Projective Dynamic Logo (PDL) — Global Mapping of Structures, Results, and Open Problems (Version 32)

This document is Version 32 of the systematic, self-contained navigation and epistemic guide to the Projective Dynamic Logo (PDL) programme — a foundational physics research programme deriving fundamental physical constants and dynamical laws from four axioms on finite signed graphs, without presupposing spacetime, particles, or fields. It supersedes DM v31 (10.5281/zenodo.21384063). What is new in v32. This version makes no addition to the document corpus; it records the outcome of an integrity audit of Document D47 (Session 74), conducted following an external confrontation of the corpus with a nuclear-physics letter on mirror energy differences near the Z=28 shell closure (Pigliapoco et al., Phys. Lett. B 878 (2026) 140564). The audit covers Open Problem OP13 (spin–orbit splitting), the Mirror Lemma, the seven nuclear magic numbers, and Open Problem OP14 (sub-shell filling rates). OP13 and the seven magic numbers are independently re-verified and unaffected. Document D40's original empirical filling-rate table is found to be internally self-consistent — its rate column (r) and excess column (E) satisfy ΔE = 2(r−1) exactly on all 31 entries — once a missing factor of 2 in the reconstruction equation N_min(Z) = 20 + Σr_exc(Z′), present in both D40 and D47v1, is corrected to N_min(Z) = 20 + 2·Σr_exc(Z′). Under the corrected formula, D40's table reproduces 74–88% of the experimental valley of stability (depending on the stability criterion used), while D47v1's simplified two-valued filling-rate rule (r_exc = 0 at the three magic closures, 1 otherwise) — previously reported as an unconditional theorem resolving OP14 — reproduces none of the 31 sub-shell boundaries under the same corrected formula. A textual remark in D47v1 asserting that D40's table contains no entries with r ∈ {2,3} in the range 22 ≤ Z ≤ 82 is also shown to be factually incorrect (19 of 31 entries). Document D47v2 (10.5281/zenodo.21410146) is deposited, formally reopening Open Problem OP14. Four independent verification scripts are deposited alongside it. Accordingly, in this document: Theorem 12.5 (D47v1) is replaced by an Open Problem statement; Corollary 12.6 (valley of stability) is rewritten to reflect the corrected, empirically-grounded reconstruction (74–88%, not the previously claimed 100% unconditional theorem); Open Problem 18.15 (OP14) is moved from "fully resolved" back to open, with high priority; the D47 entry of the document table and Layer L6 of the epistemic architecture table are updated; and the corresponding node of the foundational dependency map (Figure 1) is relabelled. OP13, the Mirror Lemma, and every other result of the corpus are unaffected by this correction. Full version history for v1 through v32 is preserved in Appendix / Section 1.2 of the document. The PDL corpus (D01–D67, plus auxiliary documents, the PDL-V series DL01–DL02, and the joint PDL–OFN bridge notes N01 and N02) is deposited open-access in the Zenodo community pdl-framework. Author website: cedriclaubscher.ch.