Manuscript Oai227-A@1 · Oai227-A.tex · section · 7f45f607

Clock histories and their actual time budget

Stage 2: price only specified finite operations › Clock histories and their actual time budget · lines 784–803

For an observation up to physical time $u$ , the attempted update count is Poisson with mean $n u$ . For the quench pair $(s, t)$ , that mean is

n T_{n} (s + t) = n^{5/3} (s + t) .

Clock attempts include updates that leave the spin unchanged. Counting flips instead would change the history law.

In the final certificate, $n = 2$ , $s + t \leq 7$ , and

T = 2^{2/3} < \frac{8}{5} .

Hence the maximum quench history has mean less than

2 \cdot 7 \cdot \frac{8}{5} = \frac{112}{5} .

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