Collusive Stagnation: Do Verifier Agents Break Deadlock, or Join It?

The field's remedy for an unreliable agent is to add another agent: a critic, judge, or verifier, often implicitly assuming that the verifier is an independent observer. It is not: it is another sample from a similar distribution, often the same model family, reading a context the first agent wrote. We ask whether adding a verifier to a stalling agent restores progress, or whether the pair stalls together in a richer and more expensive way. We identify and name two joint failure modes. In collusive approval the verifier accepts a solution still far from a correct fix, so the system halts and reports success on work that has not reached one. In revision ping-pong the verifier rejects, the coder rephrases rather than rethinks, and the pair can loop to its cap with every step looking like work. We formalize liveness over the dyad's joint state and ground progress in a reference-anchored signal, so that "the verifier approved a submission still distant from a fix" is a mechanically checkable event, and we run a 3x2x2 factorial over verifier relatedness, interaction protocol and cycle cap across 1800 dyad runs. The signal itself has to be audited first, and that is our first result: a blinded adjudicator, the only one of five candidates to reach 0.800 on both halves of a control of patches whose answer was known, puts the corrected rate at about one approval in seven where the raw proxy says seven in ten, while the repositories' own tests, run on 24 flagged approvals, imply 0.517 [0.369, 0.649], so the audit instrument over-credits in its turn. Two counts need no proxy at all: 56.9% of approvals are issued with no revision ever requested, and in 78 runs both agents repeated themselves verbatim until the budget was gone. Swapping the verifier changes which way the dyad fails; we detect no accompanying change in how much an approval is worth, though differences up to 0.20 remain compatible with our data. Against a threshold-perfect critic a real verifier captures 0.342 of the available headroom while ping-pong rises, so inaccurate approval is not necessary for it. Contrary to our own hypothesis, single-agent stop-signals are not structurally blind to dyad-level stagnation.