When is forcing one linear extension of an event order the right design, and when must the partial order survive?

## What a linear extension is Given a partial order on a set, a **linear extension** is a total order on the same set such that whenever the partial order says `x < y`, the total order agrees. It adds decisions for every pair the partial order left unrelated, and reverses nothing. Three facts shape every design built on this: 1. **Existence.** Every finite partial order has at least one linear extension. 2. **Multiplicity.** It usually has many. Two incomparable elements and nothing else admit exactly two; each additional unordered pair multiplies the possibilities. 3. **Uniqueness only for chains.** There is exactly one linear extension precisely when the order was already total. So more than one extension is the signal that the serialisation is a choice. That third fact is the sharpest test available: if several valid sequences exist, the one shipped is a decision made by the system, not a fact about what happened. ## What imposing one buys Assign every event a position from a single point of authority and the downstream world simplifies dramatically: - consumers hold **one cursor** instead of a causal graph; - replay is **deterministic** — the same sequence rebuilds the same state; - deduplication reduces to comparing positions; - "what is current" is answerable without a merge, because the order now has a maximum. ## What imposing one costs | Dimension | Total order imposed | Partial order preserved | |---|---|---| | Coordination | a single point must assign positions | none required to record events | | Concurrency in the record | erased at write time | retained and inspectable | | Conflicts | resolved implicitly by position | surfaced to a merge rule or the caller | | Consumer complexity | one cursor, simple replay | must handle several heads | | Failure mode | silent loss of one concurrent update | visible conflicts someone must resolve | The second row is the one that gets missed. Once two concurrent events are given positions, nothing downstream can tell that they were concurrent — position order looks identical to causal order. A later-position-wins rule then discards an update that never superseded anything, and no alert fires, because from the record's point of view there was never a conflict. ## Deciding between them 1. **Is a lost concurrent update recoverable or even noticeable?** Where the domain audits or reconciles independently, an occasional silent overwrite may be tolerable. Where the discarded value is the only copy of someone's work, it is not. 2. **Can you afford the coordination?** A single position-assigning authority is a point of contention and of failure. Systems that must keep accepting writes while partitioned cannot have one, which decides the matter for them. 3. **Do the values have a canonical combination?** If the value space forms a lattice, concurrent values have a join and the merge is a function, which makes preserving the partial order cheap for consumers. Without one, every consumer needs domain rules. 4. **How many consumers are there, and who writes them?** Exposed concurrency multiplies across every consumer; that cost is paid once per consumer, forever. ## The middle ground The two options are not exclusive. A system can assign positions **and** retain the causal metadata alongside them, letting simple consumers read the sequence while conflict-sensitive ones ask whether two events were actually ordered. It costs storage and a second read path, and it keeps the option to change the resolution rule later — the one thing a discarded update never allows. When the sequence is presented, the honest framing is a naming discipline: call it the *assigned* order, never *the* order. The name is what stops the next engineer from treating position as causality. ## The trap in the middle ground Retaining metadata only helps if something actually reads it. A system that stores causal information and then resolves every conflict by position has paid the storage cost for none of the benefit, and has additionally created the impression that conflicts are being handled. Decide who reads the metadata before deciding to keep it.