The Cosmic Landscape Map: Taiji Duality & Geometric Morphogenesis Blueprint
Year: 2026
Type: preprint
Abstract: 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 ($\phi$). Key theoretical highlights across the 5 layers include: 1. Layer 1 (Microscopic Seed Zone, $x \to 0^+$): Resolves UV singularities by demonstrating that the microscopic limit translates to $k \to +\infty$ and $u \to -\infty$. The field manifestation $g(x) = \phi^k$ 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 $x = 1$ ($r = r_0$), amplitude growth freezes ($\beta(g^*) = 0$) while the imaginary term $i2\pi$ in the complex anomalous dimension $\Delta_{\text{eff}} = \ln\phi + i2\pi$ drives pure $U(1)$ phase rotation $e^{i2\pi u}$, generating quantum mechanical wave functions and inherent uncertainty.3. Layer 3 (Growth Axis of Distance, $u = \ln(r/r_0)$): Establishes spatial distance as an active evolution axis. Continuous scale invariance breaks down into Discrete Scale Invariance (DSI) with exact scale multiplier $\lambda = \phi$ along a Golden Logarithmic Spiral.4. Layer 4 (Universal Force Mapping): Unifies all fundamental forces across decay exponents $p > 0$ via the Taiji Transformation $g(x) = x^{-p} = \phi^k$, establishing base duality $\phi^k \iff e^{-pu}$ with strictly locked scale index $k = -\frac{p \ln x}{\ln\phi}$.5. Layer 5 (Macroscopic Cosmos & Asymptotic Flatness, $x \to \infty$): Governed by harmonic confinement $f(r) \sim -r^2$, the macroscopic limit ($k \to -\infty$, $u \to +\infty$) gently settles into asymptotic flatness ($g(x) \to 0^+$), 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
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203873647
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