Loading skill
Install any skill in seconds. Free to start, no credit card required.
Get Started Free →Scan a pairwise comparison matrix for preference cycles and compute transitivity metrics.
.claude/skills/yogsoth-ai-cycle-detection/SKILL.md| Test case | Without → With | Effect | Δ tokens | Δ turns |
|---|---|---|---|---|
| case-07 | ✗→✓ | ▲ Improved | -60% | 0% |
| case-01 | ✗→✓ | ▲ Improved | -18% | 0% |
| case-08 | ✗→✓ | ▲ Improved | -32% | 0% |
| case-09 | ✗→✓ | ▲ Improved | 15% | 0% |
| case-11 | ✗→✓ | ▲ Improved | -28% | 0% |
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.
<!-- BEGIN available-tables (generated) -->
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. |
<!-- END available-tables (generated) -->
| Case | Status | Duration (ms) | Turns | Tokens | Tool calls | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Without | With | Δ | Without | With | Δ | Without | With | Δ | Without | With | Δ | ||
case-07 | fail→pass | 17,926 | 5,871 | -67% | 1 | 1 | 0% | 3,215 | 1,292 | -60% | 0 | 0 | — |
case-06 | pass→fail | 11,244 | 9,337 | -17% | 1 | 1 | 0% | 2,355 | 2,024 | -14% | 0 | 0 | — |
case-01 | fail→pass | 18,881 | 13,562 | -28% | 1 | 1 | 0% | 3,484 | 2,856 | -18% | 0 | 0 | — |
case-02 | fail→fail | 8,130 | 9,667 | +19% | 1 | 1 | 0% | 719 | 1,883 | +162% | 0 | 0 | — |
case-03 | fail→fail | 7,617 | 4,910 | -36% | 1 | 1 | 0% | 1,310 | 1,064 | -19% | 0 | 0 | — |
case-04 | pass→fail | 7,792 | 8,973 | +15% | 1 | 1 | 0% | 1,466 | 1,674 | +14% | 0 | 0 | — |
case-05 | pass→pass | 14,043 | 23,546 | +68% | 1 | 1 | 0% | 2,768 | 5,156 | +86% | 0 | 0 | — |
case-08 | fail→pass | 11,286 | 6,295 | -44% | 1 | 1 | 0% | 2,271 | 1,533 | -32% | 0 | 0 | — |
case-09 | fail→pass | 20,763 | 22,915 | +10% | 1 | 1 | 0% | 4,270 | 4,913 | +15% | 0 | 0 | — |
case-10 | pass→pass | 20,542 | 7,754 | -62% | 1 | 1 | 0% | 3,298 | 1,453 | -56% | 0 | 0 | — |
case-11 | fail→pass | 11,818 | 6,455 | -45% | 1 | 1 | 0% | 2,293 | 1,652 | -28% | 0 | 0 | — |
case-12 | fail→pass | 13,213 | 12,092 | -8% | 1 | 1 | 0% | 2,660 | 2,781 | +5% | 0 | 0 | — |
case-13 | fail→pass | 3,704 | 6,853 | +85% | 1 | 1 | 0% | 721 | 1,507 | +109% | 0 | 0 | — |
case-14 | fail→pass | 6,955 | 4,054 | -42% | 1 | 1 | 0% | 1,187 | 848 | -29% | 0 | 0 | — |
case-15 | fail→pass | 21,288 | 16,319 | -23% | 1 | 1 | 0% | 4,467 | 3,778 | -15% | 0 | 0 | — |
case-16 | pass→pass | 12,853 | 9,137 | -29% | 1 | 1 | 0% | 2,587 | 1,945 | -25% | 0 | 0 | — |
case-17 | fail→pass | 12,500 | 7,314 | -41% | 1 | 1 | 0% | 2,300 | 1,568 | -32% | 0 | 0 | — |
case-18 | pass→pass | 13,907 | 2,937 | -79% | 1 | 1 | 0% | 2,235 | 437 | -80% | 0 | 0 | — |
case-19 | fail→pass | 13,991 | 6,200 | -56% | 1 | 1 | 0% | 1,510 | 1,478 | -2% | 0 | 0 | — |
case-20 | pass→pass | 15,428 | 15,414 | -0% | 1 | 1 | 0% | 2,877 | 3,168 | +10% | 0 | 0 | — |
case-21 | pass→pass | 13,032 | 2,181 | -83% | 1 | 1 | 0% | 2,104 | 580 | -72% | 0 | 0 | — |
case-22 | fail→pass | 10,119 | 7,370 | -27% | 1 | 1 | 0% | 1,893 | 1,588 | -16% | 0 | 0 | — |
DecimalAI ran this skill against gemini-3.6-flash twice over the same eval suite — once with the skill loaded and once without — and compared the two runs case by case. 22 cases were attempted. The headline lift of +45 percentage points is the difference between those two pass rates over the 22 comparable cases. 2 cases got worse with the skill loaded, and they are included in that figure.
Without the skill loaded, the model failed this case. With it loaded, the same prompt on the same model passed. This is one improved case from the latest verified run; every case, including any that regressed, is in the table above.
Other measured skills in the registry, with their headline benchmark lift.