The Cost-Asymmetric Wilson Action on G■
Abstract
We construct the cost-asymmetric Wilson gauge action on the Minimal Discrete Épure G■, the dynamical object on which the programme's scale-dependent quantities rest. From link variables and a cost-weighted plaquette we obtain an action whose continuum limit is anisotropic Yang–Mills with a dimensionless coupling in d=4. A central finding: the anisotropy ξ=2 is not a free parameter but is fixed by the Lorentzian saddle x²−4y², so the action inherits the causal vertex Θ■ intrinsically. The action satisfies four structural constraints (scale invariance, β-sign reproducing the Standard-Model pattern, arrow-of-time protection, no over-fitting). We fix the bare coupling by coherence with the deployment constants: at the central-equilibrium dimension (the central binomial coefficient C(8,4)=70 of the 8-bit weight enumerator), g₀=c₉=35√5/256, giving the base 1/α₉≈134.457. Finally we prove that the reference scale μ_ref is irreducible: neither a gravitational nor a cosmological global condition derives it — both yield ratios and leave one absolute unit posed, as in any physical theory. The fine value 1/α and the Dyson resummation form remain conditional on this posed unit. Verified numerically.
Fields of Study & Subjects
Cosmology and Gravitation Theories
Noncommutative and Quantum Gravity Theories
Quantum and Classical Electrodynamics
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 22 June 2026
- Language
- EN
- Document type
- Preprint