEJV8RRuQLdmIKi2K8KW/rxi++Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:26.133006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1961","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2478344db7c548f51187316f9cae385bba00e6e40638e6940b4e698efa06c6b3","sha256:f85466d3e128bff08175e32b015a2eec184c2d14a55427e6e1ee9081e97b9a8d"],"state_sha256":"f3bb0a03b88a5ebd5acac02d572e7d9211c8d4e3ca06a5ed0803ae0a6e8ea0af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"74eACUXSS7Z0UZFSSu0cqLT+I2sn03vcj/R98esnlpZCQjapVPStj6X/adwpOdp4mZe/KyykGiGe7eUGOVWWBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T10:50:15.021332Z","bundle_sha256":"e9397be6486919d2dbfc646ab87409ef1c5a5ff86076ba1d543cacf5157e1e38"}}