Repair as Local Optimization in Constraint Geometry

Repair is local optimization under irreducible geometric constraint. This paper introduces repair as a first-class process in constraint geometry, proving via a Repair–Geometry Compatibility lemma that any repair operation traversing a non-integrable feasibility map incurs a strictly positive geometric overhead bounded below by the Hodge spectral gap. Two empirically distinct modes emerge—persistent local optimization (aging-like decay) and net-positive structural repair (sharp threshold)—captured by a single gating function whose sharpness classifies system regimes. The repair-augmented RG system couples maintenance load, effective dimension, and repair actuation with explicit parameter dependence. Empirical validation from 7,515 Gaia DR3 white dwarfs reveals a sharp compactness-controlled threshold at R/R_S ≈ 10³ (14.5σ, Wilcoxon p = 4.3 × 10⁻⁸⁴), with a monotonic gradient from +345 Myr median excess in the ultra-massive 500–700 bin (using relativistic ONe-core tracks) through +108 Myr at 700–900 to null above R/R_S ≈ 1300, yielding ξ_crit = 0.46 and total overhead c = 0.292.