Research Topic Index
Information Theory
Operator K-Theory
Lempel-Ziv Complexity
Atiyah-Singer Index
Mathematical Physics
Gauge Theory Formulas
Arithmetic Geometry
Chern Characters
Fiber Bundles
Curvature Forms
Spectral Theory
Exterior Calculus
Traces of Operators
Wedge Products
Formalized Research
Index Theorem
Global Analysis
Geometric Topology
Differential Operators
Moduli Spaces
Gauge Theory
Yang-Mills Theory
Cohomology
Torsion Classes
Formal Notes & Research Logic
A repository for structured proofs, derivations of differential operators, and the formalization of Gauge Theory invariants.
Operator Theory & Index Expressions
Formalization of the analytic index vs. topological index. We are documenting the Chern characters of the symbol and the integration of Todd classes over the manifold's tangent bundle. Current focus: Zeta-function regularization for traces of elliptic differential operators.
Gauge Theory & Curvature Form Algebra
Organizational matrix for curvature form F = dA + A ∧ A. Examining the Bianchi identities and the second Chern class as a topological invariant. These notes formalize the wedge product operations required for higher-dimensional field stability proofs.
Information Theory Arches: Lempel-Ziv
Rigorous proof structures for universal compression algorithms. Mapping the combinatorial parsing logic of sequence complexity to symbolic dynamics. Establishing entropy rate bounds through the lens of algorithmic information theory.