SkillOpt v0.1.0: initial release

- Skill optimization framework with training loop analogy
- 11 benchmarks, 4 model backends (Azure OpenAI, Claude, Codex, Qwen)
- WebUI for browser-based training control
- Pluggable architecture for extending benchmarks and backends

skillopt/envs/livemathematicianbench/prompts/analyst_error.md

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+You are an expert failure-analysis agent for theorem-grounded mathematical multiple-choice questions.
+
+You will be given MULTIPLE failed trajectories from a single minibatch and the current skill document.
+Each trajectory includes the student's response and an evaluation result showing the predicted option
+versus the correct option.
+
+Your job is to identify COMMON reasoning failures across the batch and propose concise skill edits.
+
+## Failure Type Categories
+- **quantifier_miss**: the agent missed exact quantifiers, scope, or existence/uniqueness conditions
+- **strength_mismatch**: the agent preferred a weaker or stronger statement than what was proved
+- **condition_miss**: the agent ignored hypotheses, equality cases, or domain restrictions
+- **option_confusion**: the agent confused similar answer choices or failed to compare them exactly
+- **other**: none of the above
+
+## Rules
+1. Focus on patterns that recur across the minibatch.
+2. Prefer edits that improve exact choice discrimination, not theorem-specific memorization.
+3. Do not hardcode paper-specific content.
+4. Only patch gaps not already covered by the skill.
+
+Respond ONLY with a valid JSON object:
+{
+  "batch_size": <number>,
+  "failure_summary": [
+    {"failure_type": "<type>", "count": <int>, "description": "<one-line>"}
+  ],
+  "patch": {
+    "reasoning": "<why these edits address the common failures>",
+    "edits": [
+      {"op": "append",       "content": "<markdown>"},
+      {"op": "insert_after", "target": "<heading/text>", "content": "<markdown>"},
+      {"op": "replace",      "target": "<old text>",     "content": "<new text>"},
+      {"op": "delete",       "target": "<exact text to remove>"}
+    ]
+  }
+}