The PUH Correlation Atlas — Master Synthesis (Volumes I–VI): A Structural Map of the Photonic Universe Hypothesis as a Theory Graph, with Three Sector-Roots Converging on the E8 Casimirs, the Degree-30 Casimir as Master Object, Fifteen Forced Bridges, and a Single Unified Open Frontier

STRUCTURAL SYNTHESIS — maps PUH as a single theory graph rather than ~191 separate papers. Every connection tagged FORCED / UNVERIFIED / IN-TENSION / REJECTED; only FORCED connections claimed. Six sector volumes plus this synthesis; volumes archived alongside and browsable on the PUH GitHub repository. === DESCRIPTION (abstract) === The Photonic Universe Hypothesis (PUH) comprises ~191 papers. This Atlas reads the corpus as a single theory graph and maps how the results relate, labelling every connection FORCED (a proven structural identity), UNVERIFIED (suggestive but unestablished), IN-TENSION (a genuine internal inconsistency, flagged not hidden), or REJECTED (a coincidence on inspection). Only FORCED connections are claimed. The discipline is the point: the Atlas is designed to separate genuine structure from numerology, and is as explicit about what is open or in tension as about what is solid. MAIN FINDING: PUH resolves into THREE sector-roots that all connect through the eight E8 Casimir invariants, with the degree-30 Casimir (C30) as the single deepest connecting object. The roots are the Z3 asymmetric rebound (matter), the T175 rank-drop (cosmology), and the T156 C30 level set (shell). C30 appears in all three — its frozen value is a particle-state constraint (matter), its saturation forms a Planck core (cosmology), its level set is the Planck Shell (shell) — and further underlies the freeze exponent and the real-form question (T265). FIFTEEN FORCED BRIDGES (three cross-volume) are established across six sector volumes, including: Z3 rebound to masses/cosmology/generations; the 8 Casimirs frozen (matter) equivalent to saturated (cosmology) ; C30 unifying the three structural volumes; the two maximal E8 decompositions tiling the four forces; the (56, 2) linking the force sector to the quaternionic real form; PMNS Tribimaximal structure from Koide Q=2/3 (the same Q driving masses and mixing) ; dark matter as unorganized E8 condensate (with a firm null-detection prediction) ; and the tectonic unification (the same convergent/divergent/transform boundary framework organising Earth geology and cosmic structure). UNIFIED OPEN FRONTIER: the Atlas localises PUH's open problems to two computational tools — the substrate equation of state Rₛub (shown to gate the SPF ground state phi₀, the quaternionic freeze exponent, and the microscopic derivation of the Bekenstein-Hawking area law simultaneously — three problems, one wall, three sides) and E6/E8 representation theory (the within-sector hierarchy gating absolute masses, CKM theta₁3, and deltaCP). That the entire open frontier of a 191-paper framework reduces to two well-defined tools is itself a structural finding: the difficulties are coherent, not diffuse. SIX-SECTOR REACH: the three roots govern all six sectors — matter (I), cosmology (II), shell (III), forces (IV), predictions (V), and flavour+dark (VI) — with the later sectors being observable projections of the roots rather than new roots. HONEST SCOPE: built from targeted searches, not an exhaustive reading, so gaps are possible and corrections expected (the boundary cluster was added after the initial five volumes). In-tension nodes are flagged openly (the gravity Cartan placement, since corrected; the two competing dark-energy accounts) and at least one near-miss is rejected (E8 dimension does not explain core mass-radius scaling — a category error), demonstrating the discipline is genuine rather than decorative.