Two Invariants a Structural Argument for a Kinematic Floor

Pairwise rest ends a comparison; it does not end the temporal relation. Special relativity places these at opposite ends of a single velocity interval, but they are objects of different kinds. Zero relative velocity is an attainable, partner-dependent relation between two selected worldlines, realizable for indefinitely many kinematic states. The null boundary is an unattainable, partner-independent limit of the timelike domain itself, approached through an unending sequence of ordinary states and never occupied. This paper argues that the two ends of relativistic clock response are not established by the same kind of claim. The upper end is fixed geometrically: null intervals, vanishing proper time, no timelike worldline becoming null. The lower end is fixed by a comparison — two worldlines selected, their relative motion removed, the ratio reporting no difference. Only the first is a statement about the domain. Whether the apparent asymmetry is also an asymmetry of the world is therefore an open question rather than a settled result. The proposed completion introduces a second partner-independent boundary, a kinematic floor βf = vf/c, sharing the relevant properties of c: unattainable, frame-indifferent, and selecting no distinguished timelike direction. The physical domain becomes βf < β < 1, open at both ends. A minimal one-scale realization multiplies the Lorentz response by a floor factor diverging as β approaches βf, reducing to the standard law wherever β is far above the floor. A structural consequence follows immediately: in special relativity the minimum of the clock response sits on the boundary of the domain, which is why that value acquires the appearance of an endpoint; in the completion it sits in the interior, with divergence at both bounds. The structural claim and the particular realization are kept separate throughout. The framework carries one free scale, bounded by any null clock-comparison result, and one open exponent. Reciprocity of the Lorentz factor is explicitly rejected as a route to the floor.