Into the City: A Deterministic Operator–Trace and SSB Framework for the Generalized Riemann Hypothesis

We present a fully deterministic proof of the Generalized Riemann Hypothesis (GRH) for
Dirichlet L-functions L(s, χ) using a Standing/Sitting Band Framework (SSBF) that partitions
natural numbers into bands and deterministically seats composites, including pseudo-primes
and Carmichael numbers. We construct a Dirichlet-weighted canonical self-adjoint Hamiltonian
Hχ where the discrete spectrum corresponds precisely to the nontrivial zeros of L(s, χ). The
√
n
seating horizon ensures all eigenvalues lie on the critical line, and the trace formula establishes
spectral completeness without reliance on probabilistic heuristics.
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