deltaVar
plain-language theorem explainer
deltaVar supplies the identity map on real scalars as placeholder notation for variations of state variables inside the ILG action. Researchers deriving the functional derivative of S with respect to field components would cite it when writing symbolic variations. The definition is a direct one-line identity assignment with no reduction steps or lemmas.
Claim. For any real scalar variable $x$, the variation satisfies $δx = x$.
background
The Relativity.ILG.Action module re-exports geometry and field types to support the ILG action. The action itself is defined upstream as $S[g,ψ;C_{lag},α] := S_{EH}[g] + ΨAction[g,ψ,C_{lag},α]$, reducing exactly to the Einstein-Hilbert term when the lag and alpha parameters are zero. The upstream structure for records meta-realization axioms while the and theorem supplies an explicit log-derivative bound on the circle.
proof idea
The declaration is a one-line identity wrapper that returns the input unchanged. No lemmas from the depends_on list are invoked; the body is simply the equality deltaVar x = x.
why it matters
The definition supplies the minimal scaffolding needed to write functional variations inside the ILG action S. It therefore participates in the GR-limit reduction stated in the S doc-comment and aligns with the Recognition Science program of deriving dynamics from the forcing chain (T0-T8) and the Recognition Composition Law. No downstream theorems yet reference it, so its role remains preparatory notation.
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