Testing Fixed-Point Quantum Histories: Operational Protocols, Consistency Criteria, and Experimental Limits

This paper develops a pre-registered laboratory protocol for testing a central structural commitment of the Fixed Point Formulation (FPF) of Ridley and Adlam (2025). The FPF proposes that a quantum event is a location in a history where the forward-conditioned and backward-conditioned density-matrix reconstructions — both derived from the same pre- and post-selected ensemble via weak measurements on a spin-oscillator platform — satisfy a bilateral consistency condition to within a pre-registered trace-norm tolerance. The protocol runs in three conditions: a compatible post-selection (final state aligned with the decohered intermediate pointer-basis eigenstate), an adversarial post-selection (final state misaligned by a pre-registered angle satisfying a SPAM-floor constraint), and a protocol-invariance stress test using the Kirkwood-Dirac framework to check whether any consistency verdict is stable across informationally equivalent weak-measurement implementations within a declared KD equivalence class. *** The evidentiary structure is deliberately asymmetric: a positive result — consistency in the compatible condition, failure in the adversarial condition, and within-class stability — is consistent with the FPF but does not uniquely confirm it, since the Two-State Vector Formalism can produce the same pattern. However, a persistent negative result in the compatible condition, beyond the pre-registered noise budget, places the FPF's bilateral-constraint claim under targeted protocol-specific pressure that cannot be straightforwardly attributed to measurement noise. Additionally, the paper demonstrates that decoherence is necessary but not sufficient for fixed-point formation — the adversarial condition is specifically designed to distinguish the FPF's bilateral-constraint picture from a purely decoherence-based account of classicality.