The DC bin is a product-and-sum ledger that adds every sample with the same sign, measuring the constant part of this finite trace. The result is exact only for the declared samples and basis row; real data add offset drift, calibration error, missing samples, quantization, and noise uncertainty.
A tiny bin ledger is an exact dot product. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A bin is a product-and-sum ledger
Samples 1, 1, 1, 1 dotted with the dc basis give 4.
1⋅1+1⋅1+1⋅1+1⋅1=4
The role says which finite basis was used
The role is dc, so this is not a general Fourier transform claim.