Projective Dynamic Logo (PDL) — Global Mapping of Structures, Results, and Open Problems (Version 17)

This document is the authoritative navigational and epistemic guide to the Projective Dynamic Logo (PDL) programme, updated to cover the complete corpus D01–D45. It is intended for a scientific colleague who wishes to understand, verify, or continue the research independently. PDL derives fundamental physical constants and dynamical laws from four axioms on finite signed graphs, without presupposing spacetime, particles, or fields. The minimal admissible closure under the axioms is the complete graph K₄, identified with the electron prototype. The proton is characterised by the unique integer quintuplet (24, 28, 930, 10087, 11017), from which all results flow without free parameters. Version 17 marks the closure of the PDL causal chain and incorporates documents D41–D45. Three critical Gates are resolved: the axiomatic derivation of 155/11017 (Gate 1, D29), the structural proof that the QCD correction coefficient equals 2 (Gate 2, D30), and the theorem G_eff(N) = σ(N)·G_PDL (Gate 3, D31/D36). Four fundamental dynamical equations have been derived from the (A)∧(B) coupling criterion without free parameters: the Schrödinger equation (D32), the Dirac equation (D33), Born's rule via Gleason uniqueness (D34), and the Einstein coupling equation (D35). The Hubble tension is resolved at 0.006% with zero free parameters. Black hole thermodynamics has been derived from PDL axioms: the area law S ∝ R_surf is an unconditional theorem (D37), and the Bekenstein–Hawking formula S_BH/k_B = 4π(M_eff/M_Pl)² follows algebraically from Gate 3 (D38). Nuclear stability and the valley of stability are reproduced at 100% accuracy for Z = 1–82 (D40), with a first confrontation against nuclear spectroscopy data at the 2% level (D41). The principal advances of v17 are the following. Open Problem OP1 was fully resolved by D42: the Indifference Lemma H3 is now an unconditional theorem of axioms C1–C4, making κ = 310φ/11017 ∈ Q(√5) an unconditional theorem and closing the entire derivation chain from axioms to the Bekenstein–Hawking entropy. D43 proved the geometric leakage parameters ε_geom(p) = 329/10087 and ε_geom(n) = 468/9960 as unconditional theorems (OP-A resolved). D44 derived the hierarchical filter factor k = 0.921716 from C1–C4 as an unconditional theorem (OP-B resolved), closing the complete causal chain C1–C4 → K₄ → quintuplet → ε_geom → ε_G = ε_geom × k¹⁸ → G with no remaining open problem and no free parameter beyond Δm_iso = m_d − m_u. D45 formulates the first falsifiable astrophysical confrontation: the primordial black hole survival threshold is shifted upward by +11.89% relative to the standard GR value, giving M_PDL = σ(40)^(−2/3) · M_GR ≈ 5.706 × 10¹⁴ g, with an observable excess of Hawking radiation flux at E_peak ≈ 93–104 MeV in the isotropic gamma-ray background, testable with existing Fermi-LAT data via BlackHawk and Isatis. There is no longer any foundational open problem at the axiomatic level. The remaining open problems concern higher-level derivations, extensions, and experimental confrontations.