Synchronous Spatial Linkage: A Geometric Necessity of Continuous Spacetime

Author: Zhang Xiaohui

🔷 Abstract

If space is truly continuous—as assumed by all differential geometry and relativistic field models—then any local geometric disturbance must necessarily affect the entire manifold.

This theory introduces a concrete formalism for synchronous spatial linkage, a mechanism in which curvature shifts propagate instantaneously at the structural level, even while energy signals obey relativistic limits.

🧮 Core Equation

$$ {O}(x) = \frac{dK}{dx} \cdot \frac{1}{r^2} \cdot \chi(x) \geq \epsilon $$

• $\frac{dK}{dx}$: Local curvature value
• $r$ : Distance from disturbance origin
• $\chi(x)$ : Geometric resonance or coupling function
• $\epsilon$ : Observability threshold

This expression defines when a remote curvature shift becomes observationally detectable.

🌌 Observational Implications

Predictions

1. Pre-signal distortion of nearby stars

   Celestial bodies within ~100 light-years of a supernova or neutron star merger will exhibit anomalous shifts or instabilities before electromagnetic or gravitational wave signals arrive.

2. Anomalous lensing geometry

   Gravitational lensing regions will display subtle distortions that precede any observable mass redistribution—“ghost lens” effects.

3. Redshift discontinuities in galaxy clusters

   Unexpected redshift steps or “quantized drifts” may occur in large-scale structures due to global curvature rebalance.