A reconciliation was out by precisely double the value of a set of supplier refunds, because an absolute-value conversion had moved each of them from negative to positive.
When a reconciliation is out, the instinct is to look for something missing. Sometimes nothing is missing and something is facing the wrong way.
The situation
A card statement reconciled against a rebuilt ledger. The totals disagreed. Every transaction was present, every one had been read correctly, and the count on both sides matched exactly.
The pattern
Among the ordinary charges sat a set of supplier returns — refunds, printed in the charges column as negative amounts. In converting the statement to ledger rows, an absolute-value conversion had been applied to normalise the figures. Each refund moved from negative to positive.
That is the whole defect, and its arithmetic is worth stating precisely. A refund that should subtract and instead adds does not distort the total by its own value; it distorts it by twice its value, because the figure has travelled the full distance from minus to plus. So the reconciliation difference came to exactly double the refunds in the set.
This makes the failure unusually diagnosable, and it is worth carrying as a rule of thumb:
A difference that is exactly twice a known quantity is a sign error, not a missing entry. If the discrepancy is precisely double something identifiable — a category of transaction, a single large item, a subtotal — stop looking for absent records. Something present is facing the wrong direction. Halving the difference and searching for that value is usually faster than any other approach.
The underlying cause is more general than refunds. Documents encode direction in several incompatible ways: by which column a figure sits in, by an explicit sign, by a separate indicator, and sometimes by convention alone. Reading direction from any one of these means inheriting that document’s conventions and every exception to them.
The dependable alternative is to derive direction from how the balance moves. Where a running balance is printed, the difference between consecutive balances states unambiguously whether a transaction increased or decreased the account, regardless of how the amount was presented. Where the movement and the stated amount do not agree, the row is flagged rather than guessed at — a disagreement between two independent readings is information, and discarding it in favour of either one is the decision that created this problem in the first place.
Engineering takeaway — A discrepancy that is exactly twice a known quantity is the signature of a flipped sign. Derive direction from how the balance moves rather than from the column a figure appeared in, and never normalise a sign away before the direction is settled.