The arithmetic trap: why humans miss the math that matters

There is a particular class of pay-application error that is entirely deterministic, entirely detectable, and almost never caught by human review: the G702 front-page numbers that don't foot to the G703 continuation. Total work completed on the G702 should equal the sum of every line item's 'work completed this period' on the continuation. Total materials stored should match the sum of stored-materials entries. Retainage withheld should match the contract rate applied to the appropriate base. These are arithmetic identities, not judgment calls - and they're wrong surprisingly often.

The rounding problem is real

Part of the mismatch is mundane: rounding. A G703 shows each line item rounded to the nearest dollar, but the G702 sums them before rounding, producing a penny-level discrepancy that is technically correct and practically meaningless. But part of the mismatch is a genuine error: a line was updated in the spreadsheet and the G702 wasn't recomputed, or a stored-materials entry was double-counted, or a line was transposed between the continuation and the cover sheet. The problem is that a human reviewer can't tell the difference between a $0.03 rounding artifact and a $3,000 transposition error without manually adding every line - which nobody does, because it's a hundred lines and the draw has to go out.

Math errors in a pay application aren't hard to find. They're hard to look for. The machine's advantage isn't intelligence - it's that it never gets bored.

Deterministic before judgment

The right approach to verification is to run every deterministic check first - arithmetic, footings, cumulative totals, retainage rates - and only then apply judgment to what remains. This flips the review from an open-ended search through a hundred pages into a short list of specific findings, each with a page citation and a suggested resolution. The human still decides. The human just doesn't spend two hours adding up numbers to find out which of them is wrong.