Attribution of the source and mathematical background
Jeremy Rodgers originated Shadow Theory, the source–readout architecture and the Source Lift protocol, and directed this research. The framework’s role here is the explicit realization and recovery analysis developed throughout the paper. OpenAI is credited for the underlying Lean Yang–Mills construction, represented in this edition by the expanded mathematical translation [2]. AI assisted in carrying out the research and preparing the manuscript. The earlier Einstein reconstruction [4] is a methodological and expository example; the present Yang–Mills derivations are supplied locally.
Wilson’s lattice gauge formulation is credited to Wilson [5], compact-group invariant measure to Haar [6], and the pairing formula to Wick [7]. The Euclidean reconstruction framework and reflection positivity are credited to Osterwalder and Schrader [11, 12], with the lattice-gauge setting of [13] and the chessboard estimates of [14]. The positive-functional construction is credited to Gelfand, Naimark and Segal [8, 9], and the character-algebra approximation theorem to Stone [10]. Renormalization and cluster-expansion background is provided by [17, 18, 19, 15], the axiomatic field framework by [16], and the one-loop coefficient by [20, 21]. The precise hypotheses, parameter orders, domains and readout definitions used in this application are stated in the corresponding derivations.
Funding and availability. No external funding. This flagship paper and the standalone companion A Wilson Yang–Mills Construction: A Natural-Language Mathematical Exposition form one Zenodo release under DOI 10.5281/zenodo.24173681. The release contains both editable source trees, the expanded mathematical input and the coverage, amendment and verification records.
Source: Shadow Theory and the Wilson Yang–Mills Construction: A Source–Readout Reconstruction. Both papers belong to one Zenodo record. No external funding.