Structural Density Correspondence (SDC): Observable Consequences of a Minimal Structural Framework

This work presents a minimal structural framework, Structural Density Correspondence (SDC) v1.6, in which observable physical quantities emerge from a scalar structural field C(x).

The framework proposes that gradients, fluctuations, and boundary formations of the structural field naturally correspond to effective forces, densities, and observable distinguishability. In this view, physical observables are not introduced as fundamental laws, but arise from spatial organization of an underlying structural quantity.

Key correspondences include:
- ∇C(x): effective force / gravity
- |∇C(x)|^2: effective density
- δC(x): microscopic fluctuation
- emergent boundaries: observable interfaces
- I: readable distinguishability

The paper does not attempt a full microscopic derivation, but instead provides a coherent structural mapping between abstract quantities and observable interpretations. This minimal approach is intended as a conceptual starting point for connecting geometric structure and observable physics.

All figures included illustrate:
(1) structural-to-observable mapping,
(2) gradient-force relations,
(3) density from spatial variation,
(4) boundary-mediated information,
(5) correspondence between SDC quantities and observables.

Version: v1.6 (preprint)