Dark Energy Sets the Galaxy Acceleration Scale: A Parameter-Free a0(z) Test LCDM Cannot Take

The de Sitter-MOND framework ties the galactic acceleration scale to the dark-energy density, a0 = c^2 sqrt(Lambda/32pi) = (c/2) sqrt(G rho_DE). Promoted across cosmic time this becomes a parameter-free SHAPE prediction, a0(z)/a0(0) = sqrt(rho_DE(z)/rho_DE(0)) -- both the coefficient and the MOND interpolation function cancel in the ratio, so the evolution of a0 is fixed entirely by the dark-energy equation of state w(z), with no remaining freedom. (The sqrt(rho_DE) scaling itself is not novel -- it appears in Limbach, Psaltis & Ozel 2008 -- but the framework promotes it to a forced relation and the data now make it sharp.) DESI DR2's measured time-evolving dark energy (w0 ~ -0.75, wa ~ -0.86) drives a0(z) along a distinctive NON-MONOTONIC track: a +6% rise to a peak at z ~ 0.41, precisely the phantom-divide crossing where w(z) = -1, then a decline to a0(z=3) ~ 0.74 a0(0). The cleanest measurable signature is the SIGN of the high-z deep-MOND baryonic Tully-Fisher offset: the framework predicts rotation velocities 0.033 dex (-7.3% in V) below the local relation at z=3, where standard fixed-a0 MOND sits on it and the rival rising sqrt(rho_total) reading (already disfavored by Milgrom 2017 / RC100 / cluster offsets) sits +0.166 dex above. We argue this is a near-term falsification test that LCDM STRUCTURALLY CANNOT TAKE -- cold dark matter has no acceleration scale to evolve -- while stating plainly that it is NON-DIAGNOSTIC TODAY: the framework is hostage to a DESI result it cannot influence, dissolves to ordinary fixed-a0 MOND if w reverts to -1 (dissolution, not falsification), and the present a0(z) data (including MUSE-DARK III, Ciocan 2026, whose raw rising signal de-systematizes to consistent-with-zero through the same LCDM baryon-fraction degeneracy that makes all current a0(z) inferences non-diagnostic) are systematics-limited in both directions. The verdict arrives on two independent axes: DESI DR3 / DESI-final (w(z), ~2026-27, the gate) and high-z resolved kinematics (ALMA BTFR-offset sign ~2028-30; ELT/HARMONI clean multi-redshift tracking, early-mid 2030s). Kill conditions are stated explicitly. Honesty markers: the value a0(0) is NOT derived (one free normalization kappa=1/2; only the shape is predicted); the w0wa inputs carry DESI's uncertainties and vary across SNe compilations; the covariant lensing sector remains phenomenological as in all relativistic-MOND theories. This is a falsifiable prediction of a gravity/dark-sector effective theory -- not a proven replacement for dark matter, and not a theory of everything yet, as frustrating as it may be.