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Candidates takes the label source as an argument rather than storing it, which is what keeps the asymmetry structural: the seeded picker selects by index and never calls Candidates, so the mode cannot reach it. That asymmetry is load-bearing, because it makes the two seeded cells of the factorial a manipulation check with identical draw streams. The identifier ladder deliberately has no text rung. A fallback that reached for text would silently turn one arm back into the other. Claude-Session: https://claude.ai/code/session_01A5KmftdEJ49A9z5mF5ESrX