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At critical vacancy concentration xc ≈ 12.5%, a percolation transition drives the majority-spin impurity band from flat, localized levels (W < 0.1 eV) to a dispersive 1.5 eV-wide band with 100% spin polarization and a minority-spin gap of 1.0 eV."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the supercell-size dependence (2×2 cells showing antiferromagnetism while 4×4 cells show ferromagnetism) arises solely from the presence or absence of a spanning percolation cluster rather than from finite-size artifacts, boundary conditions, or other details of the underlying electronic-structure calculations."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Geometric percolation of Ti vacancies in 1T-TiS2 monolayers triggers half-metallic ferromagnetism at xc ≈ 12.5%, creating a functional window of 11% < x < 15% with 100% spin-polarized transport."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Percolation of sulfur vacancies at roughly 12.5 percent concentration switches vacancy-doped titanium disulfide from an insulator to a half-metal."}],"snapshot_sha256":"b47a85b2b8da10cbb552eac68211a09767fa2d8671d3613a092006b7bb06c5fb"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T16:59:25.438209Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.01754/integrity.json","findings":[],"snapshot_sha256":"49aae9371967dca19823c811d1d914679e21a239902b27152f70cf9a60e34c45","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Defect engineering of two-dimensional materials routinely produces local magnetic moments, yet itinerant half-metallic\n  ferromagnetism remains elusive -- experiments frequently yield paramagnetic insulators. We resolve this paradox for vacancy-doped\n  monolayer $1T$-\\ptis~by demonstrating that the insulator-to-half-metal transition is governed by universal geometric percolation\n  of the defect network, extending the percolation framework established for three-dimensional diluted magnetic semiconductors into\n  the 2D vacancy-doped regime. 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Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Spintronics: A spin- based electronics vision for the future, Science294","work_id":"68c5794a-07c5-4c0a-b348-c71663608149","year":2001},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"E. C. Ahn, 2d materials for spintronic devices, npj 2D Materials and Applications4(2020)","work_id":"20b1eb81-e6f1-4d0b-b44b-c64a3f40efde","year":2020},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Y. Liu, C. Zeng, J. Zhong, J. Ding, Z. M. Wang, and Z. Liu, Spintronics in two-dimensional materials, Nano- Micro Letters12(2020)","work_id":"1775e3a8-4e57-4146-bbad-14edb8518214","year":2020},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. 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