T67 develops the effective phase-smoothing mechanism that reconciles the discrete holonomy structure of T66 with the continuous observable interference geometry appearing in T61--T64. The theorem models the observable phase as a composite quantity, \₎₁ₒ=₇₎₋+ₒₘ₌, the intrinsic holonomy contribution carries discrete \ (Z₄\) -type rotational structure while the symmetric transport sector contributes a continuous smoothing component. Because the symmetric and antisymmetric generator sectors do not commute, \[ₓ, R0, \]The observable phase geometry becomes effectively continuous after mediated reduction and symmetric-sector mixing. The theorem, therefore, establishes a structural mechanism through which discrete microscopic transport holonomy can coexist with experimentally continuous interference behaviour. T67 is architecturally important because it stabilizes the discrete holonomy framework introduced in T66 without discarding the underlying transport discreteness. The theorem shows that the observable interference phase is not a primitive microscopic quantity but an emergent effective observable generated by mixed-sector transport dynamics and reduction effects. Rather than eliminating the discrete holonomy layer, the smoothing mechanism embeds it within a continuous effective observable geometry produced through admissible reduction and averaging. Status: solid for the mixed-sector phase decomposition and the effective smoothing mechanism under the stated operator assumptions; conditional on the mediated averaging framework and dominance of the symmetric transport sector; speculative for any physical claim regarding hidden microscopic phase discreteness in actual quantum systems.
Craig Edwin Holdway (Sat,) studied this question.