Cosmological Rupture: The Big Bang as a Physical N1 Boundary

We define the Big Bang as a physical N1 boundary—a structural limit of admissibility—rather than a dynamical event or a stochastic fluctuation. Applying the TNA framework, we demonstrate that the origin of the universe constitutes a non-derivable rupture that invalidates internal spacetime dynamics (N0), rendering cosmological intelligibility fundamentally retrodictive. This paper extends the Theory of Structural Necessity (TNA) to cosmology, providing a formal interpretation of the Planck scale as a structural threshold ($S$). We argue that the Big Bang is not an instance of deterministic chaos or noise, but a boundary where the state space $X$ and the transition function $F$ cease to be well-defined. By distinguishing between internal irreversibility (entropy) and structural invalidation (rupture), we show that quantum gravity models may regularize the mathematical singularity but cannot eliminate the structural non-derivability across the $N_1$ boundary. The framework clarifies why the "before" of the Big Bang lacks operational meaning and establishes that the early universe is intelligible only through retrodictive reconstruction, not forward derivation. Core Reference: This work is an integral component of the Theory of Axiomatic Necessity (TNA) framework developed by Claudio Bresciano. It formalizes specific domain constraints within the global $N_1$ structural logic. For the complete axiomatic foundation, refer to the TNA System Manifest (DOI: 10.5281/zenodo.19115157) and the Core Theory (DOI: 10.5281/zenodo.18098558)