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    "title": "Filling constraints extend to interacting spin-orbit coupled insulators",
    "summary": "Watanabe, Po, Vishwanath and Zaletel derived electron-filling constraints for symmetry-preserving, gapped, short-range-entangled insulators while allowing spin-orbit coupling and charge fluctuations. A Schmidt-state argument uses charge conservation and time reversal rather than conserved spin. A second approach places the system on suitable compact flat geometries to strengthen the constraints. Together these methods give necessary filling conditions for all230three-dimensional space groups, with stronger restrictions for non-symmorphic groups.",
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        "description": "The electrons carry Kramers time reversal, with charge and the specified crystal symmetries preserved. The compact-geometry argument uses the principle that a short-range-entangled phase has a unique ground state on sufficiently large, locally identical flat geometries, with consistent spin or Pin boundary identifications. The paper establishes sharp bounds for most groups but leaves ten groups with an unresolved interacting-versus-band-insulator gap. Constraints for fixed localized spins cannot automatically be transferred to mobile electrons, and proposed material applications assume exact clean-system symmetries.",
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      "statement": "# Filling constraints extend to interacting spin-orbit coupled insulators\n\nWatanabe, Po, Vishwanath and Zaletel derived electron-filling constraints for symmetry-preserving, gapped, short-range-entangled insulators while allowing spin-orbit coupling and charge fluctuations. A Schmidt-state argument uses charge conservation and time reversal rather than conserved spin. A second approach places the system on suitable compact flat geometries to strengthen the constraints. Together these methods give necessary filling conditions for all230three-dimensional space groups, with stronger restrictions for non-symmorphic groups.\n\n## Scientific scope\n\nThe electrons carry Kramers time reversal, with charge and the specified crystal symmetries preserved. The compact-geometry argument uses the principle that a short-range-entangled phase has a unique ground state on sufficiently large, locally identical flat geometries, with consistent spin or Pin boundary identifications. The paper establishes sharp bounds for most groups but leaves ten groups with an unresolved interacting-versus-band-insulator gap. Constraints for fixed localized spins cannot automatically be transferred to mobile electrons, and proposed material applications assume exact clean-system symmetries.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nHaruki Watanabe; Hoi Chun Po; Ashvin Vishwanath; Michael P. Zaletel\n\nThese are the listed authors of the cited contribution sources. Paper authorship does not quantify individual effort. An incomplete list is explicitly marked; same names are not automatically merged.\n\n\n\n## Original sources\n\n- [Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals (arXiv1505.04193v4)](https://arxiv.org/pdf/1505.04193v4)\n",
      "summary": "Watanabe, Po, Vishwanath and Zaletel derived electron-filling constraints for symmetry-preserving, gapped, short-range-entangled insulators while allowing spin-orbit coupling and charge fluctuations. A Schmidt-state argument uses charge conservation and time reversal rather than conserved spin. A second approach places the system on suitable compact flat geometries to strengthen the constraints. Together these methods give necessary filling conditions for all230three-dimensional space groups, with stronger restrictions for non-symmorphic groups.",
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    "title": "Filling constraints extend to interacting spin-orbit coupled insulators",
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    "evidence_summary": "The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. The electrons carry Kramers time reversal, with charge and the specified crystal symmetries preserved. The compact-geometry argument uses the principle that a short-range-entangled phase has a unique ground state on sufficiently large, locally identical flat geometries, with consistent spin or Pin boundary identifications. The paper establishes sharp bounds for most groups but leaves ten groups with an unresolved interacting-versus-band-insulator gap. Constraints for fixed localized spins cannot automatically be transferred to mobile electrons, and proposed material applications assume exact clean-system symmetries.",
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