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

Document D45 of the PDL corpus — Version 2 (25 June 2026) 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 that the effective gravitational coupling is density-dependent: G_eff(N) = σ(N)·G_PDL, where σ(N) = 1−(1−κ_PDL)N and κ_PDL = 310φ/11017 ∈ ℚ(√5) is an unconditional theorem of the axioms. At the epoch of primordial black hole (PBH) formation (N = N_CMB = 40, derived from the neutron quintuplet without cosmological input), this coupling suppression 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, an upward shift of +11.89% relative to the standard general-relativistic value M*_GR ≈ 5.1×1014 g. A complete calculation of the multi-component Hawking spectrum (direct emission, secondary radiation, final-state radiation, and in-flight positron annihilation), performed with the public pipeline GammaPBHPlotter (Carlini & Cholis 2025) built on BlackHawk spectral tables, locates the spectral peak at E_peak(M*_GR) ≈ 130.1 MeV under standard GR and at E_peak(M*_PDL) ≈ 117.5 MeV under PDL — a fractional displacement of −9.65%, falling within the Fermi-LAT energy range. The prediction is fully determined by a single unconditional theorem (κ_PDL) and contains no free parameter beyond the standard-model degrees of freedom entering the Hawking spectrum. We identify the precise observational test using the public codes BlackHawk, GammaPBHPlotter and Isatis together with the Fermi-LAT IGRB measurements of Ackermann et al. (2015) and the constraint compilation of Carr et al. (2021), and invite the community to carry it out. We note that a very recent independent analysis of the same IGRB data (Cholis, Krommydas & Carlini 2026, arXiv:2606.10013) constrains the PBH abundance near this mass to f_PBH ≲ 10−10, which may render the present signal too faint to discriminate regardless of which cutoff is correct. Changes in v2 (25 June 2026): Replaced the v1 primary-emission-only estimate of the spectral peak (≈93–104 MeV) with the full multi-component calculation (130.1 MeV GR / 117.5 MeV PDL, −9.65%), using GammaPBHPlotter (Carlini & Cholis 2025) and BlackHawk spectral tables. Added an honest detectability caveat citing the very recent f_PBH ≲ 10−10 constraint of Cholis, Krommydas & Carlini (2026). Updated the epistemic status table, test procedure (Section 4), discussion, and conclusion accordingly. No change to the underlying causal chain (C1–C4 → κ_PDL → σ(N) → G_eff(N) → N_CMB → M*_PDL), which remains an unconditional theorem. Corpus: cedriclaubscher.ch | github.com/laubscher-lab/PDL-framework | zenodo.org/communities/pdl-framework