The Pauli Exclusion Principle and Informational Geometry: An Injectivity Constraint in Viscous Time Theory

The Pauli exclusion principle is traditionally introduced in quantum mechanics as a postulate encoded in the antisymmetry of the fermionic wavefunction. While extraordinarily successful, this formulation leaves open a deeper question: why must nature forbid the perfect overlap of identical fermions? In this work, we propose a reinterpretation of Pauli exclusion within the framework of Viscous Time Theory (VTT), where physical law emerges from the geometry of informational state space under constraints of memory, recoverability, and causal trace preservation. We propose that the coincidence of two identical fermionic states can be interpreted, in informational-geometric terms, as a loss of injectivity of the causal mapping, i.e., to an informational singularity where distinct histories become non-separable. To prevent this collapse of recoverability, the joint state manifold naturally develops a “diagonal barrier”: a forbidden submanifold where the informational cost diverges and admissible trajectories are repelled. Within this perspective, antisymmetry of the wavefunction appears not as the cause of exclusion, but as its mathematical symptom. Within this perspective, Pauli exclusion can be interpreted as a geometric and informational constraint rather than a primitive quantum axiom. The framework further suggests a unified interpretation of the difference between fermions and bosons: the former may be viewed as carriers of identity-bearing, non-overwritable informational structure, while the latter correspond to additive excitations that do not threaten causal injectivity. In this way, the exclusion principle appears as a consequence of informational geometry in a universe characterized by viscous time and memory.