Published Work

We test a dark matter halo velocity profile v(r) = v₀ r / √(φ²r₀² + r²) motivated by the Z⁵ quasicrystalline substrate of the RIG framework against the complete SPARC rotation curve catalogue (175 galaxies). The golden ratio φ = 1.6180… is fixed by the substrate geometry before any data contact. Baryonic contributions are subtracted with a fixed stellar mass-to-light ratio Y★ = 0.5 M☉/L☉. Across 172 successfully fitted galaxies, the φ-core profile achieves median χ² = 1.221, outperforming the pseudo-isothermal sphere (median 1.289, same parameter count) and NFW (median 2.239, more parameters). A parameter-free prediction for the half-power velocity ratio v(φr₀)/v₀ = 1/√2 = 0.7071 is confirmed at 0.7005 ± 0.054 (+0.067σ, n = 140). Code and per-galaxy results are publicly available.

We present the Reflexive Information Geometry (RIG) framework, in which physical law emerges from a two-dimensional quasicrystalline substrate, a Penrose tiling, whose structure is governed by the golden ratio φ as a self-referential substitution constant. The framework rests on three axioms: the holographic principle (the fundamental substrate is two-dimensional), Fibonacci quasicrystalline order (the substrate has Penrose tiling structure), and the de Bruijn projection (the Penrose tiling arises from projecting a five-dimensional integer lattice Z⁵ onto the 2D plane). We derive: the Z⁵ frame identity Σeₖ⊗eₖ = (5/2)I exactly; the minimum stable vortex spanning two adjacent Z⁵ sectors; the eigenvalue ratio λ₂/λ₁ = φ² exactly; the Koide formula Q = 2/3 for charged lepton masses from Z⁵ representation theory with zero free parameters; the Standard Model gauge group SU(3)×SU(2)×U(1) from the Z⁵ Wilson loop holonomy theorem; and the Yang-Mills kinetic Lagrangian from the Wilson action on the A₄ root lattice. We state explicitly which results are exact derivations, which are motivated proposals, and which are open problems. We invite collaboration on the identified open derivations.