Silent Mass Theory Dark Matter as Frozen Topological States from a Cosmic Glass Transition

We introduce a rigorous mathematical framework for the Cosmic Glass Transition in Δ-Field theory as a way to explain the nature of dark matter.In this approach, knot-like configurations are described by an energy function that includes both elastic geometric terms and topological barrier terms.By giving the space of knots an energy-dependent Riemannian metric, we show that the time required for a knot to change its topology diverges during cosmic cooling, following an Arrhenius-type law.We prove the Freeze-out Theorem, which states that once the relaxation time becomes longer than the age of the universe, the knot configuration can no longer explore its possible shapes. It becomes trapped in a local energy minimum and effectively turns non-ergodic. These “Frozen Knot States” obey the Silent Mass Condition — they are neutral, pressureless, and topologically static — making them physically indistinguishable from cold dark matter.Finally, we propose the Dark Matter Identification Theorem, which states that dark matter is precisely the set of these Silent Mass configurations.