In an ideal doubling ledger, twice the start reaches the same threshold one cycle earlier. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Twice the start reaches one cycle earlier

Start with 6 copies. The same threshold 24 is reached at cycle 2.

6,12,246,12,24
PCR threshold crossingExact doubling pins the first cycle that reaches the threshold.c0=6c1=12c2=24start=6threshold=24Ct=2crossed=1accepted=1

The one-cycle shift is exact in this toy model

The first row reached threshold at cycle 3. This row reaches at cycle 2, one cycle earlier.

3    2=13\;-\;2=1
PCR threshold crossingExact doubling pins the first cycle that reaches the threshold.c0=6c1=12c2=24start=6threshold=24Ct=2crossed=1accepted=1