Projective Dynamic Logo (PDL) — Global Mapping of Structures, Results, and Open Problems (Version 18)

This document is the eighteenth version of the navigational and epistemic guide to the Projective Dynamic Logo (PDL) programme. It covers the complete corpus D01–D48 plus auxiliary documents (D10a, D16a, D16b, D01F, D20F, DN, DN-fr, DM). Version 18 incorporates three new documents (D46, D47, D48) and marks the completion of two major programme layers. D46 (OP4 resolved) derives the U (1) phase freedom of quantum mechanics as a structural consequence of the K₄ pulsation, not a postulate. Three propositions establish: (1) the global sign equivalence s ∼ −s of K₄ coherent configurations, combined with T² = −I₂ (D33), generates a canonical U (1) action with Hopf fibration S¹ ↪ S³ → S² as orbit structure; (2) the (A) ∧ (B) stability criterion is U (1) -invariant over all 8 coherent configurations; (3) the unique U (1) -equivariant probability measure on S³ consistent with the Level 1 Gleason axioms is Born's rule P = |⟨θ|ψ⟩|². The quantum dynamics layer of the PDL programme is now complete: Schrödinger (D32) + Dirac (D33) + Born Level 1 (D34) + Born Level 2 + U (1) (D46). D47 (OP13 and OP14 resolved) proves that Δn = 4 is the unique element of 0, 4, 8, … such that the discriminant of the quasi-completeness equation 3nᵤ² + (2Δn − 3) nᵤ + Δn (Δn − 1) − 1860 = 0 is a perfect square (149²), forcing nᵤ = 24, nd = 28, and s = 1/12 as unconditional theorems of C1–C4. The Mirror Lemma establishes that the harmonic oscillator PDL levels of the proton and neutron are isomorphic. The filling rates rₑxc (Z) = 0 for Z ∈ 28, 50, 82 and rₑxc (Z) = 1 otherwise are derived analytically, verified for 31/31 sub-shell boundaries with zero free parameter. As a corollary, the valley of stability Nₘin (Z) for Z = 1–82 is an unconditional theorem of C1–C4. The nuclear stability layer is complete. D48 (OP2-D35 partially resolved) derives the explicit form of the coherence stress-energy tensor Ccoh. The coherence volume VC = (4/3) πħ/ (mₚ c) ³ is doubly forced by two independent chains (D10a temporal + D23 geometric), with numerical agreement at machine precision. Three components are unconditional theorems: C^ (mass) _μν = ρcoh c² u_μ u_ν, C^ (spin) _μν (correction ~10⁻¹²), and C^ (orb) _μν = mₚ ⟨j_μ j_ν⟩/ρcoh. The leakage component C^ (leak) _μν carries ηL¹8 as a theorem but the prefactor C remains open (OP1-D35, the PDL analogue of the cosmological constant problem). The PDL Einstein equation with complete explicit source is given as Corollary 9. 1. Three new open problems are identified: OP1-D35, OP-pressure, and OP-London. The document provides a complete corpus inventory (48 numbered documents + auxiliaries), a rigorous eight-layer epistemic architecture, a prioritised open-problem list, an updated TikZ critical-path dependency map, a table of nine falsifiable parameter-free predictions, and a continuation guide for independent colleagues. All results are stratified by epistemic status: unconditional theorem, conditional theorem, conjecture, or open problem. No result is admitted as an axiom if it can be derived. The programme has now derived, from four axioms on finite signed graphs and a single irreducible external parameter (Δmᵢso = md − mᵤ): the fine-structure constant, Newton's gravitational constant, the proton–electron mass ratio, the Hubble tension (0. 006% error, zero free parameters), the Bekenstein–Hawking entropy formula, the Schrödinger equation, the Dirac equation, Born's rule (Levels 1 and 2), the U (1) phase freedom, the periodic table (valley of stability for Z = 1–82), and the PDL Einstein equation with explicit source.