Convergent Cosmological Architecture: A Computational Graph-Theoretic Analysis of Emanation Hierarchies Across Nine Sacred and Philosophical Traditions

all data files at https://github.com/OwainGlyndwr1400/emanation-topology zenodo just holds the paper. PurposeThis study tests whether the deep linear-chain architecture observed in Mediterranean Late Antique emanation cosmologies is a structurally distinctive feature of that tradition or a trivially common property of all religious cosmological hierarchies.Design/methodology/approachNine cosmological hierarchies —six primary emanation traditions (Plotinian Neoplatonism, Sethian Gnosticism, Valentinian Gnosticism, the Hermetic Corpus Hermeticum, Chaldean Oracles, Lurianic Kabbalah), two culturally independent cross-cultural comparanda (classical Samkhya, Daodejing Chapter 42), and one creationist negative control (Genesis 1:1–2:3) —were encoded as labelled directed acyclic graphs (DAGs). Topological invariantswere computed for all nine schemas and compared against a null distribution of 7,000 randomly generated rooted trees. Six formal statistical tests and six graph-theoretic similarity tests (including VF2 exact isomorphism, Weisfeiler-Leman kernel similarity, and graph edit distance) were applied across all 36 pairwise schema comparisons.FindingsSix of nine schemas are structurally exact linear chains (p < 0.001 vs.null baseline of 6.4%). Real schemas are significantly deeper than random trees of equivalent size (Mann-Whitney U = 6,105; p = 0.028). Two pairs of structurally isomorphic schemas were identified: Plotinian Neoplatonism and Daodejing (GED = 0; WL similarity = 1.0), and Lurianic Kabbalah and classical Samkhya (GED = 0; WL similarity = 1.0). The Genesis negative control is maximally distant from all emanation schemas (GED range: 8–12; family separation ratio: 2.46).OriginalityThis is the first computational graph-theoretic cross-cultural comparison of cosmological emanation schemas, and the first to include culturally independent (Indian, Chinese) and creationist negative-control comparanda.Contribution to the field of Digital HumanitiesThe study demonstrates a reproducible pipeline —schema encoding, invariant computation, null-model generation, 
statistical testing, similarity analysis —applicable to any structured comparative religion or intellectual history question expressible as a labelled DAG.