Three-bit parity with a single conductance threshold: the role of multiple scattering in passive three-arm interferometers

This non-peer-reviewed theoretical and computational preprint studies a passive, phase-coherent electronic network with three individually blockable parallel arms and a single conductance-threshold readout for three-input parity. It gives analytic parity solutions for a symmetric junction family, including a coupling bound for unit transmission in all odd configurations, and examines the role of internal multiple scattering and sensitivity to phase errors. The work presents an idealized scattering model, not a fabricated device or experimental demonstration. Classical coherent waves can realize the same interference functions; no quantum-computing advantage is claimed.Substantial assistance from Claude (Anthropic) and ChatGPT (OpenAI) in calculation, coding, mathematical development and manuscript work is disclosed in the manuscript. Marc Wäsche is the sole human author. The mathematical proofs and complete numerical study have not received independent human peer review. Supplement S1 contains LaTeX equation sources; supplement S2 contains source scripts, reference results and verification instructions.