{"paper":{"title":"Topological Classification of Insulators: III. Non-interacting Spectrally-Gapped Systems in All Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The space of gapped Hamiltonians has path-connected components exactly matching the strong topological invariants in all dimensions and symmetry classes.","cross_cats":["math.FA","math.MP","math.OA"],"primary_cat":"math-ph","authors_text":"Jacob Shapiro, Jui-Hui Chung","submitted_at":"2026-02-13T01:30:28Z","abstract_excerpt":"We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so that the so-called strong topological invariants become \\emph{complete} invariants yielding the Kitaev periodic table, but now derived as the set of path-connected components of the space of Hamiltonians, rather than as $K$-theory groups. We thus confirm the conjecture (phrased e.g. in \\cite{KatsuraKoma2018}) regarding a one-to-one correspondence between to"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The strong topological invariants become complete invariants yielding the Kitaev periodic table, now derived as the set of path-connected components of the space of Hamiltonians.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The chosen notions of locality and bulk non-triviality on the space of Hamiltonians are the natural ones that make the strong invariants complete; if a different notion of locality is required by physics, the classification may change.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Strong topological invariants are complete invariants for the path-connected components of the space of spectrally gapped non-interacting Hamiltonians across all dimensions and Altland-Zirnbauer classes.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The space of gapped Hamiltonians has path-connected components exactly matching the strong topological invariants in all dimensions and symmetry classes.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4430b92d8d463c4190d34c8dd73b9b8bc1628a01ab81903b2ac6929c731b2df0"},"source":{"id":"2602.12512","kind":"arxiv","version":3},"verdict":{"id":"ab9321ab-53ba-435b-89b4-a2213cab5f94","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T22:58:51.138986Z","strongest_claim":"The strong topological invariants become complete invariants yielding the Kitaev periodic table, now derived as the set of path-connected components of the space of Hamiltonians.","one_line_summary":"Strong topological invariants are complete invariants for the path-connected components of the space of spectrally gapped non-interacting Hamiltonians across all dimensions and Altland-Zirnbauer classes.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The chosen notions of locality and bulk non-triviality on the space of Hamiltonians are the natural ones that make the strong invariants complete; if a different notion of locality is required by physics, the classification may change.","pith_extraction_headline":"The space of gapped Hamiltonians has path-connected components exactly matching the strong topological invariants in all dimensions and symmetry classes."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.12512/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"c80856c2346b91913839f82fd38a320330bf225d2346214fbe99f172183e4d9e"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}