Registered predictions and falsification criteria for a dark-energy density that follows the growth of structure (fD model)

Predictions and falsification criteria for a cosmological model in which the dark-energy density follows the growth of structure per e-fold of expansion, ρDE(a) = ρDE,0 fD(a)/fD(1) with fD = dD/d ln a. Spatial flatness fixes the normalization, so the model has the same free parameters as flat ΛCDM. The system is solved self-consistently; the effective equation of state crosses w = −1 where fD peaks (z ≈ 0.46). The record contains: (1) the original prediction file of 10 October 2026 with BAO distances DM/rd and DH/rd at the DESI DR2 redshifts and fσ8(z) for ΛCDM, w0wa and two variants of the model; (2) the addendum of 12 October 2026 with the w0wa (CPL) point of the model, (w0, wa) = (−0.81, −0.65) ± 0.01, and falsification criteria F1 and F2; (3) criteria F3 and F4 added on 14 October 2026. The internal dates are recorded in the files; the public time stamp is the publication date of this record. A paper with the full analysis is in preparation. This work was done in collaboration with the AI system Claude (Anthropic). The author is responsible for the content.