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Sprint projectOct 24, 2026

Take Away the Means: a Proved Capacity Cap on Covert Signalling between Procurement Agents

Tony Gair · Team The Dark Factory

Submitted to AI Collusion Research Sprint. Sprint projects are early-stage work by participants, not Apart Research publications.

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Report: Take Away the Means: a Proved Capacity Cap on Covert Signalling between Procurement Agents

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Two LLM agents, one ordering stock and one supplying it, try to pass a 24-bit secret while still doing the job. Most defences watch the conversation and give you a detection rate, so something always gets through. Every message has to be a form, an item from 1 to 8 and a quantity from 0 to 3, or nothing. A chain of proofs in SPARK Ada, made by our own software factory, rewrites each message into a fixed line, so the sender's own words never reach the other agent. A capacity proof made in the sprint shows there are exactly 33 possible lines, so four messages carry at most 20.2 bits. Even with a perfect codebook a whole secret gets through at most about 1 time in 14 (7.07%), whatever the model does. With gpt-oss:120b colluding on plans written by Claude Opus, free text with no defence leaked the whole secret in 26/30, 22/30 and 11/30 episodes (seeds 1–3). Through the gate it was 0/90, with the order right in 97–100% of episodes. The leftover leak, 0.93–1.13 digits above chance, sits just under the 4.585 bits of item order the proof allows. An attacker who knew the gate reached the cap. Kimi and DeepSeek judges let 1.03–3.59 digits past, depending on the plan. A heuristic filter blocked only typography, and on one seed whole secrets got past it in 16/30 episodes. The cap counts message order and silence but does not remove them; shared knowledge is outside the proof.

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  1. Good: Strong engineering work and direction, specifically the use of formal verification to establish enforceable security properties rather than leaning on other probabilistic detection methods. Limitations are acknowledged.

    Weakness: Main takeaway is straightforward in that restricting communication to a finite set of messages will bound its capacity. The reduction limits how much information can be communicated, but it is unclear whether the remaining capacity is enough for meaningful collusion or not. For example, while the trials showed 0/90 of the whole secret recovered with the defense in play, there was still partial recovery demonstrated above chance. It's unclear how many bits of information were leaked in such cases, and if those remaining bits are sufficient for collusion.

    Recommendations: Review all attacker controlled positions, determine how much leakage is required for meaningful collusion, then test channel capping and see if legitimate functionality is preserved. Good direction.

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Cite this project

@misc{gair2026take,
  title = {{Take Away the Means: a Proved Capacity Cap on Covert Signalling between Procurement Agents}},
  author = {Tony Gair},
  year = {2026},
  month = oct,
  note = {Submitted to AI Collusion Research Sprint, an Apart Research Sprint},
  howpublished = {\url{https://apartresearch.com/sprints/projects/take-away-the-means-a-proved-capacity-cap-on-covert-signalling-between-procurement-agents-9n9f}},
  url = {https://apartresearch.com/sprints/projects/take-away-the-means-a-proved-capacity-cap-on-covert-signalling-between-procurement-agents-9n9f}
}

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