Non-Hermitian Spectral Asymptotics of Hyper-Combinatorial Spin-Foam Lattices: Rigorous Derivation of Causal Violations via the Cohomological Instability of Infinite-Valence Intertwiners

Mathematical Applications of Science Fiction We present a rigorous derivation of the spectral instability inherent in hyper-combinatorial spin-foammodels when extended to the infinite-valence limit (v → ∞) under non-Hermitian boundary conditions.By constructing a generalized Gelfand-triple framework for the Hilbert space of graph-dependentintertwiners, HΓ, we analyze the asymptotic behavior of the volume operator ˆV perturbed by acomplex-valued Immirzi parameter γ ∈ C \ R. We demonstrate that the resulting non-HermitianHamiltonian HN H exhibits a spectral explosion characterized by the migration of eigenvalues into theupper complex half-plane, leading to a breakdown of unitarity. Furthermore, we employ sheaf-theoreticcohomology to map these spectral anomalies to topological defects in the underlying simplicial complex.The central result establishes that for intertwiners of valence N > Ncrit, the first cohomology groupH1(Γ, FN H ) becomes non-trivial, implying the existence of closed timelike curves (CTCs) at thePlanck scale. This provides a mechanism for causal violations in quantum gravity regimes dominatedby high-density crystalline computation nodes.