Dark Energy from Discrete Stochastic Cascade Dynamics: A Coupled DSCD+GR System, DESI Audit, and a Calibrated DR3 Forecast

We construct a cosmological realization of the Discrete Stochastic Cascade Dynamics (DSCD) model as one coupled stochastic dynamical system, rather than as a phenomenological equation-of-state ansatz. Standard general relativity and a flat FLRW background supply the gravitational closure; asymmetric DSCD interactions, beat phase, structural memory, and funded free-capacity depletion generate the dark sector trajectory directly, producing ρ(t), p(t), H(z), and BAO distances as outputs of the simulation rather than as fitted functional forms. A funded-monotonicity proposition establishes that the free-capacity density is pathwise nonincreasing by construction; a corollary of this proposition is that the emergent equation of state satisfies w(z) ≥ −1 whenever the density is positive, a conditional structural bound rather than an imposed prior. Two inference layers share this one simulation engine. The first freezes a single declared configuration and asks whether official DESI DR1 and DR2 compressed BAO data, fit with full covariance matrices, can identify its internal parameters. A whitened-Jacobian identifiability audit finds they cannot (condition number 1.06×10⁷ against a predeclared 10⁴ limit), and the complete system is observationally indistinguishable from ΛCDM and from its own structural ablations (no memory, no regime feedback, no transport, symmetric depletion, zero beat) at current precision. No single frozen configuration is therefore forecast-eligible on identifiability grounds, superseding an earlier single-configuration retrodiction against DESI Year 1 data. The second inference layer poses the question the identifiability audit never asked: treating the present DSCD state as latent, an eight-dimensional prior over complete realizations is sampled with a scrambled Sobol sequence, and each realization is weighted by its joint DR1+DR2 marginal likelihood, with the common BAO scale marginalized analytically in closed form rather than profiled. The resulting history-compatible ensemble converges under four predeclared gates: stability under sample halving and disjoint seed banks, robustness to DR1/DR2 reweighting, and an end-to-end synthetic coverage calibration recovering 94.9% (95% level) and 73.7% (68% level) coverage of withheld truths. All four gates pass, and a sealed forecast of thirteen falsifiable DESI DR3 credible intervals is issued, with 68% widths between 0.16 and 1.10 DR2 standard deviations and medians within 0.06σ of best-fit ΛCDM. The intervals are narrower than, and in five of thirteen components disjoint from, the phantom-side excursion preferred by an unconstrained CPL fit to the same data, which is itself statistically degenerate (rank-deficient Hessian, disagreeing optimizer seeds). The forecast is therefore falsifiable in both directions: a DR3 departure below the intervals falsifies the non-phantom realization family, and a departure above falsifies the calibrated depletion realization family used here. All validation, identifiability-audit, calibration, and forecast artifacts are hash-chained and reproducible from declared seeds. Source code, the small validation ladder, the version-1 identifiability disposition, and the sealed version-2 forecast record are available at github.com/Shiv2071/Discrete-cascade-model.