Slope Traversal and Time: A Minimal Statement of Gravitational Phase-Cancellation Theory (gPCT)

This note presents a minimal geometric formulation of Gravitational Phase-Cancellation Theory (gPCT). The theory proposes that quantum-state collapse symmetry is locally modulated by the slope of gravitational phase, a scalar quantity derived from the gravitational potential, as it varies along an observer’s worldline. Local asymmetries accumulate as slope-dependent contributions, while global neutrality is preserved through phase cancellation across complete gravitational cycles. The paper introduces three postulates: Slope Memory — clocks accumulate gravitational phase-slope asymmetry along their worldlines. Dual Recursion — curvature and time co-determine one another through a symmetric differential recursion. The White Equation — a conjectured invariant linking slope derivatives and curvature recursion, yielding 1/2π in the weak-field limit. From these postulates, the theory recovers a cos² collapse law that depends explicitly on gravitational phase slope. This dependence cancels globally through phase cancellation, preserving classical statistical neutrality. A natural consequence of the formulation is the emergence of an intrinsic Arrow of Time. Because gravitational phase evolves monotonically along a worldline, slope-dependent collapse modulation is not symmetric under time reversal, even though global neutrality is maintained. The note is deliberately brief and self-contained, presenting only the minimal structure required to state the theory and its consequences.