Primordial Black Hole Evaporation Threshold from the Projective Dynamic Logo Framework: A Falsifiable Prediction for Fermi-LAT

The Projective Dynamic Logo (PDL) framework derives all fundamental physical constants from four axioms on finite signed graphs, without presupposing spacetime, particles, or fields. A central result of the framework is the density-dependent effective gravitational coupling G_eff(N) = σ(N)·G_PDL, where σ(N) = 1−(1−κ)^N and κ = 310φ/11017 ∈ Q(√5) is an unconditional theorem of the PDL axioms (D42). At the epoch of primordial black hole (PBH) formation, characterised in PDL by N_CMB = 40 derived from the neutron quintuplet without cosmological input (D27), the suppression of the gravitational coupling extends PBH lifetimes by a factor σ(40)^(−2) = 1.4007. The resulting shift in the PBH survival mass threshold is M_PDL = σ(40)^(−2/3) · M_GR = 1.1189 · M_GR ≈ 5.706 × 10¹⁴ g, corresponding to an upward shift of +11.89% relative to the standard general-relativistic value M_GR ≈ 5.1 × 10¹⁴ g. This prediction implies an excess of Hawking radiation flux in the isotropic gamma-ray background (IGRB) at E_peak ≈ 90–105 MeV from PBHs in the mass window [5.10, 5.71] × 10¹⁴ g that are still active according to PDL but are predicted to have already evaporated by standard general relativity. The prediction is fully determined by the single unconditional theorem κ_PDL and contains no free parameter beyond the Standard Model degrees of freedom entering the Hawking spectrum. The precise observational test is identified using the public codes BlackHawk (Arbey & Auffinger 2019) and Isatis (Auffinger 2023) together with the Fermi-LAT IGRB measurements of Ackermann et al. (2015) and the constraint compilation of Carr et al. (2021). This document constitutes D45 of the PDL corpus.