trureturingGitHub MATHEMATICAL ATLAS

SpectralTopology / CONCEPT

The mass gap of the four Hofstadter bands

The third and fourth Hofstadter bands have a uniform gap at Fermi energy two for every nonzero mass in the interval from minus two to two.

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DIRECT PREREQUISITES4
DIRECT CONSEQUENCES0
PROOF DEPTH8
DOCUMENT LINKS0
THEOREM

Hermiticity for all real parameters

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Type-A SLn Unipotent CommutatorsType-A SLn UnipotentCommutatorsScalar perturbation of sorted singular valuesScalar perturbation of sortedsingular valuesPoint-Gap Exact InertiaPoint-Gap Exact InertiaInvertible Hermitian Inertia PullbackInvertible Hermitian InertiaPullbackThe mass gap of the four Hofstadter bandsThe mass gap of the fourHofstadter bands
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Lean sourceResearch workspace
Status
Closed
Depth
8
Layer
D5/S3
Domain
SpectralTopology
Node ID
D5/S3/SpectralTopology/HalfFluxHofstadterMassGap
Repository path
D5/S3/SpectralTopology/HalfFluxHofstadterMassGap.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.