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: Gₑff (N) = σ (N) ·GPDL, where σ (N) = 1− (1−κPDL) N and κPDL = 310φ/11017 ∈ ℚ (√5) is an unconditional theorem of the axioms. At the epoch of primordial black hole (PBH) formation (N = NCMB = 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 Eₚeak (M*GR) ≈ 130. 1 MeV under standard GR and at Eₚeak (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 (κPDL) 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 fPBH ≲ 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 fPBH ≲ 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 → κPDL → σ (N) → Gₑff (N) → NCMB → M*PDL), which remains an unconditional theorem. Corpus: cedriclaubscher. ch | github. com/laubscher-lab/PDL-framework | zenodo. org/communities/pdl-framework