BU44 Time under B_U Settlement Sequence, Fixed-Boundary Arrow, and the One-Way Entropy Gradient

Time under B_U: Settlement Sequence, Fixed-Boundary Arrow, and the One-Way Entropy Gradient reclassifies time as a settlement sequence in the projection stratum under a fixed single-universe boundary. The paper does not treat time as an abstract container, an independent fourth-dimensional background, or a direction selected by a special initial condition. It defines time as the lawful retained sequence that begins only after microscopic disturbances have been cleared through zero-mean projection and fast-slow orthogonal separation. Under B_U, the arrow of time is the one-way readout of the fixed boundary B_0, while the one-way entropy gradient is its thermodynamic face. Microscopic reversibility is therefore reclassified as a local notation within a lower-resolution window, not as a global authority capable of overturning macroscopic irreversibility. The paper further repositions the special initial condition as an early readout plane of the fixed boundary, not as the root cause of temporal direction. Fluctuation-based explanations, multi-history models, and branch-time accounts are adjudicated as boundary-misplaced explanations when they attempt to generate global direction without prior boundary standing. The final claim is that physical time is a non-asymptotic settlement sequence: exact clearing prevents residual debt from accumulating into background drift, while lawful retention gives reality a stable temporal order.