Variational Selection of Local Metric Stars and Scalar-Sector Robustness in Quantum Informational Geometrodynamics

The scalar geometric sector of Quantum Informational Geometrodynamics (QI-G) requires a controlled passage from local quantum-informational data to an effective curvature observable. Recent work in the QI-G program fixed a canonical angular informational curvature, introduced dual nodal weights, and clarified the coarse-grained scalar estimator. A residual ambiguity nevertheless remains: the local metric-star selection rule, which maps candidate metric triangles incident on a node to the selected local star used in the angular deficit and dual-volume normalization. This paper formulates that ambiguity as a local variational problem. It defines an admissible-star space, introduces an objective functional balancing angular anisotropy, geometric degeneracy, combinatorial redundancy, and parsimony, and specifies geometric and combinatorial control rules against which the variational prescription can be compared. It further introduces star distances and scalar-sensitivity observables that quantify the dependence of the emergent scalar curvature on the local rule. Two baseline results are isolated: existence of a local minimizer and a conditional local stability estimate for the nodal scalar curvature away from degenerate dual weights. The work is methodological rather than final: it does not claim a tensorial reconstruction, a Bianchi identity, or a derivation of Einstein dynamics. Its contribution is to turn a previously implicit triangulation ambiguity in the QI-G scalar sector into a mathematically explicit and numerically testable problem.