GQR17 v3.1: Synthetic Gauge Fields and Reciprocal-Port Nonreciprocity in Open Networks

QGRE Scientific Portfolio CorePost-GQR89–91 Architecture Audit RevisionSeptember 2026 AbstractWe present the finalized, audited GQR90-compliant refactoring of GQR17. We eliminate historical ad-hoc non-Hermitian Hamiltonian artifacts (H = ̸H†) by constructingnonreciprocal open-system transport strictly through physical time-reversal symmetry (T )breaking. In Model A (the primary core), nonreciprocity is diagnosed by reciprocal source–drain exchange across a 3-site Aharonov–Bohm (AB) interference ring governed by a gaugeinvariant flux Φ. Using transient Liouvillian residence times T1→2(Φ) and T2→1(Φ), wedefine the reciprocal directional contrast ∆T↔(Φ) = T1→2(Φ) − T2→1(Φ) and the normalized residence asymmetry AT (Φ) = ∆T↔(Φ)/[T1→2(Φ) + T2→1(Φ)].We prove thegauge-invariant mirror-flux covariance relation ∆T↔(−Φ) = −∆T↔(Φ) and establish theZeno-robust strong-dephasing limit AT (Φ) → 0. Finally, Model B introduces chiral bathengineering via counter-rotating jump operators L± to explicitly contrast coherent loopnonreciprocity against reservoir-engineered nonreciprocity.