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skills/systematic-enumeration/SKILL.md

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+---
+name: Systematic Enumeration
+description: Forces element-by-element verification for finite sets to prevent counting errors.
+version: 1.0
+user-invocable: true
+disable-model-invocation: false
+---
+
+# Systematic Enumeration & Verification Skill
+
+## **Objective**
+To eliminate heuristic errors and "hallucinated patterns" when analyzing finite sets. This protocol overrides the model's tendency toward "holistic recognition" in favor of systematic, element-by-element verification.
+
+## **Execution Protocol**
+When this skill is triggered, you MUST NOT provide a direct answer immediately. Follow these three phases to ensure accuracy:
+
+### **Phase 1: Set Definition**
+Explicitly define the boundaries and members of the finite set being analyzed. 
+*   **Requirement:** List the members before performing any tests.
+*   *Example:* "The set consists of the files in the `/src` directory: [main.rs, utils.rs, types.rs]."
+
+### **Phase 2: Atomic Element Testing (O(n))**
+Iterate through every item in the set. For each item, perform a literal check against the target property.
+*   **Format:** Use a list or table to force token-level focus on each element.
+*   **Structure:** `[Item] -> [Logic/Observation] -> [Boolean Result]`
+*   *Note:* For character-based tests, split the string into individual characters to bypass tokenization bias.
+
+### **Phase 3: Reduction & Summation**
+Aggregate the `True` results from Phase 2 to derive the final answer.
+*   **Self-Correction:** Verify that the count of items tested in Phase 2 exactly matches the count of the set defined in Phase 1. If there is a mismatch, restart Phase 2.
+
+## **Constraints & Anti-Patterns**
+*   **STRICT BAN on Heuristics:** Do not use phrases like "typically," "usually," or "it appears that."
+*   **NO Pattern Matching:** Do not extrapolate a rule (e.g., "every other item") as a substitute for testing every item.
+*   **Computational Justification:** Treat the process as an $O(n)$ operation where $n$ is small enough that accuracy is the only priority.
+
+## **Trigger Scenarios**
+*   Counting specific characters or substrings within a string.
+*   Verifying property adherence across a list of variables, files, or objects.
+*   Membership testing in sets where false negatives are high-risk.