A fixed point can return without being a two-cycle. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
A fixed point also returns
The candidate one half maps back to itself.
1 2 → 1 2 → 1 2 \frac{1}{2}\to\frac{1}{2}\to\frac{1}{2} 2 1 → 2 1 → 2 1 Fixed return candidate The return bit alone is not enough. mapId=reflection parameter=1 xValue=1/2 yValue=1/2 returnValue=1/2 returnedBit=1 bit nonfixedBit=0 bit periodTwoBit=0 bit
The non-fixed bit blocks the period claim
The non-fixed bit is 0, so period-two bit is 0.
nonfixed = 0 ⇒ 0 \text{nonfixed}=0\Rightarrow 0 nonfixed = 0 ⇒ 0 Rejected period spoof The rejected candidate is still a checked ledger. mapId=reflection parameter=1 xValue=1/2 yValue=1/2 returnValue=1/2 returnedBit=1 bit nonfixedBit=0 bit periodTwoBit=0 bit