Quantum Chaos of Arithmetic Origin: Deterministic L-function Jacobi Hamiltonians exhibit GUE/GOE level statistics without random disorder or classical chaos (v2)

Abstract

We construct explicit one-dimensional tight-binding (Jacobi) Hamiltonians whose recurrence coefficients are generated purely from the arithmetic of completed L-functions (Riemann zeta, Dirichlet beta, Ramanujan delta), via circle sampling, moments of the log-derivative Taylor coefficients, and the orthogonal-polynomial (Gram-Schmidt) construction. No zero location, prime table, random number, or fitted parameter enters the construction. Despite being deterministic, one-dimensional, disorder-free, and having no classical chaotic limit, the locked spectra display Wigner-Dyson (GUE/GOE) level repulsion, a spectral form-factor ramp, extended eigenstates, and collapse of the signal under coefficient shuffling and under a percent-to-ten-percent hardware-noise threshold. v2 additions: pure-zeta finite-size scaling extended to N=100 via a 1300-digit construction (b_n^2 > 0 on all 99 off-diagonals; 55 locked zeros at relative error ~1e-15..1e-16; locked gap ratio 0.61-0.62 from N=22 up with zero sub-0.3 gaps); and an Eisenstein E4 discriminative control L(E4,s)=zeta(s)zeta(s-3), whose zeros lie on Re(s)=1/2 and Re(s)=7/2 off the symmetry center: the identical pipeline reproduces Xi_E4(2)=1/72 to ~15 digits but the moment sequence turns negative at order 8 and the Jacobi chain fails at order 4, showing long positive-definite chains co-vary with on-line zeros. The bundle also ships the Quantum Arithmetic Benchmark Dataset (five tridiagonal Hamiltonians with metadata and a loader) as a turnkey quantum-simulation target. All results are finite-truncation numerical evidence; the spectra are computer-generated, not measured; 'quantum chaos of arithmetic origin' is a physical hypothesis, not an established fact. The construction assumes neither RH nor GRH.