The initial-action branch of everpresent Lambda: an e-fold law, the exit, and what late acceleration would require

In the volume-based everpresent Lambda model of Das, Nasiri and Yazdi, the cosmological term is Lambda = (8 pi G S0 + fluctuations)/V, where V is the past light-cone four-volume and S0 an initial action. A recent no-go result (Güz, 2026) shows that the smooth 1/sqrt(V) branch with S0 = 0 cannot start acceleration on power-law backgrounds, and leaves the branches carrying a 1/V term uncovered. This note treats the smooth part of that S0 branch. Main results, using the first Friedmann equation (background-equivalent to the authors' Scheme 1): An exact reduction of the past-cone volume to ordinary differential equations. Dependence of the accelerated e-folds essentially only on u_i = 4 pi V_i/(3 kappa^2), with kappa = 8 pi G S0/3. An e-fold law N = 1/u_i + (13/6) ln(1/u_i) + c, where the coefficient 13/6 comes from the memory kernel of the past cone. An exit that freezes the expansion (a tends to a constant, V tends to pi t^4/3), with no reheating. w_eff = 1 + 2w for the S0 term in decelerating eras, and w_eff = 0.29 today on a LambdaCDM history. With Lambda(x0) set to today's Lambda, no acceleration before a = 30 unless the seed volume exceeds 1.55 times today's past-cone volume (about 5.8e242 in Planck units). The authors' Scheme 2 (the second Friedmann equation) is used as a cross-check. There the corresponding threshold is 0.48, but the Ahmed-Sorkin fictitious dust contributes substantially. The model's noise at alpha = 0.015 leaves the mean e-fold count unchanged within its error. Late acceleration from this branch therefore requires both the size of Lambda and a seed comparable to the observable past cone to be put in by hand. Code and all numbers are in the deposit.