Time as Ordered Update

Canonical preprint manuscript. Paper 3 of 12 in Series A of the Theory of Difference / Information Update Physics (ToD/IUP) Foundational Physics Program. This paper follows Paper 1, “Difference as the First Physical Primitive” (DOI: 10.5281/zenodo.21025246), and Paper 2, “Update as the Minimal Dynamics of Reality.” Paper 1 established physical difference as the minimal condition for physical articulation and constructed physical states as quotient classes. Paper 2 introduced admissible non-null update as the first active layer of physical dynamics. Paper 3 asks the next structural question: what must be in place before time can function as a physical variable? The answer proposed here is ordered update. Time is not introduced as a background container, universal parameter, primitive flow, coordinate axis, or psychological present. At this layer, physical time is reconstructed as a constraint-supported, trace-carrying, registerable order of updates capable of supporting comparison among update chains. The central claim is a necessity claim, not a sufficiency claim: without physically meaningful update order, no first-layer physical time can be defined. No before/after relation, clock reading, duration, history, temporal direction, simultaneity, temporal metric, or global time assignment has physical content unless supported by ordered, trace-bearing, and comparable update. The manuscript defines update occurrences, update chains, pre-temporal dependency relations, trace structures, registration relations, clock regimes, duration as comparative update separation, regime-relative simultaneity, local and global time, temporal direction, and the zero-update-order temporal silence theorem. This paper does not derive all temporal physics. It does not claim to derive Lorentz transformations, a spacetime metric, thermodynamic entropy, quantum time, causal cones, or the observer-level experience of the present. It establishes the minimal ordered-update condition that later temporal, spatial, causal, and geometric structures must inherit.