DERF: A Controlled NEC-Violating Bounce from a Derivative-Energy-Regulated Fluid

I present DERF, a minimal, computable bounce framework in which a transient NECviolating phase produces a non-singular transition from contraction to expansion while maintaining explicit numerical control of the effective description. We provide (i) a benchmark background evolution near the bounce, (ii) scalar-sector ghost/gradient stability diagnostics in a finite time window around the bounce for representative modes, (iii) a broad k-sweep stress test, and (iv) a strict-tolerance robustness cross-check. The present manuscript emphasizes what can be claimed invariantly at the level of an operational closure (computable reduced stability matrices) and clearly labels which interpretations are deferred to a full ADM reduction and canonical normalization.