Self-contained formula index for Dark Geometry, an independent framework exploring how far a single relation (the Hertault axiom, e^{dσ} = I) can be developed from one input, d = 3. Collects the derivations, the constrained-mode interpretation, particle and cosmological expressions, and falsifiable predictions. Includes companion-article sources.

A geometric and computational study of Koide’s charged-lepton mass relation, separating preservation from dynamical selection. Includes SM running checks and numerical tests of minimal S3-invariant gradient flows on the root-mass sphere.