Projective Dynamic Logo (PDL) — Global Mapping of Structures, Results, and Open Problems (Version 26)

This document is the twenty-sixth version of the global mapping of the Projective Dynamic Logo (PDL) programme. It provides a complete and current inventory of the PDL corpus (D01--D58, plus auxiliary documents DS01, DL01--DL02, D-exp series, N01), the logical dependency structure of all results, a rigorous epistemic taxonomy (theorems, conjectures, open problems), and a continuation guide for new contributors.Version 26 incorporates two new items relative to v25. Document D58 derives SU(3) as an unconditional algebraic theorem of the PDL axioms C1--C4, via five lemmas (L1: S4/V4 = S3, Weyl group of A2; L2: S4-equivariant bijection V4\{e} <-> V4-orbits on edges of K4; L3: A4/V4 = Z3, centre of SU(3); L4: rank-2 Cartan subalgebra from Re = 6 invariance; L5: A2 root system), each verified by exhaustive integer computation in the supplementary script PDL_SU3_script1.py. By the Cartan--Killing--Weyl classification, the unique compact simply connected simple Lie group with these invariants is SU(3). Combined with D46 (U(1)) and D57 (SU(2)), this establishes the algebraic structure SU(3) x SU(2) x U(1) of the Standard Model gauge group as an unconditional theorem of C1--C4. A documented negative result establishes that V4 acts faithfully on H1(K4; R), clarifying why the natural S3-set is V4\{e} and not the cycle homology. Open Problem OP-SU3 / OP-D57-3 is thereby resolved at the algebraic level. Three new open problems are added: OP-D58-1 (physical identification of SU(3)_c), OP-D58-2 (relationship between the three triplets of K4), and OP-D58-3 (fundamental representation 3 from C1--C4). The dependency diagram is updated with a D58 node and an SU(3) x SU(2) x U(1) node. The recommended next documents are updated accordingly. The bibliography gains two entries (D58, PDL_SU3_script1.py).The causal chain C1--C4 -> Lambda_PDL remains complete. The algebraic gauge group structure of the Standard Model is now a theorem of C1--C4.