In an ideal doubling ledger, twice the start reaches the same threshold one cycle earlier.

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