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

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-t₀)² / 2σ²), 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 Ωₘ, H₀, ωb free, is run for 100,000 emcee steps with differential-evolution moves, reaching formal convergence N / (50τ) = 9.02. We obtain κ_Λ = 0.368+0.218-0.150 (P(κ_Λ < 0) = 0.35%, a 2.70σ preference), t₀ = 8.50 ± 0.33 Gyr, σ = 0.485+0.311-0.232 Gyr, with Ωₘ = 0.3144 and H₀ = 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 Δα/α prediction fall in the ESPRESSO band: zₚₒₛ = 0.589 (55%), zneg = 0.453 (85%). Statistically, Δχ² = -10.5, = -4.5, = +11.6. Finally, we test the non-circular ansatz σ = rd/c (the light-crossing time of the drag-epoch sound horizon, an independently measured scale): fixing σ this way costs only Δχ² = 0.16 and yields a measured = -6.36, = +4.38 (Δ k = 2) --- the weak-evidence boundary, with κ_Λ at a 2.19σ preference