The Causal Chain of Physical Reality: From Four Axioms to Newton's Constant via the Geometric Leakage Parameter (PDL Framework — D43v3)

The Projective Dynamic Logo (PDL) programme derives the whole of known fundamental physics from four axioms on finite signed graphs, without presupposing spacetime, particles, fields, or continuous geometry. This document presents the complete causal chain and its central missing link, identified in Session 21 through the first three-dimensional geometric realisation of the PDL proton closure. Prior to this work, the gravitational leakage parameter εG ≈ 0. 007519 — which connects the proton's relational architecture to Newton's constant G via 18 hierarchical coherence filters — was computed from the experimental value of G and then reinterpreted within the framework. The link was logically circular at its first step. The missing piece is the geometric leakage parameter εgeom = 329/10087 = 0. 032616, derived here without invoking G, without calibration, and without any free parameter, from the Euler characteristic of the proton's three-dimensional quad-grid realisation on S² with three valence holes (χ = −1). This quantity is the irreducible boundary fraction of the sea sector, rendered visible by the simulation but invisible in the purely algebraic formulation. The causal chain is now established: C1–C4 → K₄ → (24, 28, 930, 10087, 11017) → εgeom = 329/10087 → εG = εgeom × k¹8 → G, with k = 0. 921716 and two remaining open problems (OP-A: exact analytic derivation of Ebord = 329; OP-B: derivation of k from the axioms alone). The document assembles the complete PDL derivation chain alongside this new result: the four relational axioms and the unique minimal closure K₄ (electron prototype) ; the proton integer quintuplet (24, 28, 930, 10087, 11017) and active surface Rₛurf = 310φ; the (A) ∧ (B) coupling criterion as the pivot of all dynamical derivations; the fine-structure constant α⁻¹ = φ²rᵥal²/ (9μ) ≈ 137. 022; the Indifference Lemma H3 (unconditional theorem, D42) ; the gravitational engagement fraction κ = 310φ/11017; the effective coupling Gₑff (N) = σ (N) ·GPDL (Gate 3) ; the Hubble tension resolution at 0. 006% with zero free parameters; the Schrödinger, Dirac, and Einstein equations and Born's rule; the Bekenstein–Hawking entropy formula SBH/kB = 4π (Mₑff/MPl) ²; and the complete valley of nuclear stability for Z = 1 to 82. Three falsifiable predictions are stated: a +11. 89% upward shift in the primordial black hole survival threshold (Fermi-LAT), B (E2) ratios for ⁸⁸Ru/⁹⁰Ru and ⁹²Pd/⁹⁴Pd (FRIB/RIKEN), and a redshift-dependent entropy-to-energy ratio in AGN populations. The sole irreducible external input is Δmᵢso = md − mᵤ, forced by the axioms at the PDL–QCD boundary.