Provenance and mathematical contract
3.1 Source provenance and attribution
OpenAI is credited for the underlying Lean Yang–Mills construction. The mathematical source used here is the project’s expanded natural-language extraction, prepared with AI assistance: Wilson Yang–Mills Construction: Mathematical Translation [2]. Its complete text is reproduced unchanged in this release as sources/Full_pre_source_translation.md. The 15,788-line source is numbered using universal-newline counting; the package manifest records its full hash. No model, repository, version or generation-date identifier is assigned where the supplied materials do not establish one.
Jeremy Rodgers originated Shadow Theory, the source–readout architecture and the Source Lift protocol, and directed this research using those methods and examples. He is the author of the reconstruction and its mathematical presentation. AI assisted in developing and checking the realization, preparing the exposition and performing the recorded computational checks. The source–readout definitions and proofs needed for this application are contained in this paper.
3.2 Mathematical contract
The physical group and faithful representation, lattice dimension, Wilson law, preparation and analytic conditions are the inputs to the realized sector. The public conclusion is recovered with its original hypotheses, witnesses and order of limits: the full mesh limit at each suitable fixed period precedes the permitted refined volume limit. Native admission and physical realization remain distinct layers, as developed in Section 2.1.
The derivations are retained with their original equation tags. The explicit formula amendments, typography clarifications and local recovery corrections are documented with their supporting calculations in Section I.1. The preserved source remains unchanged. The verification record in Section J distinguishes general recovery proofs, finite computational checks and the scope of the supplied Yang–Mills construction.
Source: Shadow Theory and the Wilson Yang–Mills Construction: A Source–Readout Reconstruction. Both papers belong to one Zenodo record. No external funding.