A widening finds two rows supplying the same cell — what can a tool do about it, and which choice actually tells you?

## Why there is a decision at all A **widening** turns one column's distinct values into new headers, filled from a second column. The result's cells are addressed by a row key — the identifying values — together with a header, and each address is one slot. If two input rows share an address, the shape cannot hold both numbers. Whatever happens next is a decision, and the interesting thing is that it is usually made by the tool rather than by you. ## The three dispositions | Disposition | What the caller sees | What it costs you | |---|---|---| | **Refuse** — uniqueness is a stated precondition, so the pairs are checked and no result is produced | An explicit failure at the widening | Nothing silent; you must resolve the grain before continuing | | **Reduce** — the surface accepts a reduction and supplies a default one, applied to the colliding values | A clean table, same shape you expected | The arithmetic is somebody else's choice and appears nowhere in your code | | **Keep both** — the cell holds a collection of the colliding values | A table whose cell holds more than one value | The column no longer holds plain measurements, and every later step meets that | The distinction that matters is not which is most convenient but **which of them is observable**. Only the refusal generates a signal. The second produces a table indistinguishable from the one you wanted; the third produces one that at least looks unusual at the next step, but nothing was raised at the widening. ## The reasoning error this invites The error is a silent inference: *the widening returned, therefore the input had one value per cell.* That inference is only sound under the first disposition, and you generally do not get to choose which disposition you are under — it is a property of the tool and sometimes of the surface you called within it. Worse, the belief travels. Somebody who learned the subject where widening refuses carries 'it would have errored' into a place where it never would, and somebody who learned it where a default reduction exists carries 'a widening averages duplicates' into a place where it refuses. The repair is not to memorise one tool's behaviour. It is to stop making the outcome claim at all and make the **precondition claim** instead, which is true everywhere. ## The two rules that hold under all three 1. **Count distinct key-and-header pairs against the input row count before you widen.** Equal means the widening is a rearrangement. Fewer distinct pairs than rows means at least one cell is being decided, and the difference is how many values are being absorbed. This check is arithmetic you own, not a feature you hope the tool has. 2. **If a reduction is genuinely what you want, state it.** A stated reduction is a visible line of code with a reviewable meaning: these two readings are averaged, or summed, or the later one wins. An inherited one is arithmetic that appears in no diff and in no review. Stating it also has a useful side effect where the surface allows it: naming a reduction that cannot silently absorb anything — one that fails or flags when handed more than one value — turns a permissive tool into a loud one for this call. ## What varies, and a cost claim not to make Two things genuinely differ across designs and should never be asserted flatly. - **Whether a default reduction exists, and what it is.** Some widening surfaces have none and refuse; others carry one. Where one exists you are inheriting a choice of arithmetic made by the tool's authors, and it is not the same choice everywhere. - **What it costs to supply your own reduction.** A common belief is that handing in your own function is inherently slow because it is called once per colliding value. That is one calling convention among several: some designs hand the reduction the whole set of colliding values at once under the same surface name, and some recognise a named reduction and dispatch it to a compiled path, so only an arbitrary supplied function ever takes the slow route. Establish which convention is in play before making a cost claim — and never let a cost belief talk you out of stating the reduction. ## The shape of a good answer in an interview Name the precondition, name the three dispositions, say which one is silent, and then give the advice that survives all three. A candidate who answers with a single outcome — 'it errors' or 'it averages them' — has described the tool they happen to know and has told the interviewer that they would not catch this anywhere else.