A Wilson Yang–Mills Construction: A Natural-Language Mathematical Exposition

Name: A Wilson Yang–Mills Construction: A Natural-Language Mathematical Exposition
Author: Jeremy Rodgers

Jeremy Rodgers

doi:10.5281/zenodo.24173681

Source Lift / Complete reading edition

The Wilson construction, developed in full.

Follow the mathematical construction from finite Wilson measures through calibrated continuum limits, physical fields and Wightman reconstruction to operator products and the centered trace. A standalone companion to the Shadow Theory reconstruction.

Jeremy Rodgers · Independent Researcher · 2026-11-12
Shared publication DOI: 10.5281/zenodo.24173681

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A Wilson Yang–Mills Construction: A Natural-Language Mathematical Exposition

Follow the mathematical construction from finite Wilson measures through calibrated continuum limits, physical fields and Wightman reconstruction to operator products and the centered trace. A standalone companion to the Shadow Theory reconstruction.

This companion follows the Wilson construction on its own terms: finite group-valued configurations, controlled integration, calibrated scale histories and one common continuum hierarchy. It retains the derivations and their hypotheses throughout.

OpenAI is credited for the underlying Lean work. Jeremy Rodgers prepared the mathematical exposition with AI assistance. The flagship reconstruction develops his Shadow Theory source–readout architecture across the same construction.

The gauge group, faithful representation, four-dimensional Wilson law and stated analytic hypotheses are inputs. The full fixed-period mesh limit precedes the permitted outer volume extraction. The centered trace and comparison exclusions retain their own hypotheses; a positive mass gap is not a conclusion of these editions.

The Einstein reconstruction develops the same discipline in classical gravity →

The argument in full

Source: A Wilson Yang–Mills Construction: A Natural-Language Mathematical Exposition. Both papers belong to one Zenodo record. No external funding.

A Wilson Yang–Mills Construction: A Natural-Language Mathematical Exposition

The argument in full

The contribution and the reading path

Introduction: the construction and its dependencies

Statement of the public conclusion

Notation and analytic conventions

Finite-lattice positivity

Quadratic kernels and their ultraviolet limit

Quadratic kernels and their ultraviolet limit · Part 2

Quadratic kernels and their ultraviolet limit · Part 3

Quadratic kernels and their ultraviolet limit · Part 4

Local nonlinear geometry and estimates

Local nonlinear geometry and estimates · Part 2

Local nonlinear geometry and estimates · Part 3

Local nonlinear geometry and estimates · Part 4

Local nonlinear geometry and estimates · Part 5

Local nonlinear geometry and estimates · Part 6

Local nonlinear geometry and estimates · Part 7

Local nonlinear geometry and estimates · Part 8

Local nonlinear geometry and estimates · Part 9

Local nonlinear geometry and estimates · Part 10

Marked integration and the coupling reset

Marked integration and the coupling reset · Part 2

Marked integration and the coupling reset · Part 3

Marked integration and the coupling reset · Part 4

Marked integration and the coupling reset · Part 5

Convergence of the interacting scale histories

Convergence of the interacting scale histories · Part 2

Convergence of the interacting scale histories · Part 3

Convergence of the interacting scale histories · Part 4

Convergence of the interacting scale histories · Part 5

Convergence of the interacting scale histories · Part 6

Convergence of the interacting scale histories · Part 7

Convergence of the interacting scale histories · Part 8

Convergence of the interacting scale histories · Part 9

Convergence of the interacting scale histories · Part 10

Convergence of the interacting scale histories · Part 11

Convergence of the interacting scale histories · Part 12

Physical labels and their detection

Physical labels and their detection · Part 2

Physical labels and their detection · Part 3

Free shell charges and separation of the Ward kernel

Free shell charges and separation of the Ward kernel · Part 2

Free shell charges and separation of the Ward kernel · Part 3

The common continuum hierarchy

The common continuum hierarchy · Part 2

Phase decomposition and Wightman reconstruction

Phase decomposition and Wightman reconstruction · Part 2

Phase decomposition and Wightman reconstruction · Part 3

Phase decomposition and Wightman reconstruction · Part 4

Phase decomposition and Wightman reconstruction · Part 5

Phase decomposition and Wightman reconstruction · Part 6

Phase decomposition and Wightman reconstruction · Part 7

Separated and nested operator products

Separated and nested operator products · Part 2

Separated and nested operator products · Part 3

Extension across collision sets

Extension across collision sets · Part 2

The Gaussian short-distance comparison

The Gaussian short-distance comparison · Part 2

The centered trace and its non-freeness test

The centered trace and its non-freeness test · Part 2

The centered trace and its non-freeness test · Part 3

The centered trace and its non-freeness test · Part 4

The centered trace and its non-freeness test · Part 5

The centered trace and its non-freeness test · Part 6

The centered trace and its non-freeness test · Part 7

The centered trace and its non-freeness test · Part 8

The centered trace and its non-freeness test · Part 9

Completion of the proof

Conclusion

Editorial amendments and conventions

Source, attribution and reproducibility

References