The Geometry of Initiatory Symbol Systems: A Comparative Graph-Theoretic Investigation of the Askew Codex and Masonic Degree Structures

This paper proposes a comparative mathematical investigation of two historically distinct symbolic systems: the Askew Codex (particularly its Pistis Sophia material) and Freemasonry, with particular attention to the Ancient and Accepted Scottish Rite for Australia. The research asks whether these systems exhibit comparable relational structures when represented through independently constructed graphs. The Askew Codex is approached through three analytical layers: alphabetic transitions, lexical composition, and narrative relationships. The Masonic system is approached through a fourth: degree structures, institutional relationships, and documented symbolic associations. The 33rd degree is treated as a specific institutional and symbolic designation within a historically situated Masonic jurisdiction. It is not presumed to represent a universal terminal stage, a mathematical constant, or a hidden numerical encoding. The proposed mathematical methods include directed and undirected graph construction, typed relational networks, graph isomorphism and homomorphism tests, spectral analysis, persistent homology, and null-model comparisons. The inverse golden ratio ϕ−1 = (√5−1)/2 is retained as a candidate spectral correspondence inherited from the author’s Relational Operator System (ROS). No relationship between the Masonic degree structure and this constant is assumed. A versioned Unresolved-Edge Register (v1.2) records relationships that cannot yet be entered as established edges, distinguishing not documented from formally absent. The 32°–33° prerequisite in the Australian jurisdiction is classified as unresolved (reason codes U-A, U-C, U-E), not as absent. A relationship-level candidate-resolution sensitivity procedure for the 32◦–33◦ pair (R0 AUS = {r0,...,r4}, evaluated over admissible combinations R∗ AUS) permits institutional-layer analysis to proceed while the degree-layer graph is blocked pending documentary retrieval. The central hypothesis is that independently documented symbolic systems may exhibit comparable relational organisation. Such a correspondence, if observed, would require mathematical demonstration and would not by itself establish historical transmission, common authorship, or metaphysical equivalence.