{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NW66XPHUBRZLHUROMUKAXAE2I2","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":"3c5223af47c1af2bbc66b5cfc97cf37a47bc0863f10703fd8466bce86a04c6f1","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-02-12T20:24:02Z","title_canon_sha256":"43e65abd85f727f9d4f016944814624689fbdc96cf6a6187349a90553e2344e3"},"schema_version":"1.0","source":{"id":"2602.12382","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.12382","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"arxiv_version","alias_value":"2602.12382v2","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.12382","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"pith_short_12","alias_value":"NW66XPHUBRZL","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"NW66XPHUBRZLHURO","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"NW66XPHU","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:48109a35183d2916aa2dc85a23ea9491902627763928a783e765009108e07d71","target":"graph","created_at":"2026-05-18T02:44:31Z","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":"By exploiting an efficient evaluation of the Hessian-vector product, k-CIAH achieves O(N_k^2 n^3) scaling in both CPU time and memory, matching that of previously reported first-order k-space approaches while improving upon the O(N_k^3 n^3) scaling of Γ-point CIAH... yields an overall computational efficiency approximately 2-3-fold higher than first-order k-space methods and orders of magnitude higher than Γ-point CIAH for localizing 1000-5000 orbitals. The quality of the resulting PMWFs is further validated by accurate electronic band structures obtained via PMWF-based Wannier interpolation."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the efficient Hessian-vector product evaluation in the k-CIAH extension maintains numerical stability and robust convergence for all tested systems (insulators, semiconductors, metals, surfaces) without hidden costs or post-hoc adjustments that affect the claimed scaling."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"k-CIAH enables efficient second-order optimization of Pipek-Mezey Wannier functions with O(N_k² n³) scaling, yielding 2-3x speedup over first-order k-space methods."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"k-CIAH extends second-order CIAH optimization to k-point Pipek-Mezey Wannier functions while achieving O(N_k² n³) scaling."}],"snapshot_sha256":"35aee3e633c0a753bdce3cff54283019ccb98c3e0c43ccd7b18885aea70a7975"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"94c7d7f621b035fbbc709b268b9900a6ed897eb797e49c0e5d3d94f33ec9ab47"},"paper":{"abstract_excerpt":"We report a $k$-point extension of the second-order co-iterative augmented Hessian (CIAH) algorithm, termed $k$-CIAH, for Pipek-Mezey (PM) localization of Wannier functions (WFs). By exploiting an efficient evaluation of the Hessian-vector product, $k$-CIAH achieves $O(N_k^2 n^3)$ scaling in both CPU time and memory, matching that of previously reported first-order $k$-space approaches while improving upon the $O(N_k^3 n^3)$ scaling of $\\Gamma$-point CIAH, where $N_k$ denotes the number of $k$-points sampling the first Brillouin zone and $n$ characterizes the unit-cell size. Benchmark calculat","authors_text":"Gengzhi Yang, Hong-Zhou Ye","cross_cats":["cond-mat.mtrl-sci"],"headline":"k-CIAH extends second-order CIAH optimization to k-point Pipek-Mezey Wannier functions while achieving O(N_k² n³) scaling.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-02-12T20:24:02Z","title":"Fast Generation of Pipek-Mezey Wannier Functions via the Co-Iterative Augmented Hessian Method"},"references":{"count":34,"internal_anchors":0,"resolved_work":34,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"The special case in which this real-space unitary is constrained to be real-valued is discussed in sec- tion II G","work_id":"1d476f56-8fee-4eea-a0c8-0124e4b4c97d","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"using the second-order co-iterative augmented Hes- sian (CIAH) algorithm. 43 CIAH is a modified trust-region Newton method46 that has been successfully applied to orbital localization in molecules 43,4","work_id":"e2c9356b-dabb-4659-a7ad-ecb4f50e5216","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"(The Hessian diagonals are used to precondition the Davidson update","work_id":"911c0253-c00b-4259-87da-7ff04a1edb73","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"We summarize the working equations be- low. We first define two types of matrix elements of the atomic projection operators, (PTTT A,kkkkkk′)i j = 1 Nk ⟨φ kkki|ˆPTTT A|φ kkk′j⟩ = 1 Nk ∑ µ ∈ A O∗ TTT µ ,","work_id":"35f64ee8-e8a5-41de-8734-c43529694bb3","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"35,38 In section IV, we compare the performance and computational efficiency of k-CIAH- and k-BFGS-based PMWF optimization","work_id":"a1bb785e-2186-4c3d-a10c-17bbddbbad04","year":null}],"snapshot_sha256":"94ea7ea2469ddbd4dfa5b3db9f5bebf0d831007c8cd930daaf4fe2b1af8f7efa"},"source":{"id":"2602.12382","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-16T05:11:33.636827Z","id":"9181938b-e0af-4e8b-a1d4-d01dc8c4b60a","model_set":{"reader":"grok-4.3"},"one_line_summary":"k-CIAH enables efficient second-order optimization of Pipek-Mezey Wannier functions with O(N_k² n³) scaling, yielding 2-3x speedup over first-order k-space methods.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"k-CIAH extends second-order CIAH optimization to k-point Pipek-Mezey Wannier functions while achieving O(N_k² n³) scaling.","strongest_claim":"By exploiting an efficient evaluation of the Hessian-vector product, k-CIAH achieves O(N_k^2 n^3) scaling in both CPU time and memory, matching that of previously reported first-order k-space approaches while improving upon the O(N_k^3 n^3) scaling of Γ-point CIAH... yields an overall computational efficiency approximately 2-3-fold higher than first-order k-space methods and orders of magnitude higher than Γ-point CIAH for localizing 1000-5000 orbitals. The quality of the resulting PMWFs is further validated by accurate electronic band structures obtained via PMWF-based Wannier interpolation.","weakest_assumption":"That the efficient Hessian-vector product evaluation in the k-CIAH extension maintains numerical stability and robust convergence for all tested systems (insulators, semiconductors, metals, surfaces) without hidden costs or post-hoc adjustments that affect the claimed scaling."}},"verdict_id":"9181938b-e0af-4e8b-a1d4-d01dc8c4b60a"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bb00770968f296323947f457a77966512d4eada9ebabb065b8665f0dab8e737b","target":"record","created_at":"2026-05-18T02:44:31Z","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":"3c5223af47c1af2bbc66b5cfc97cf37a47bc0863f10703fd8466bce86a04c6f1","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-02-12T20:24:02Z","title_canon_sha256":"43e65abd85f727f9d4f016944814624689fbdc96cf6a6187349a90553e2344e3"},"schema_version":"1.0","source":{"id":"2602.12382","kind":"arxiv","version":2}},"canonical_sha256":"6dbdebbcf40c72b3d22e65140b809a46a9b320935b425caba1e4b07f18ae9ebf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dbdebbcf40c72b3d22e65140b809a46a9b320935b425caba1e4b07f18ae9ebf","first_computed_at":"2026-05-18T02:44:31.190282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:31.190282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jc5kFlX17UYOMBL5AnX01N7hsqBHXF3RIATZ0XiS75MHx+a+QP5LaTDqp1L0nZb769mE1nb9m3cG9qfAL60JAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:31.190772Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.12382","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb00770968f296323947f457a77966512d4eada9ebabb065b8665f0dab8e737b","sha256:48109a35183d2916aa2dc85a23ea9491902627763928a783e765009108e07d71"],"state_sha256":"5b0df7a5dde767d92aceb31b9c1734bd8d777351ab840c5da507a4229cbb6080"}