A Computable Emergent Spacetime Sector from an Equilibrium Framework Consistency with Standard Physics and Numerical Demonstrations

This repository contains the main article and complete supplementary materialfor a restricted, computable spacetime sector within the ManifestationalEquilibrium (Tajalaei–Yazdan) framework. The central idea is that spacetime-based physics does not represent the fullphysical structure of reality, but rather a closed operational sector emergingfrom a broader equilibrium background. The present work does not attempt toreplace standard physics or derive it from first principles. Instead, itdemonstrates how Newtonian mechanics, relativistic geometry, and quantumdynamics consistently operate within this spacetime equilibrium sector. The main article establishes:• an operational definition of the spacetime equilibrium sector,• consistency with Newtonian, relativistic, and quantum formulations,• and a minimal, fully computable scalar-field realization. The accompanying supplements provide structural completeness:• Supplement N: full numerical implementation, convergence criteria, and falsifiable forbidden regions.• Supplement K: interpretation of fundamental constants (c, ħ, G, gauge couplings) as operational conversion scales within the spacetime sector.• Supplement G: gauge structures as equilibrium redundancies (non-dynamical).• Supplement C: interfaces between spacetime and non-spacetime regimes (horizons, dark sectors).• Supplement U: programmatic map clarifying scope, sectorization, and logical relations between all documents. This work is explicitly connected to the foundational Zenodo release"Manifestational Equilibrium Theory (MET)" (DOI: 10.5281/zenodo.18134323),which presents the broader conceptual framework. The present repository shouldbe read as a focused, mathematically explicit, and testable spacetime-sectorrealization within that larger program. No claims are made regarding a completed theory of quantum gravity, derivationof fundamental constants, or full cosmological dynamics. All assumptions,limitations, and exclusions are stated explicitly to ensure scientific clarityand reproducibility.