On the Absolute Spectral Rigidity of Automorphic L-Functions Over Rigid Calabi-Yau Orbifolds: An Algebraic Proof of the Exact Zeta Spectrum

We present a purely algebraic proof demonstrating that the non-trivialzeros of the Riemann zeta function, and more generally the spectral poles of automorphicL-functions associated with rigid Abelian varieties, are identically locked to thecritical line Re(s) = 1/2. Eschewing continuous analytic extensions and unboundeddifferential operators, we construct an unconditional arithmetic framework over the6-dimensional twisted orbifold T^6/Z_3. Under the global rigidity constraint h^(2,1) = 0,the continuous topological classes freeze into algebraic cycles, degenerating the Jacobi-Gauss theta identity into a singular arithmetic period I_CM = Γ(1/3)^3 / 2^(4/3π)^2).By applying Deligne’s Weight Theorem to the global Frobenius endomorphismover finite fields, we establish an absolute local modulus| α_(p,j) |= p^(1/2). We rigorouslyprove via the Adelic Trace Formula that the global spectrum is synthesized purelyby the coherent superposition of these discrete local phases, mathematically obstructingany transcendental spectral leakage. Crucially, the mathematical proofspresented herein are strictly independent of any physical or cosmologicalconjectures. However, as a profound mathematical corollary, we demonstrate thatwhen quantum gauge theories are formally pulled back onto this rigid arithmetic background,continuous infrared divergence is structurally obstructed. This establishes astrictly positive mathematical lower bound for the Yang-Mills mass gap (Δm > 0),dictated by the fundamental automorphic resonance γ1 and the geometric invariantICM, thereby providing an exact algebraic substrate for Topological Quantum FieldTheory (TQFT).