Version vectors: distinguish later from concurrent

Give each participating writer a stable identity and an increasing local event counter. A vector entry records the prefix of that actor’s updates incorporated into the relevant history. Before creating a new version, combine the causal context actually read or received, then increment the origin actor’s component. The scope matters: an object-version vector, a process-wide vector clock, and a replication stream watermark can have different meanings. Comparing integers is easy; defining which events the integers summarize is the important design work.

Vector v is no later than w when every component of v is at most the matching component of w. Strict domination also requires at least one smaller component. If neither dominates, the versions are concurrent under this model. They need not have occurred at the same physical instant. A disconnected update from yesterday can be concurrent with today’s update when neither observed the other. A total timestamp ordering would hide that causal distinction by selecting a winner even when the histories are incomparable.

The componentwise maximum summarizes both represented prefixes. It does not by itself decide what two conflicting application values mean. A multi-value register can retain both incomparable versions for explicit resolution; a CRDT may combine them using type-specific rules. If an application resolves two siblings, its replacement must carry the context of both so subsequent readers know the new version supersedes both histories. Omitting one sibling’s context can make that supposedly resolved sibling reappear on the next synchronization.

A compact vector is valid only under its identity and prefix assumptions. Reusing an actor identity after losing its counter can make an old event indistinguishable from a new one. Pruning entries or compressing sparse histories also needs a justified rule. Dotted version vectors separate a specific new event from causal context and can address practical sibling-tracking issues, but their correctness comes from the actual protocol. Do not implement arbitrary vector truncation merely because a drawing becomes crowded.

With r actors and fixed-width counters, the counter payload alone grows proportionally to r, before actor identifiers and encoding overhead. A mobile system with unbounded transient writers therefore needs an explicit membership and compaction design. Clients must return causal context when the API requires it; a write without the context it read can look concurrent even if a human intended a replacement. Test interleavings with delayed delivery, repeated messages, restarted actors, and clients that accidentally drop their version token.

The geometry lab can show why two-coordinate comparison is not a single numeric ranking. Reset, set angle to 0 degrees and magnitude to 2, predict projections (2,0), then Step. Change angle to 90 degrees with magnitude still 2 and predict (0,2). Neither coordinate pair dominates the other componentwise. The lab draws a continuous 2D vector, not a causal clock; rounding near zero and its angular interpolation are irrelevant to exact event counters. Write the discrete history alongside it.