Read the construction in full
Follow the full finite-to-continuum Wilson construction in its conventional mathematical language. The chapters retain the complete mathematical development, with the original notation visible in the vector expressions and its extracted text available for search.
Abstract
This paper gives a self-contained natural-language exposition of the expanded Wilson Yang– Mills Construction: Mathematical Translation. For a given closed matrix subgroup of
) with nonabelian simple real Lie algebra, the construction supplies one calibrated four-dimensional Wilson family, full fixed-period mesh limits and a subsequential outer volume limit, a common hierarchy of local fields and phases, and a selected local Wightman theory with Poincaré covariance, forward-cone spectrum and a unique vacuum. We give the finite quadratic kernels and nonlinear geometry, marked integration, coupling reset and shooting histories, physical detector and equation quotient, phase and boundary reconstruction, separated and nested operator products, contact extensions, and the finite-to-continuum stress and trace calculation with their hypotheses and derivations. The centered trace obeys
Searchable transcription
lim r↓0 r8 log2(1/r)GΘ(r) = 3 dimR g π4 > 0.
The associated exclusions retain their stated finite mass-shell and Maxwell comparison hypotheses. No positive mass gap is asserted. Two formula amendments are derived and documented with the conventions used throughout the argument.
Attribution. The underlying Yang–Mills Lean work is credited to OpenAI. Jeremy Rodgers prepared this mathematical exposition with AI assistance.
Searchable transcription
Funding. No external funding.
Source: A Wilson Yang–Mills Construction: A Natural-Language Mathematical Exposition. Both papers belong to one Zenodo record. No external funding.