Dark Energy as Cascade Dynamics: Empirical Validation and Sealed Prediction for DESI DR3

The Discrete Stochastic Cascade model on finite graphs is applied to the dark energy equation of state through a single physical identification: the cascade's global beta density maps to the dark energy density. Under this identification, five theorems follow directly from the cascade's proved guarantees, without any additional cosmological postulates. Most critically, the no-phantom theorem establishes that w(z) greater than -1 at all active steps, proved from the energy monotonicity supermartingale. This constraint is tested against the DESI Year 1 Baryon Acoustic Oscillation dataset (April 2024). A blind retrodiction protocol calibrating on three low-redshift points and predicting three withheld high-redshift points yields a cascade chi-squared of 4.44 on unseen data, compared to 22.81 for CPL which has twice as many free parameters. A cross-release test training on DESI Year 1 and predicting DESI DR2 (March 2025) shows cascade performing at the LCDM level while CPL achieves a lower chi-squared only via a phantom crossing at z = 0.345 that violates the Null Energy Condition. Six specific D_H/r_d predictions for DESI DR3 (expected 2027) are sealed in this document. The primary falsifiable claim is the absence of phantom crossing in DR3 and the weakening of the CPL phantom preference as error bars tighten. All simulation scripts and the sealed prediction record are available at github.com/Shiv2071/Discrete-cascade-model.