Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
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These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Finite-dimensional gapped free Hamiltonians and stable equivalence
Definition
A finite-dimensional free-fermion Hamiltonian is a self-adjoint matrix on a finite-dimensional complex Hilbert space. It is gapped at zero if 0 is not in its spectrum. A symmetry class is specified by named unitary and antiunitary operators and exact commutation, anticommutation and square relations with H. Stable equivalence means gap-preserving homotopy after direct sum with fixed reference trivial bands; phases are differences of stabilized systems, not absolute modules.
Class A has no additional antiunitary constraint. A symmetry is unitary or antiunitary and its relation is recorded as S H S^{-1}=σH, σ∈{+1,−1}; any additional square relation is part of the declared model data.
Used by
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.
Sources
- Alexei Kitaev, Periodic table for topological insulators and superconductors (2009) (standard reference, not scraped)
- M. F. Atiyah, R. Bott, and A. Shapiro, Clifford Modules, Topology 3, Supplement 1 (1964) (standard reference, not scraped)
- M. F. Atiyah, K-Theory (lectures, notes by D. W. Anderson, 1967), with K-Theory and Reality reprint (standard reference, not scraped)