Stellar Stability Vector Space: Stability Gates, Homeostatic Windows, and Time-Weighted Ripeness in Kepler–Gaia Dwarfs

Stellar stability is typically characterized by instantaneous structural parameters, while age is treated as an external attribute. This work tests whether a class-conditioned stability space can be operationalized such that bounded basin membership and extremal subsets couple to residence time. A Kepler–Gaia dwarf sample is constructed and a temperature-binned stability gate is identified in log10 Prot using a two-component Gaussian mixture model. Within the gated sample, a bounded homeostatic window is defined in a scalar potential Φ⋆. Gyro ages are obtained for 6447/7366 post-gate stars (87.5% coverage), spanning 1.51–13.77 Gyr (median 5.10 Gyr). In the pooled sample, window members are older than non-members with Δ˜t = +0.316 Gyr (Kolmogorov–Smirnov p = 8.24 × 10−59). Per-bin time-weighted ripeness tails isolate older subsets in the 4000–5200 K and 5200–6000 K regimes. A residualized permutation null that removes temperature-bin geometry yields an empirical p ≃ 0.002, supporting within-bin time coupling beyond bin composition. A scaling variance tests was used to evaluate whether the stability coordinate exhibits non-random organisation that persists under progressive coarse-graining.