We define a new scalar invariant on the moduli space of one-parameter families of elliptic curves, measuring the deviation between the score-squared Fisher-Rao metric and the Weil-Petersson metric. For a family with real period w (t), the conformity gradient is D (t) = (w²) '' (t) / w (t) ². We prove D (t) = 0 for all t if and only if w (t) ² is affine in t, which is generically false for non-isotrivial families. Numerical verification on y² = x³ + tx + 1 confirms D is nonzero with |D|/|Y| ~ 95, where Y is the Yukawa coupling. Applications to cryptographic curve health verification, numerical period stability, and natural gradient correction on moduli spaces are discussed. Integration with a multi-engine field-native algebraic verification pipeline is described.
Nicholas Daniel Maino (Sun,) studied this question.