Temporal-Stability Requirements for Sustained Postselected Gravitational Repulsion: A Chronos/X Extension of Quantum-Gravity Interference

A recent quantum-gravity proposal by Saldanha, Marletto, and Vedral shows that two individually attractive gravitational interaction branches can, through coherent interference and postselection, produce a conditional momentum shift directed away from the source mass. The effect is not a conventional repulsive gravitational force, but an anomalous postselected momentum outcome whose existence depends on sustained coherence between gravitationally correlated quantum histories. This paper examines whether such an apparent repulsive-gravity signal can persist over an extended interaction period without an explicit temporal-stability condition. The original postselected momentum expression is generalized by introducing a time-dependent coherence factor containing both visibility loss and accumulated relative-phase drift. An exact threshold is derived for the minimum effective coherence required to preserve the negative conditional momentum shift. A Chronos/X stability extension is then introduced. The model assumes a physical temporal equilibrium characterized by the dimensionless stability constant χ = 0.5512855984. A general candidate stabilization value q is compared with χ. It is shown that, within the proposed dynamics, q = χ eliminates persistent equilibrium mismatch, while every q ≠ χ produces a nonzero asymptotic temporal offset. This offset generates cumulative phase drift and exponential coherence loss, causing the postselected negative-momentum signal eventually to cross zero and return to an ordinary attractive gravitational mixture. A toy numerical parameter sweep compares χ with several nearby candidate values. In the idealized model, χ preserves the negative conditional momentum branch, whereas displaced candidate values fail after finite interaction times. The failure time decreases as the magnitude of the mismatch |q − χ| increases. The paper proposes an experimental protocol in which candidate stability values are scanned while the interaction duration is varied. The Chronos/X prediction is that the measured coherence-loss rate forms a minimum centered at χ and that χ maximizes the lifetime of the postselected negative-momentum signal. The work is presented as a falsifiable theoretical extension of the gravitational-interference proposal. It does not claim that the original authors derived or assumed Chronos/X, nor that the toy model independently establishes χ as a physical constant. Rather, it identifies a possible experimental route for testing whether sustained gravitational quantum interference requires a distinct temporal-stability equilibrium.