Environment as a Modulator of Homeostatic Potential: Galaxy Stability Gates Across Density and Group Scale

Galaxy evolution models usually treat environment as a driver of quenching and morphological transformation, but less often as a regulator of how systems retain or erase long-term memory of past conditions. This paper uses the homeostatic potential framework $\hat{\phi}$ to ask a focused question: once a galaxy has crossed the structural ``stability gate'', how much additional leverage does environment still have on its chemical memory?Using SDSS DR8 and GAMA DR4 as low-redshift benchmarks, and the EAGLE RefL0100N1504 simulation as a controlled comparison, galaxies are split into structurally ``infant'' and ``adult'' regimes by the stability proxy $\hat{S}$. For each regime, the dispersion of the metallicity-based memory proxy $\hat{M}$ is measured as a function of local density and group-scale environment (k-nearest-neighbour density, projected surface density, and host-group halo mass). The same diagnostics are then applied to the TNG suite to test whether the infant/adult environmental contrast is a robust feature of hydrodynamical models with different feedback prescriptions. A MaNGA pilot sample provides an independent sanity check that $\hat{S}$ behaves as a structural maturity indicator rather than a data-quality or environment artefact. In SDSS, metallicity scatter rises with local density for structurally infant galaxies, but remains lower and only weakly environment-dependent for adults at fixed mass and stability. In GAMA, the scatter is nearly flat across four decades in projected density once $\hat{S}$ is fixed, with only a mild broadening in the highest-density adult bin. In EAGLE, the dependence of scatter on host halo mass is similarly weak at fixed structural state. TNG runs show very weak correlations between the homeostatic components and local density once mass selection is imposed, indicating that the stability gate is not simply a field--cluster split in disguise. The MaNGA pilot confirms that the entropy-like component $\hat{S}$ correlates strongly with galaxy size but only weakly with S/N, behaving as a structural maturity coordinate. Together, these results support a simple picture: environment acts as a strong modulator of homeostatic potential before the stability gate is crossed, but mainly tunes residual variance once galaxies have internalised their history into a stable configuration. Environment is a modulator of memory, not its primary container.