One Cycle, Many Dilations Dual Closure, Temporal Resistance, and the Origin of Spectra, Vacuum, and Black Holes in the Alpha Void Ontology Paper 13

This paper develops a unified account of spectral structure, the quantum vacuum, and black holes within the Alpha Void Information Ontology (AVIO). Persistent structures are shown to obey a dual integer-closure condition (spatial and temporal) around Alpha Void Tears. Satisfaction of this condition forces every locked mode to propagate at \(c\), with the entire observed frequency spectrum arising solely as a distribution of local temporal resistance \(\alpha\). Modes that remain marginally superluminal cannot meet the dual condition and constitute the unlocked quantum foam. The same continuous parameter \(\alpha\) reaches a critical value at the Schwarzschild radius, recovering the standard gravitational time-dilation factor, the event horizon, and Hawking temperature as exterior manifestations of extreme temporal resistance. The framework therefore collapses spectroscopic diversity, the vacuum, and black-hole physics to a single ontological field: the spatial variation of temporal resistance required to keep one fundamental cycle phase-locked around Alpha Void Tears.