The Cosmic Landscape Map: Taiji Duality & Geometric Morphogenesis Blueprint

This work presents "The Cosmic Landscape Map: Taiji Duality & Geometric Morphogenesis Blueprint", establishing a comprehensive 5-layer cosmological map where physical distance fundamentally emerges and evolves through geometric morphogenesis in accordance with the Fibonacci sequence and the Golden Ratio (φ). Key theoretical highlights across the 5 layers include: 1. Layer 1 (Microscopic Seed Zone, x → 0⁺): Resolves UV singularities by demonstrating that the microscopic limit translates to k → +∞ and u → -∞. The field manifestation g(x) = φᵏ smoothly ascends the Golden Ratio scale ladder, eliminating coordinate singularity divergences at the Big Bang boundary.2. Layer 2 (Critical Pivot & Quantum Heart, $x = 1$): Demonstrates that at the anchor $x = 1$ (r = r₀), amplitude growth freezes (β(g^*) = 0) while the imaginary term i2π in the complex anomalous dimension Δeff = lnφ + i2π drives pure $U(1)$ phase rotation ei2π u, generating quantum mechanical wave functions and inherent uncertainty.3. Layer 3 (Growth Axis of Distance, u = ln(r/r₀)): Establishes spatial distance as an active evolution axis. Continuous scale invariance breaks down into Discrete Scale Invariance (DSI) with exact scale multiplier λ = φ along a Golden Logarithmic Spiral.4. Layer 4 (Universal Force Mapping): Unifies all fundamental forces across decay exponents $p > 0$ via the Taiji Transformation g(x) = x⁻ᵖ = φᵏ, establishing base duality φᵏ e⁻ᵖᵘ with strictly locked scale index k = -p ln x/lnφ.5. Layer 5 (Macroscopic Cosmos & Asymptotic Flatness, x → ∞): Governed by harmonic confinement f(r) ~ -r², the macroscopic limit (k → -∞, u → +∞) gently settles into asymptotic flatness (g(x) → 0⁺), maintaining global self-similar geometric structure. This paper synthesizes and builds directly upon our theoretical series:- Yu (2026), Zenodo DOI: 10.5281/zenodo.21965279- Yu & Liang (2026), Zenodo DOI: 10.5281/zenodo.22004755- Yu & Liang (2026), Zenodo DOI: 10.5281/zenodo.22019915