Beyond the Maximum Index: General Theory of Saturation, Rupture, and Re-Indexing

This work extends the "Time as Index" framework by addressing the structural regime that appears once a system reaches its maximum irreversible index. Rather than treating saturation as termination, this paper shows that:– saturation is a necessary structural limit in bounded non-closed systems,– rupture is not failure but the only consistent continuation beyond that limit,– apparent endpoints correspond to phase inversion and re-indexing under new constraints. This paper provides a general post-maximum-index description applicable across physics, cosmology, biology, and cognition. Irreversibility precedes entropy.Time does not end at saturation; it changes the structure in which it is indexed.