From Geometric Realization to Physical Admissibility: Infinitesimal Realizability, Constraint-Preserving Dynamics, and Observable Handoff

This paper develops the passage from constructively induced geometry to a physically admissible and operationally distinguishable realization within the OFT/VGM research programme. Starting from a pullback metric, it formulates an ordered set of conditions for admissible variations, preservation of the induced-metric relation, projected dynamics, dimensional closure, causal propagation, stability, and observable response. The analysis derives the linearized induction operator and its tangential–normal decomposition. It distinguishes the constructive Euler–Lagrange equation from an unrestricted metric equation and identifies an adjoint-kernel criterion for their equivalence on a declared sector. A composite transfer operator connects admissible constructive initial variations to reduced evolution and detector readouts; its kernel defines the linearly silent sector. A normal-deformation example on a de Sitter hyperboloid supplies an exact induced metric and a controlled linear operational response. In the stated test-apparatus approximation, a minimally coupled scalar probe has a retarded response to the metric perturbation, while a calibrated massive clock supplies a proper-time readout. The analysis states the local Lorentzian domain, kinetic-sign conditions, hyperbolicity requirements, and finite-time energy control. A response channel can close in a regular Minkowski limit without metric degeneracy. The framework separates geometric, dynamical, operational, and empirical conditions. The worked example establishes a theoretical handoff under its declared assumptions; empirical comparison remains a separate step. This deposit contains the English manuscript, revised version 1.1 dated 7 November 2026, its XeLaTeX source, and the accompanying Peaceful Civilian Use Licence. Version 1.1 corrects the missing addition sign between the kinetic and mass terms in the scalar probe action and clarifies the admissible variation sector and cone-matching sign convention. Series: OFT/VGM Research Program — Paper XXII.DOI: https://doi.org/10.5281/zenodo.24036520