DARK MATTER AS SPECTRAL-CONSISTENCY EXCITATIONS IN GRAND CONSISTENCY THEORY

Abstract

This paper develops a candidate dark-matter realization within Grand Consistency Theory (GCT), in which dark matter is interpreted as a stable spectral excitation of the theory’s microscopic consistency structure rather than as an independently introduced particle sector. The construction links the proposed dark sector to the discrete geometry, spectral structure, and residual symmetries already present in GCT. A protected two-state spectral sector provides a mechanism for stability and predominantly inelastic interactions. The framework identifies correlated candidate scales corresponding to a dark-matter mass of approximately 294 GeV, a consistency-mediator scale of approximately 1 GeV, and an internal state splitting of approximately 340 keV. The paper distinguishes explicitly between exact combinatorial results, conditional spectral statements, and physical predictions that require further microscopic verification. In particular, the proposed mass and splitting become genuine predictions of GCT only if the required neutral two-state spectral structure and associated mixing emerge from the complete finite spectral operator. The framework therefore provides a falsifiable research program connecting three levels of investigation: microscopic spectral structure, cosmological dark-matter abundance, and inelastic direct-detection signatures across different nuclear targets.