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Scan a pairwise comparison matrix for preference cycles and compute transitivity metrics.
Passed 18 of 22 test cases with the skill, and 8 of 22 without it.
and 16 more in the full report
12 fixed6 passed either way2 still failing2 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 12 test cases the skill fixed. Same model, same prompt, with and without the skill.
We only compared item A and item B, where A > B. Report all circular loops and the transitivity score for this 2-element matrix.
| Checked | Without skill | With skill |
|---|---|---|
| Output cycles array is empty. | Missed | Passed |
| Output contains a transitivity_score of 1. | Missed | Passed |
The instructions your model reads when the skill loads.
Scans a pairwise comparison matrix for preference cycles (A>B>C>A) and computes transitivity metrics. Identifies all minimal cycles and quantifies overall consistency.
Runs as a subagent. Receives a comparison matrix, returns all detected cycles and transitivity scores.
Cycle detection requires graph traversal algorithms (Johnson's algorithm or DFS-based enumeration) applied to the preference digraph. Isolating this keeps algorithmic complexity out of the orchestrator.
Output MUST contain a cycles array (empty if none found) and a numeric transitivity_score in [0, 1]. All reported cycles MUST be verifiable against the input matrix.
Optional, no fixed order; the final leaf is always a sop.
| SOP | When to use |
|---|---|
| spawn-agent | Spawn a customized CC subagent with full MCP tool access. Used by SOPs that declare execution: subagent. |
test cases passed, vs 8 / 22 without
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