The Coupled Dirac–Λ Dynamical System: Unified Operator Equations for a Capacity-Constrained Spectral Action Framework
Authors: Jeremy, Rodgers
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Role: The Coupled Dirac–Λ Dynamical System: Unified Operator Equations for a Capacity-Constrained Spectral Action Framework
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.
Quantum Gravity and Spacetime Structure
Lawful emergence of spacetime dimensionality, null structure, and causal geometry via recursive gauge collapse and stability selection.
Cosmological Constant Problem
Vacuum energy control via the canonical Λ-field and universal spectral budget constraints.
Quantum Measurement and the Origin of the Born Rule
Definite outcomes and |ψ|² probability weights emerge from closure-stable admissibility constraints. Measurement is not an external postulate but a structural consequence of operator-theoretic stability, probability rigidity, and decision-level closure.