{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XC2TXH7IBKUE4KCMOS4H4NCX6C","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":"310702de3bdff596954ac68ea9d69a8bd191172456d46fa68f7e14dd934a3ca7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2026-05-14T05:58:36Z","title_canon_sha256":"c2971728da4ee9e5c79cf1f22cdd2df4ba4399dee49d1a2a88e6c858ac702197"},"schema_version":"1.0","source":{"id":"2605.14414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.14414","created_at":"2026-05-17T23:39:07Z"},{"alias_kind":"arxiv_version","alias_value":"2605.14414v1","created_at":"2026-05-17T23:39:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14414","created_at":"2026-05-17T23:39:07Z"},{"alias_kind":"pith_short_12","alias_value":"XC2TXH7IBKUE","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"XC2TXH7IBKUE4KCM","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"XC2TXH7I","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:8d59dd012ca1e00a76b8ec729a2365886c4e369467c38f4fe68a7072a78f1530","target":"graph","created_at":"2026-05-17T23:39:07Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"In this transport-aligned gauge, the Bloch overlaps exhibit an approximately linear phase dependence, allowing the Wannier centers to be extracted via deterministic fixed-point iterations and self-consistent updates rather than spread-functional minimization."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The assumption that discrete adiabatic transport across band degeneracies emerges naturally and produces approximately linear phase dependence in the Bloch overlaps for general systems, without post-hoc adjustments."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A non-variational algorithm constructs maximally localized Wannier functions by treating discrete adiabatic transport across band degeneracies as part of solving the projected position operator eigenvalues, yielding linear phase overlaps and fixed-point extraction of centers."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Maximally localized Wannier functions can be constructed deterministically by following discrete adiabatic transport across band degeneracies instead of minimizing a spread functional."}],"snapshot_sha256":"6ae1270ace259bdb611939fe745cc9ccc63a78d9e733665f7f5d36d777a33dca"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"330a73bc545273b59d2dab411db2527c270cbd93658c463248d36274cbf5a6c3"},"paper":{"abstract_excerpt":"Maximally localized Wannier functions (MLWFs) are conventionally constructed by iteratively minimizing a spread functional over a high-dimensional gauge landscape. In this work, we present a non-variational constructive algorithm that unifies gauge smoothing and the eigenvalue problem of the projected position operator into a single deterministic framework. We demonstrate that discrete adiabatic transport across band degeneracies emerges naturally as an integral part of the solution procedure for the position eigenvectors. In this transport-aligned gauge, the Bloch overlaps exhibit an approxim","authors_text":"Katsunori Wakabayashi, Yuji Hamai","cross_cats":[],"headline":"Maximally localized Wannier functions can be constructed deterministically by following discrete adiabatic transport across band degeneracies instead of minimizing a spread functional.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2026-05-14T05:58:36Z","title":"Shaping Maximally Localized Wannier Functions via Discrete Adiabatic Transport"},"references":{"count":84,"internal_anchors":1,"resolved_work":84,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"(33), (55) and (57), we have a WF with a candidate Wannier center r, |WM (r)⟩ = L− d/2 ∑ k e− ir·keik·( ˆx− M )|uk⟩, r ∈ [0,1)d","work_id":"382343cd-df90-4e1b-b6f5-61b366b199df","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"The multidimensional formulation is given in Appendix D 4","work_id":"b0f6c243-4a3a-4b73-a329-6b091a06d80b","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Matrix elements of ˆx In 1D cases, the real-space evaluation of the projected- position matrix elements Xs1s2 is explicitly calculated as fol- 10 FIG. 4. (Color online) Phases of the inner products of","work_id":"80c86021-84a2-421f-b74f-14161a3a379d","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"The spa- tial and k-space resolutions are N = 40 and L = 200, respec- tively","work_id":"7990b4b5-0ccc-47c7-8e57-86cb466a9d90","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"The potential energy employed is of Kr¨ onig-Penney type, V (x) = ∑ V0 δ (x− n)","work_id":"3d0e2278-210f-4946-a246-60ea2b3f7092","year":null}],"snapshot_sha256":"7e761c1a6e62c25100d7fe1a324b44e558bc67f49c0839793ffbeb2fc4ea0d68"},"source":{"id":"2605.14414","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-15T02:03:40.902248Z","id":"7cd1b6c9-a0ba-45df-b266-9fd69bea09ef","model_set":{"reader":"grok-4.3"},"one_line_summary":"A non-variational algorithm constructs maximally localized Wannier functions by treating discrete adiabatic transport across band degeneracies as part of solving the projected position operator eigenvalues, yielding linear phase overlaps and fixed-point extraction of centers.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Maximally localized Wannier functions can be constructed deterministically by following discrete adiabatic transport across band degeneracies instead of minimizing a spread functional.","strongest_claim":"In this transport-aligned gauge, the Bloch overlaps exhibit an approximately linear phase dependence, allowing the Wannier centers to be extracted via deterministic fixed-point iterations and self-consistent updates rather than spread-functional minimization.","weakest_assumption":"The assumption that discrete adiabatic transport across band degeneracies emerges naturally and produces approximately linear phase dependence in the Bloch overlaps for general systems, without post-hoc adjustments."}},"verdict_id":"7cd1b6c9-a0ba-45df-b266-9fd69bea09ef"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a08fb599c30af6207a50d533c5c7a70e85eb3149b5c145d6f96555712c08fc88","target":"record","created_at":"2026-05-17T23:39:07Z","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":"310702de3bdff596954ac68ea9d69a8bd191172456d46fa68f7e14dd934a3ca7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2026-05-14T05:58:36Z","title_canon_sha256":"c2971728da4ee9e5c79cf1f22cdd2df4ba4399dee49d1a2a88e6c858ac702197"},"schema_version":"1.0","source":{"id":"2605.14414","kind":"arxiv","version":1}},"canonical_sha256":"b8b53b9fe80aa84e284c74b87e3457f0b162cadf6b66e032983bd8c26804c743","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8b53b9fe80aa84e284c74b87e3457f0b162cadf6b66e032983bd8c26804c743","first_computed_at":"2026-05-17T23:39:07.327628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:07.327628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JHvF39WG1/pS/M4/HBD5SfTouST8lv8uZFhQxILqgAWxDMeBm7EVZiy7wlbgVATmRRkW2hzCdx90UVjB46xBCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:07.328274Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.14414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a08fb599c30af6207a50d533c5c7a70e85eb3149b5c145d6f96555712c08fc88","sha256:8d59dd012ca1e00a76b8ec729a2365886c4e369467c38f4fe68a7072a78f1530"],"state_sha256":"9e8c3b845f57a065ce7c0d610f294a766032b3226afd0d2e4b751389c11ac23b"}