Every multi-agent verification design runs on a theorem borrowed from somewhere else — the Condorcet Jury Theorem, Byzantine fault tolerance, the Universal Scalability Law, computational complexity bounds. Each one shipped with a warranty: conditions the proof depends on, fine print nobody reads until something breaks. Stochastic LLM committees operate outside several of those conditions by default, and a guarantee doesn't fail loudly when it lapses — it just quietly stops covering what it was never proven to cover. This series finds exactly where coverage runs out, and builds what replaces it.
4 posts in this series
More voters should mean more truth — that's the promise behind the jury theorem, Byzantine fault tolerance, and the scalability law alike. All three need the voters to disagree, when they're wrong, for genuinely different reasons. Stochastic agents pulled from overlapping training data don't fail that way: they agree, confidently, for the same reason, and a headcount can't tell independent judgment from an echo. Opening Theorems Out of Warranty.
08 July 2026A judge should catch what a writer misses — that's the whole point of a second opinion. But if the judge finds an argument convincing mainly because it sounds like something the judge itself would write, the second opinion isn't independent, it's a compliment. Auditors from different adapter families converged on the same verdict for a proposal neither of them actually executed — full agreement, and not one shred of independent confirmation in it. Continuing Theorems Out of Warranty.
15 July 2026A single word — passed — sounds like a verdict. It's actually doing the work of several different claims at once: checked and confirmed true, checked and confirmed false, and never checked at all because no method existed to check it, quietly rounded up to a pass anyway. Treating that boolean as if it always means the same thing is the boolean fallacy, and Rice's theorem gives the honest reason no execution-based check can fully cure it. Still inside Theorems Out of Warranty.
22 July 2026One more pass. That's the entire logic of a repair loop: whatever failed, better context and another attempt will eventually fix it. For most failures, that logic works — which is exactly what makes it a trap for the failures it doesn't. A recent complexity-theoretic result proves a specific class of task cannot be solved or verified within a bounded forward pass, no matter how many passes are chained together. A retry budget spent chasing that class buys nothing back — not a partial refund, nothing. Closing out Theorems Out of Warranty.
29 July 2026