Relational Schwarzschild Metric v3.1-Fusion: Bridging General Relativity, LoE Resonance, and Cosmological Coherence

The paper “Relational Schwarzschild Metric v3.1-Fusion” extends General Relativity by embedding it in the Logic of Existence (LoE) framework, where spacetime curvature arises from relational coherence rather than geometry alone. Gravity is interpreted as synchronization among existence nodes, governed by the meta-extremal principle of minimal existential cost, $\delta J=0$.

By introducing a relational operator

RLoE=(1−rsr)+αΦorderΦchaos,\mathcal{R}_{\text{LoE}} = \left(1 - \frac{r_s}{r}\right) + \alpha \frac{\Phi_{\text{order}}}{\Phi_{\text{chaos}}},RLoE=(1−rrs)+αΦchaosΦorder,

the classical Schwarzschild metric becomes dynamic, linking geometric curvature with informational fields of order and chaos.

This coupling yields small corrections to gravitational dynamics and provides theoretical mechanisms for Dark Matter (as gradients of relational order) and Dark Energy (as large-scale synchronization loss). The framework unifies geometry, information, and observation through the Observer Boundary Term $\mathcal{B}_{obs}$, suggesting that physical reality is a coherent, self-referential network where existence and measurement co-emerge.

Keywords: Logic of Existence, General Relativity, Relational Gravity, Schwarzschild Metric, Coherence Field, Dark Matter, Synchronization Loss, Informational Cosmology.