Projective Dynamic Logo (PDL) — Global Mapping of Structures, Results, and Open Problems (Version 24)

Version 24 of the PDL Global Mapping document, covering the complete corpus D01–D56, DL01–DL02, and all auxiliary documents. This document is the navigational and epistemic backbone of the Projective Dynamic Logo (PDL) programme — a foundational physics programme that derives all fundamental physical constants, dynamical laws, and structural hierarchies from four combinatorial axioms (C1–C4) on finite signed graphs, without presupposing spacetime, particles, or fields. Version 24 incorporates document D56, which resolves Open Problem OP-D41-1-A: the linear scaling N_comp(k) = k for the number of maximal partial closures on a k-particle–k-hole nuclear interface surface is now an unconditional theorem of C1–C4, proved via three lemmas (L1: uniqueness of the maximal closure on a single interface unit, D16a; L2: disjointness of the mixed-triangle sets of k distinct (A)∧(B) couplings, D29; L3: C3-irreducibility of the k-unit assembly, axiom C3 directly). A corollary establishes R_surf(k) = k·T for the effective active surface of a k-ph nucleus. The experimental motivation comes from Ha et al. (Nature Communications 16, 10631, 2025) on ⁸⁴Mo/⁸⁶Mo, and from Escudeiro, Recchia, Lenzi et al. (Physical Review C 113, 044304, 2026) on the f₇/₂ mirror nuclei ⁴⁷Cr–⁴⁷V and ⁴⁹Mn–⁴⁹Cr. The conjecture H_B (B(E2) ∝ N_comp(k) = k) is reformulated: N_comp(k) = k is now a theorem; the remaining gap is the formal identification of the E2 multipole operator in the PDL signed-graph formalism, identified as Open Problem OP-E2-PDL. What this document maps and transmits:The complete causal chain from axioms to the cosmological constant Λ_PDL (D51–D53), verified to 0.17 ppm with no free parameter. The three Gates of the programme (D29–D31), deriving 155/11017, the QCD correction coefficient a=2, and G_eff(N) = σ(N)·G_PDL. The full quantum dynamics layer: Schrödinger (D32), Dirac (D33), Born's rule Levels 1 and 2 (D34, D46), U(1) phase freedom, London equation (D49). The nuclear stability layer: valley of stability, all seven magic numbers, sub-shell filling rates r_exc(Z) for Z=1–82, 31/31 boundaries verified (D40, D47), and the closure multiplicity theorem N_comp(k) = k (D56). The black hole thermodynamics layer: area law, Bekenstein–Hawking entropy, coefficient 1/4 (D37, D38, D50), primordial black hole threshold +11.89% (D45). The coherence stress-energy tensor and equation of state of the PDL coherence fluid: w(N) = −ρ_Λ/ρ_coh(N), with Ω_Λ^PDL = 0.6838 agreeing with Planck 2020 at 0.17% (D48v3, D54). The electroweak sector: SU(2) in K₄ (D33), U(1) from Hopf fibration (D46), θ_W = 19π/119 from dephasing sequencing via Lemma D (D55). The PDL-V programme: self-replication thresholds, the hierarchy 4 < n*_life < n*_consciousness < n*_max < ∞ as an unconditional theorem (DL01, DL02). The document also provides: the complete critical-path dependency map (now including the electroweak chain and the nuclear spectroscopy layer), the full epistemic architecture table stratifying all results as unconditional theorems, conditional theorems, conjectures, or open problems, the complete list of 10 falsifiable parameter-free predictions (P1–P10), and a continuation guide identifying OP-E2-PDL as the highest-priority open problem. The unique external parameter of the programme is Δm_iso = m_d − m_u. All other constants — G, α, μ*, Λ, θ_W, the periodic table, the cosmological constant, and now the closure multiplicity N_comp(k) — are derived without calibration.