Projective Dynamic Logo (PDL) — Global Mapping of Structures, Results, and Open Problems (Version 22)

This document provides a systematic and self-contained guide to the Projective Dynamic Logo (PDL) programme, covering the complete corpus D01–D54 plus the PDL-V series DL01–DL02 and all auxiliary documents. PDL derives fundamental physical constants and dynamical laws from four combinatorial axioms on finite signed graphs, without presupposing spacetime, particles, or fields. Version 22 introduces two additions relative to v21: (1) D54 resolves OP-pressure: the equation of state of the PDL coherence fluid is w (N) = -rhoLambda / rhocoh (N), an unconditional theorem of C1–C4. In the homogeneous ground state, wₘass = wₛpin = wₒrb = 0 exactly (three independent theorems), and wₗeak = -1 intrinsically. The PDL dark-energy fraction OmegaLambdaPDL = 0. 6838 agrees with Planck 2020 (OmegaLambdaᵒbs = 0. 685) to 0. 17%, with no cosmological parameter as input. The PDL coherence fluid provides a unified description of pressureless cold matter (|w| ~ 10^-44 at sub-nuclear scales) and dark energy (at cosmological scales) from the proton quintuplet (24, 28, 930, 10087, 11017) under axioms C1–C4 alone. (2) PDL-V Programme (DL series, Part III): DL01 establishes the self-replication operators S and L, proves S (K4) ≅ K4 over all 8 coherent configurations, and derives the exact rarity law f (n) = 2^n+1-C (n, 2) with exponents equal to triangular numbers. DL02 proves three analytical theorems: K4 is the unique fixed point of S (Theorem 1) ; the life threshold strictly precedes the consciousness threshold (Theorem 2) ; all thresholds are finite (Theorem 3). The unconditional hierarchy 4 < n*ₗife < n*consciousness < n*ₘax < infinity follows from C1–C4 alone. The PDL-V programme is presented in a separate Part III, clearly distinguished from the physical constants programme of Parts I–II. The causal chain C1–C4 → LambdaPDL is complete (D51–D53). The quantum dynamics layer (Schrödinger, Dirac, Born, U (1), Einstein, London), the nuclear stability layer (valley of stability Z=1. . 82, magic numbers, periodic table), the black hole thermodynamics layer (area law, Bekenstein–Hawking, 1/4 coefficient), the coherence tensor layer (all four components, dimensionally consistent), and the equation of state layer are all complete unconditional theorems of C1–C4. Supersedes DM v21 (doi: 10. 5281/zenodo. 20154945).