The contribution and the reading path

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Recover the Wilson Yang–Mills construction through explicit source records, compatible operations and proved readout interfaces. The chapters retain the complete mathematical development, with the original notation visible in the vector expressions and its extracted text available for search.

Abstract

We construct a source–readout realization of the Wilson Yang–Mills construction within Jeremy Rodgers’s Shadow Theory. The framework separates an admitted native support, its literal preparation, the realized physical histories and the readouts that recover configurations, effective quantities, field labels and operator correlations. Reflective mathematics makes the relation between these layers explicit: reverse sections establish coverage, fibres identify redundant or discarded information, operation identities establish compatibility, and residuals quantify departures from exact recovery. The paper proves normalized finite-measure recovery and classifies the frame fibres; transports activity domains and budgets; recovers the stationary vertical discrepancy from its residual; and establishes the compatibility of coefficient readers, physical equation quotients, Hilbert-space reconstruction, phases and operator products. These interfaces are developed through the complete quadratic, nonlinear, marked-integration, calibration, continuum and stress calculations. One compatible Wilson family carries full fixed-period mesh limits followed by the permitted refined volume limit. Its selected centered trace has the asymptotic log 3 dim g, with the stated finite mass-shell and Maxwell comparison exclusions. No positive mass gap is asserted. OpenAI’s underlying Lean construction is presented through the supplied expanded mathematical translation. The contribution here is the explicit source–readout construction and its recovery proofs, with all substantive Yang–Mills derivations retained. The given gauge group, faithful representation, four-dimensional Wilson law and analytic hypotheses remain the physical inputs to this conditional realization.

Authorship. Jeremy Rodgers originated Shadow Theory, the source–readout architecture and the Source Lift protocol, and directed this research using those methods and examples. AI assisted in carrying out the work.

Release. This paper and its standalone mathematical companion form one Zenodo release under the DOI above.

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Funding. No external funding.