This work presents a self-consistent modular theta topological framework rooted in Ramanujan's mock theta functions and the holographic principle, designed to unify general relativity, quantum mechanics, and cosmological phenomenology within a single number-theoretic structure. Dark matter is reinterpreted as the nonlocal gradient of holographic entanglement entropy density (defined as spacetime eigenweight), which mimics the observed gravitational dynamics of galactic and cluster scales without invoking exotic fundamental particles. The Big Bang is redefined as a modular topological phase transition: a non-perturbative analytic continuation event of the moduli field τ across a number-theoretic boundary, which naturally resolves the primordial singularity of classical cosmology while preserving cosmic information conservation. We emphasize that this work only verifies the mathematical self-consistency and theoretical plausibility of the proposed framework, without making empirical claims or asserting its direct correspondence to physical reality. All derivations are grounded in the intrinsic analytic and modular properties of Ramanujan's mock theta functions, with no ad hoc parameter fitting or fine-tuning. This framework is presented as a theoretical exploration of unifying gravity, quantum information, and cosmic evolution via number theory, rather than a confirmed physical model.
leo Jony (Sat,) studied this question.