{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IR5UXVWVQ5FD5MARA7CL44NGKO","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":"1b3f954d289694faef14f10678f8cd866f04822e4b992eb635f11be24f6ce43b","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2016-08-16T18:23:32Z","title_canon_sha256":"e0b3ddaa729884923e7996e9aff2481c12dcd835813b81a357510e252ff26605"},"schema_version":"1.0","source":{"id":"1608.04696","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04696","created_at":"2026-05-18T00:47:50Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04696v3","created_at":"2026-05-18T00:47:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04696","created_at":"2026-05-18T00:47:50Z"},{"alias_kind":"pith_short_12","alias_value":"IR5UXVWVQ5FD","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IR5UXVWVQ5FD5MAR","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IR5UXVWV","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:395effed9a6fa03b0d67910fbfdaf074b3093bdcce9d7f555b312e2ddb31f178","target":"graph","created_at":"2026-05-18T00:47:50Z","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 a tight-binding lattice model with $n$ orbitals (single-particle states) per site, Wannier functions are $n$-component vector functions of position that fall off rapidly away from some location, and such that a set of them in some sense span all states in a given energy band or set of bands; compactly-supported Wannier functions are such functions that vanish outside a bounded region. They arise not only in band theory, but also in connection with tensor-network states for non-interacting fermion systems, and for flat-band Hamiltonians with strictly short-range hopping matrix elements. In e","authors_text":"N. Read","cross_cats":["cond-mat.mtrl-sci","math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2016-08-16T18:23:32Z","title":"Compactly-supported Wannier functions and algebraic $K$-theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04696","kind":"arxiv","version":3},"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":"sha256:0118b552f8ef356e9f5203adf481c712452fbd13ff00aa697c68d49b92e2ac71","target":"record","created_at":"2026-05-18T00:47:50Z","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":"1b3f954d289694faef14f10678f8cd866f04822e4b992eb635f11be24f6ce43b","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2016-08-16T18:23:32Z","title_canon_sha256":"e0b3ddaa729884923e7996e9aff2481c12dcd835813b81a357510e252ff26605"},"schema_version":"1.0","source":{"id":"1608.04696","kind":"arxiv","version":3}},"canonical_sha256":"447b4bd6d5874a3eb01107c4be71a653aa36051fb09c7b5bf1fa254c1d6c87e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"447b4bd6d5874a3eb01107c4be71a653aa36051fb09c7b5bf1fa254c1d6c87e6","first_computed_at":"2026-05-18T00:47:50.249292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:50.249292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o0wQYyVBRvZPQFYdQi6jRqp3Ma1nvMEJaw26MScfgkvJLEaoDLlf76dkuUx6FV8DkQY70aR3VLGEkk/ty6x3CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:50.249948Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04696","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0118b552f8ef356e9f5203adf481c712452fbd13ff00aa697c68d49b92e2ac71","sha256:395effed9a6fa03b0d67910fbfdaf074b3093bdcce9d7f555b312e2ddb31f178"],"state_sha256":"44ce166b3cf4e46e329418e65f0f191cafa7923be8c13f1d50e872fe66a9232e"}