Derivation of the quenched offset-and-flight-time distribution

Derive the setting-independent joint density ρ of frozen per-station lattice offsets and flight times from a physical formation process for the moiré phase-locking mechanism.

Background

The moiré phase-locking mechanism uses a setting-independent distribution ρ over frozen apparatus offsets and flight times. In the paper, ρ is optimized numerically by linear programming over discretized offset grids, flight times, and coupling scales to obtain the reported measurement-dependence and fidelity costs.

Although this optimized distribution enables the deterministic mechanism to reproduce the targeted behavior, its physical origin is not derived. The paper explicitly identifies deriving ρ from a formation process as an open problem, leaving unresolved how such a distribution could arise from a concrete preparation or dynamical history.

References

The optimizer's freedom in \rho is the one non-dynamical ingredient; deriving \rho from a formation process is an open problem, which I state as such.

— The exact price of local realism in CHSH experiments: a measurement-dependence-detection trade-off surface, a moiré phase-locking mechanism that saturates it, and an unmeasured fringe in the fourfold coincidence sum  (2608.18886 - Alai, 19 Aug 2026) in Section 7, paragraph beginning ‘The residual correlation pattern’