Prime-Shift Magnetic Operator

# Prime-Shift Magnetic Operator (PSMO) This document is part of the **Quansistor Field Computing (QFC)** research program. The **Prime-Shift Magnetic Operator (PSMO)** is a self-adjoint operator frameworkacting on truncated arithmetic Hilbert spaces. It extends classical prime-shiftdynamics by introducing **non-gauge-trivial phase structure**, designed to producemeasurable **cycle holonomy** on the arithmetic graph. ## ScopePSMO is introduced as a **spectral probe**, not as a proof mechanism.No claim is made regarding the Riemann Hypothesis or the identification of spectrawith the zeros of the Riemann zeta function. The focus is on:- verifiable operator construction,- gauge-invariant observables (Wilson loops),- reproducible numerical protocols,- strict falsifiability and control comparisons. ## StructureThe chapter develops:1. the arithmetic graph and prime-shift core,2. phase structure beyond gauge twists (magnetic holonomy),3. a minimal observable suite (spectral flow, Wilson loops, traces),4. a reproducibility standard with explicit controls,5. falsifiability and persistence criteria,6. integration into the broader QFC / SMRK framework. ## How to use- Treat PSMO as an **experimental operator module within QFC**.- Always compare against **untwisted, gauge, and random-phase controls**.- Interpret spectral behavior **only after** verifying nontrivial holonomy.- Publish results as replayable artifacts (configs, eigenvalues, Wilson loops). ## StatusConceptual framework and reproducibility protocol.Numerical exploration is ongoing; negative results are explicitly acceptable. ## LicenseSee accompanying LICENSE file.