Topological Resonance Theory: Zero-Parameter Predictions from Algebraic Geometry (Papers 1-5)

We present five self-contained papers developing Topological Resonance Theory (TRT), a framework in which physical constants are derived from a single algebraic constraint linking the golden ratio φ = (1+√5)/2, the circle constant π, and a topological constant ξ = 1/(φπ) ≈ 0.1967. The theory uses zero adjustable parameters. Paper 1 derives the algebraic foundations: ξ·φ·π = 1 Paper 2 derives the inverse fine-structure constant as α⁻¹ = (φπ)³ + 2π − 3ξ = 137.038 (12 ppm accuracy). Paper 3 links the Weinberg and Koide angles via a constrained identity verified to 0.022%. Paper 4 fixes the Barbero-Immirzi parameter as γ = φπ Paper 5 derives dark energy density ΩΛ = φ²/3 ≈ 0.873 (tree-level), corrected to 0.657 (4.1% vs Planck 2018). All claims are verified by companion Python scripts. Combined probability of coincidence: P < 10⁻¹³. Package includes: 5 PDFs, 5 LaTeX sources, and 5 Python verification scripts