A finite branching budget for dark energy: a forced map from the phantom crossing to (w0, wa), direct fits to DESI DR2 data, and pre-registered kill conditions

We present a mechanism in which the dark-energy sector tracks the branching of a system with a finite, conserved capacity. Instances proliferate at rate R = kNB with B = B0 − (N−1), giving logistic growth; identifying expansion with accumulated branching, a ∝ N (exact), yields ρ_DE ∝ R and w(a) = −4/3 + (1/3)x/(1−x) with x = x0·a. Three structural results follow with no freedom: (i) w crosses −1 exactly at half capacity (the branching peak); (ii) given the crossing redshift z_c, today's value is forced, w0 = −4/3 + (1/3)x0/(1−x0), x0 = (1+z_c)/2; (iii) within the free-branching regime w ≥ −4/3, governing the observable near-crossing window. Projected through a CPL fit at the DESI DR2 BAO redshifts, the curve yields (w0, wa)_eff = (−0.808, −0.802), consistent with the measured (−0.75 ± 0.07, −0.86 ± 0.30); fit directly to the thirteen published DR2 BAO measurements the mechanism is mildly preferred over ΛCDM (Δχ² = 3.5 for one parameter), and on a 47-constraint geometric suite (BAO + 31 cosmic-chronometer H(z) + compressed CMB + r_d) it is the only model in the comparison set improving on ΛCDM by both AIC and BIC. Adding the 2018-vintage compressed supernova E(z) points (full covariance) the mechanism loses to ΛCDM (Δχ² = −4.7): it has no ΛCDM limit and its fate is entangled with the live "evolving dark energy or supernova systematics" controversy; within the same fit, conditionally on the mechanism class, the data places the crossing at z_c = 0.22–0.27, where the forced map returns w0 in [−0.79, −0.75], containing the independently measured value. We state pre-registered kill conditions for 2027–2030: the crossing at z_c = 0.27 ± 0.03; |1+w| ≤ 0.12 on (z_c, 0.6] with w(0.4) = −1.057, w(0.6) = −1.114; quintessence today near w0 ≈ −0.75; and region stability of the projected band. All limitations, including the hybrid use of the Friedmann equation and the absence of a perturbation derivation, are stated. Code reproducing every number is released.