The Relational Vortex Principle (RVP): A General Condition for Rotational Coherence in Asymmetric Transport Systems

January 2026 Update This revision refines the internal structure of the coherence corridor [ \sqrt{e},\, 7/4 ] by identifying three distinct organizational thresholds: geometric coherence (\varphi \approx 1.618), the duality boundary (\sqrt{e} \approx 1.649), and an optimal stability point (\lambda = e/\varphi \approx 1.68). New cross-domain analyses (including Kerr geometry and damping behavior in coherent systems) are incorporated as supporting validation, while the original RVP framework, scope of validity, and falsification criteria remain unchanged. _______________________________________________________________________________________________________________________________________ The Central Inequality (Vortex-Onset Condition) Vortex formation occurs when the asymmetry-weighted transport drive exceeds the effective relaxation capacity of the medium: Transport Asymmetry: directional imbalance in flow, drift, or flux Resistance Asymmetry: non-uniform mass, density, friction, or gradient barriers Environmental Factors: forcing, shear, heating/cooling, external fields τ₍relax₎: time the medium needs to restore equilibrium This inequality is the universal onset threshold for rotational coherence. 2. What the Inequality Means Physically When a system tries to push material through an uneven resistance field, and the environment adds extra forcing or drive, the medium can no longer re-equilibrate linearly. Rotation emerges as the self-correcting response, redistributing stress and stabilizing flow. Rotation = the “pressure valve” of asymmetric transport. 3. Universal Directionality Rule Once the inequality is met: The gradient sign sets the vortex handedness The spatial asymmetry sets the curvature The boundary geometry sets the spiral structure This rule holds across fluids, plasmas, chemical media, and astrophysical disks. 4. Coherence Window (Dynamic + Structural Modes) Experiments show that rotational coherence persists only inside a narrow coupling corridor: \lambda \approx 1.70 \pm 0.05 Structural Mode: mean flow and vorticity align (ϕ₍F,ω₎ ≈ 0°). Dynamic Mode: time-evolution locks into a quarter-cycle delay (|ϕ₍Ux,Uy₎| ≈ 90°). Below this window → coherence dissolves. Above it → over-locking collapses rotation. Inside → stable vortex. 5. Universality Across Domains This inequality collapses to familiar control parameters: Fluid mechanics: Reynolds number thresholds Plasma drift: asymmetric E×B transport and shear Reaction–diffusion: inhibitor–activator imbalance (Dᵤ/Dᵥ) Atmosphere / oceans: shear + Coriolis imbalance Astrophysical disks: angular-momentum transport vs cooling time Each domain is simply a special case of the RVP inequality. 6. Why RVP Matters Provides a single structural law behind vortex formation Predicts when and why rotation emerges Explains coherence across micro-, meso-, and astrophysical scales Offers a falsifiable inequality linking gradient geometry, relaxation, and asymmetry Connects structural and dynamic coherence through the same λ corridor 7. Reference Experiment De Jesús, Elias. Dynamic π/2 Lock near the 1.7 Threshold: Ring–Star Consensus Experiment (2025). Zenodo. https://doi.org/10.5281/zenodo.17582293 This work is exploratory and open, released to enable evaluation, extension, refinement, or reinterpretation by the scientific community. Contact: dejesuselias10@gmail.com Author Contact:LinkedIn: https://www.linkedin.com/in/reflectionsofinnerlight/