A Parameter-Free Radial Acceleration Relation from the Dark-Energy Scale

We remove the MOND acceleration scale as an independent parameter. If the interpolating function's argument is the acceleration in units of the dark-energy acceleration s = c sqrt(G rho_Lambda) rather than in units of a_0, then a_0 is an OUTPUT and the coefficient kappa in a_0 = kappa c sqrt(G rho_Lambda) is exactly the reciprocal of the function's deep-MOND slope. Every parameter-free interpolating function in common use has slope one, predicting kappa = 1, which two independent measurements exclude at 7-10 sigma. We exhibit a family, mu_n(Y) = 1 - (1+Y)^(-n), whose deep-MOND slope IS its integer exponent, so the slope is a count rather than a dial; it obeys the composition law 1 - mu_n = (1 - mu_1)^n and is, to our knowledge, new -- absent from the standard catalogues and genuinely distinct from the standard n-family, with which it coincides only at n = 1. Each integer is then a COMPLETE PREDICTION of the radial acceleration relation with NOTHING fitted, neither the scale nor a shape parameter. On 155 SPARC rotation curves (2788 points, standard mass-to-light ratios) the data select n = 2: rms residual 0.1502 dex against 0.1660 for n = 1 and 0.1853 for n = 3 on the dark-energy convention, and 0.1438 against 0.1846 and 0.1684 on the critical-density one. For comparison nu_RAR, FITTED at a FITTED scale, gives 0.1453 dex on the same data. The two acceleration footings this programme carries are exactly n = 2 on the two density conventions, to 0.02 and 0.33 percent. PREDICTIONS: a POWER-LAW rather than exponential approach to Newton, leaving a solar-system anomaly of 5.8e-16 m/s^2 at Saturn, seventeen times below the Cassini residual, where the fitted kernel predicts exactly zero; a wide-binary boost differing from the fitted kernel by up to 0.28 in the velocity ratio; a Tully-Fisher zero point with no freedom; and an a_0 that inherits the dark energy's equation of state, exactly flat for w = -1 and 1.31 times higher at z = 5 for w = -0.9, so that measuring a_0 at high redshift measures w. WE DO NOT DERIVE THE INTEGER. Four structural angles were searched and none fixes it, and two point elsewhere: the algebraically distinguished member is n = 3, degree-of-freedom counting wants 3/2, and the AQUAL-QUMOND duality favours n = 1. The data select the exponent and the mathematics does not, and we report that as prominently as the fit. No published work derives an interpolating exponent at all. This is single-field AQUAL, an rms comparison rather than a likelihood, with fixed mass-to-light ratios and no per-galaxy nuisance parameters. AI-assisted research programme; not peer reviewed.