The Temporal Fractal Influx Model Version 28.0: A Converged Joint SNe+BAO+CMB Fit, a Non-Circular Pulse-Width Ansatz $\sigma=r_d/c$, and Phantom Crossing at $z=0.52$.

Abstract

We present the final results of the Temporal Fractal Influx Model (MIFT): a transient Gaussian modulation of the dark-energy density, $f(t) = \exp(-(t-t_0)^2 / 2\sigma^2)$, phenomenologically anchored in Vaidya–AdS5 geometry. A joint fit to Pantheon+ (1580 SNe Ia), DESI DR1 BAO (12 points), and Planck distance priors (R, l_A), with $\Omega_m$, $H_0$, $\omega_b$ free, is run for 100,000 emcee steps with differential-evolution moves, reaching formal convergence $N / (50\tau) = 9.02$. We obtain $\kappa_\Lambda = 0.368^{+0.218}_{-0.150}$ ($P(\kappa_\Lambda < 0) = 0.35\%$, a $2.70\sigma$ preference), $t_0 = 8.50 \pm 0.33$ Gyr, $\sigma = 0.485^{+0.311}_{-0.232}$ Gyr, with $\Omega_m = 0.3144$ and $H_0 = 67.09$ consistent with Planck. The implied phantom crossing lies at $z = 0.518^{+0.048}_{-0.044}$ (94% of the posterior within [0.4, 0.6]), centred on the DESI signal. Both lobes of the antisymmetric $\Delta\alpha/\alpha$ prediction fall in the ESPRESSO band: $z_{\rm pos} = 0.589$ (55%), $z_{\rm neg} = 0.453$ (85%). Statistically, $\Delta\chi^2 = -10.5$, $\Delta\text{AIC} = -4.5$, $\Delta\text{BIC} = +11.6$. Finally, we test the non-circular ansatz $\sigma = r_d/c$ (the light-crossing time of the drag-epoch sound horizon, an independently measured scale): fixing $\sigma$ this way costs only $\Delta\chi^2 = 0.16$ and yields a measured $\Delta\text{AIC} = -6.36$, $\Delta\text{BIC} = +4.38$ ($\Delta k = 2$) --- the weak-evidence boundary, with $\kappa_\Lambda$ at a $2.19\sigma$ preference