{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:IC4QD4QT2AZP4YYGDGAYA2HBVF","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":"b0bc81594fb748653bcfaeeb3f6b9dabc1bf45c644052602878e6f6f574773f5","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.mtrl-sci","submitted_at":"1997-07-14T13:45:26Z","title_canon_sha256":"20037da08df1036122e632b3b965617844c4f2854d1cdf5c6f8fc4b813ff4f65"},"schema_version":"1.0","source":{"id":"cond-mat/9707145","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9707145","created_at":"2026-07-04T16:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9707145v1","created_at":"2026-07-04T16:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9707145","created_at":"2026-07-04T16:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"IC4QD4QT2AZP","created_at":"2026-07-04T16:04:05Z"},{"alias_kind":"pith_short_16","alias_value":"IC4QD4QT2AZP4YYG","created_at":"2026-07-04T16:04:05Z"},{"alias_kind":"pith_short_8","alias_value":"IC4QD4QT","created_at":"2026-07-04T16:04:05Z"}],"graph_snapshots":[{"event_id":"sha256:aabf5b9519d989aabefd050a3c646c9755efe392397f8a0a5a0812da19521da0","target":"graph","created_at":"2026-07-04T16:04:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cond-mat/9707145/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss a method for determining the optimally-localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ``generalized Wannier functions'' we mean a set of localized orthonormal orbitals spanning the same space as the specified set of Bloch bands. Although we minimize a functional that represents the total spread sum_n [ <r^2>_n - <r>_n^2 ] of the Wannier functions in real space, our method proceeds directly from the Bloch functions as represented on a mesh of k-points, and carries out the minimization in a space of unitary matrices U_mn^","authors_text":"Astronomy, David Vanderbilt (Department of Physics, Nicola Marzari, Rutgers University)","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.mtrl-sci","submitted_at":"1997-07-14T13:45:26Z","title":"Maximally-localized generalized Wannier functions for composite energy bands"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9707145","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":"sha256:781376c83ddd3355822ac9fe5977e856f2f74c6ce02263731ca5639b7a01f1a7","target":"record","created_at":"2026-07-04T16:04:05Z","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":"b0bc81594fb748653bcfaeeb3f6b9dabc1bf45c644052602878e6f6f574773f5","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.mtrl-sci","submitted_at":"1997-07-14T13:45:26Z","title_canon_sha256":"20037da08df1036122e632b3b965617844c4f2854d1cdf5c6f8fc4b813ff4f65"},"schema_version":"1.0","source":{"id":"cond-mat/9707145","kind":"arxiv","version":1}},"canonical_sha256":"40b901f213d032fe630619818068e1a97a8089ca950a58c3512b1da47424da1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40b901f213d032fe630619818068e1a97a8089ca950a58c3512b1da47424da1d","first_computed_at":"2026-07-04T16:04:05.672714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:04:05.672714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RJJUWYNqxgvYmBhfmxPWXoX42sgmbmMhIjCVVXtPzlzFXH0ES8CzRkHUezmkxUXF+5Gb6WDdl2ly9bbx6ohVCw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:04:05.673094Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9707145","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:781376c83ddd3355822ac9fe5977e856f2f74c6ce02263731ca5639b7a01f1a7","sha256:aabf5b9519d989aabefd050a3c646c9755efe392397f8a0a5a0812da19521da0"],"state_sha256":"39dca2bb447e735722613b712cbc32edb63ec1f6c049f46e2254ba630d86cfe0"}