Resolved Homeostasis: Mapping Stability, Memory, and Regeneration with MaNGA Spaxels

Galaxy evolution is often modelled in terms of global scaling relations and single-fibre measurements, but the physical regulation of structure and star formation takes place in resolved patches inside galaxies. The homeostatic potential framework $\hat{\phi}=(\hat{H},\hat{S},\hat{M},\hat{R})$ treats galaxies as systems that can cross a structural ``stability gate'', switching from a dynamically infant regime where recent energy injection erases chemical memory to an adult regime where depth, memory and regeneration are tightly coupled. Previous work established this picture at the galaxy level and showed that the environment acts mainly as a modulator of the memory budget once the gate is crossed. Here MaNGA galaxies are used as resolved laboratories for this framework.Using a sample of $N_{\rm gal}=50$ integral-field units and $N_{\rm spax}\simeq 3.8\times 10^{4}$ spaxels, simple spaxel-level proxies are constructed for the homeostatic components and normalised as robust $z$-scores. Stacked in units of the half-light radius, the MaNGA spaxels show a clean radial gradient: inner regions ($r\lesssim 0.5\,R_{\rm half}$) lie in a high-stability, high-memory, high-regeneration state, while outer regions ($r\gtrsim 2\,R_{\rm half}$) are systematically depleted in all four components. Across all radii the regeneration proxy remains strongly correlated with both energy and memory, but its coupling to the stability coordinate weakens in the outskirts, consistent with tightly bound central ``adult'' engines surrounded by more weakly regulated, infant-like discs.Variance–energy and variance–memory scalings measured in the resolved MaNGA field show that regions with stronger local chemical memory also host larger structural excursions, in contrast to galaxy-level tests in IllustrisTNG where stronger memory compresses structural variance. This sign difference suggests that the resolved MaNGA analysis is dominated by actively driven patches inside otherwise regulated galaxies, while the simulations emphasise globally relaxed systems. Taken together, the results show that the stability gate is a resolved property inside galaxies, not just a global label, and they set the stage for mock-IFU comparisons that connect local regulation to global homeostasis.