A Constructive Zero-Only Cosmogony via Minimal Extension, Local Relational Dynamics, and Emergent Geometry

We propose a constructive framework for “something from nothing” in which absolute nothingness is modeled as a closed one-element algebra and nontriviality enters only through a minimal closure-breaking extension. The framework separates ontic existence from measurement reports, defines an accumulation index without presupposed time, and constructs emergent geometry from local relational structure derived from correlation-like weights. We introduce a degree-controlled threshold rule that fixes graph sparsity and prevents degeneracy into complete graphs or disconnected dust. A computable set of observables is obtained from graph distances and Laplacian harmonics, yielding numerical evidence that (i) locality is structurally necessary for low-dimensional scaling and (ii) the low-mode spectral shape converges with system size. Topology diagnostics show an emergent closure signature consistent with a closed three-manifold; current distance statistics correlate more strongly with T3 than S3, motivating additional invariants for topology discrimination. We include a program-level proposition giving a Friedmann-like closure relation in a continuum limit as a formalization target, and we replace previously free placeholders by operational definitions suitable for calibration once a unit mapping is fixed.