Projective Dynamic Logo (PDL) — Global Mapping of Structures, Results, and Open Problems — Version 34

Abstract

Version 34 of the PDL Global Mapping. This is the first version of this document to withdraw a standing claim of unconditional causal closure. Two independent gaps are now recorded on the chain from axioms C1–C4 to Newton's constant G. First, the active surface R_surf = φ·r_val/3 is reclassified from theorem to named hypothesis (Hφ), following an audit of D05 that found four errors in version 1 of that document; D05 v2 (10.5281/zenodo.22066454) corrects them and states explicitly that the self-similarity condition is imposed, not derived. The epistemic tables of D39 and D43, which recorded it as a theorem, are superseded. Consequently κ, α, σ(N), G_eff (Gate 3), the Hubble prediction and Λ are conditional on Hφ. Second, OP-B is reopened by D44v2: both constructions of the filter factor k fail arithmetic verification. Neither correction introduces an adjustable parameter. The statement that the programme carries no free parameter beyond Δm_iso survives literally; what it carries is an undemonstrated structural hypothesis, repaired by a proof and not by a fit. The quintuplets, Δn = 4, E_bord, ε_geom and the gauge chain D57–D61 do not pass through R_surf or k and are unaffected. Three factual errors in the v33 glossary are corrected: σ = 930 was described as "the active surface" (the active surface is 310φ ≈ 501.59); n_u = 24 was described as the number of u-valence cores (it counts entities in one core); and the two-factor decomposition of κ was given as κ = 3/σ (which evaluates to 0.003226 against κ = 0.045529). Three sections are new: the active surface and Hφ; the sea counting rule, where the apparent contradiction between R_sea = 2·n_sea and the odd value 10087 is resolved as the boundary signature of a quadrangulation with three holes; and D68/D69, integrated into the mapping for the first time. Nine open problems are introduced or reopened, of which OP-B and OP-Hφ-1 sit directly on the causal chain to G. A new falsifiable prediction (P20) provides a route to refuting Hφ. Known limitation: the TikZ dependency figures still show the chain as unconditional and are not yet redrawn; a warning to that effect precedes them, and the text is authoritative where it conflicts with a figure.