Geometric Fixed-Point Existence and Spectral Rigidity in the Coupled Dirac–Lambda System
Authors: Jeremy, Rodgers
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Role: Geometric Fixed-Point Existence and Spectral Rigidity in the Coupled Dirac–Lambda System
Supported Problems
The Yukawa Gap in the Spectral Action
The Chamseddine–Connes spectral action determines the bosonic Standard Model sector but leaves the Yukawa sector unconstrained. In the Dirac–Λ framework, this gap is closed by the Dirichlet-to-Neumann Osterwalder–Schrader boundary operator K_OS together with the capacity inequality, which supplies the missing boundary-channel constraint on the internal Dirac operator and its admissible couplings.
Why Is the Fine-Structure Constant 1/137?
Within the Dirac–Λ framework, the Standard Model parameter set is reduced to a single geometric modulus, but Tier-1 cannot determine that modulus internally. The Everything Equation resolves the remaining ambiguity at Tier-0: the one-parameter family collapses to a unique fixed point, yielding the fine-structure constant as a law-level output rather than a free physical input.