Emergence of Macroscopic Scaling Laws from Microscopic Generative Rules: A Four-Part Study on Synergy–Friction Dynamics, Chaos Resistance, and the Identifiability of Inverse Inference

This deposit contains a four-part, AI-assisted independent study on howmacroscopic power-law scaling (Y ∝ N^β) emerges from microscopic generativerules, and whether those rules can be recovered from macroscopic data. Part I introduces a synergy–friction growth dynamics parameterized by a synergyexponent σ and a friction exponent φ, derives a coherence-dome structuregoverning order–disorder transitions, and proposes a periodic table of fifteencross-disciplinary laws on the (σ,φ) plane. Part II models law coupling as coupled ordinary differential equations, proves a1D non-blowup theorem, a 2D no-chaos theorem (Poincaré–Bendixson), and a 3Dboundedness theorem (Lyapunov sum), and establishes an empirical chaosresistance across four coupling configurations with a Mackey–Glass control. Part III proves that microscopic parameters are non-identifiable from a singlerelaxing trajectory (2 observables vs 5 unknowns), shows that activeperturbation recovers exponents exactly, and demonstrates partialidentifiability in coupled systems. Part IV discovers a robustness hierarchy: σ survives ~10% noise, φ is ~10× morevulnerable, and scale coefficients (A,C,μ) are unidentifiable—quantifying thehierarchical information loss of macroscopic compression. All claims are accompanied by numerical verification, explicit tested ranges,acknowledged counterexamples (Lorenz, Rössler, Mackey–Glass), and self-verification checklists. The deposit includes four LaTeX manuscripts,simulation/inverse-identification code, and figures. AI-ASSISTANCE STATEMENT: This work was produced through human–AI collaboration.The AI collaborator (Qwen) contributed methodology, software, formal analysis,and drafting; the human author takes responsibility for the integrity of thework.