Update README.md

README.md

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----
-license: mit
----
+---
+pretty_name: Math-HQ-20k
+language:
+  - en
+license: mit
+size_categories:
+  - 10K<n<100K
+task_categories:
+  - text-generation
+  - question-answering
+  - mathematical-reasoning
+tags:
+  - math
+  - reasoning
+  - synthetic
+  - instruction-tuning
+  - algebra
+  - combinatorics
+  - geometry
+  - number-theory
+  - discrete-math
+  - verification
+---
+
+# Math-HQ-20k
+
+A synthetic dataset of 20,000 English-language math reasoning examples designed for supervised fine-tuning, reasoning evaluation, and error-analysis workflows.
+
+Each record contains a problem statement, one or more solution paths, a consistency reconciliation, a catalogue of plausible mistakes, and a short conceptual takeaway.
+
+## Dataset summary
+
+- **Records:** 20,000
+- **Topics:** 120
+- **Difficulty levels:** 1–10
+- **Format:** JSONL
+- **Language:** English
+- **License:** MIT
+- **File size:** ~72.2 MB
+
+## What is inside
+
+Each example includes:
+
+- `id` — unique row identifier
+- `topic` — topic label
+- `difficulty` — integer difficulty rating from 1 to 10
+- `problem_statement` — the task prompt
+- `solution_paths` — multiple worked solution methods
+- `reconciliation` — cross-check and robustness notes
+- `error_catalogue` — plausible mistakes and why they are wrong
+- `conceptual_takeaway` — short summary of the key idea
+
+## Technical specifications
+
+| Metric | Value |
+|---|---:|
+| Total examples | 20,000 |
+| Unique topics | 120 |
+| Difficulty range | 1 to 10 |
+| Difficulty distribution | 2,000 examples per level |
+| JSONL validity | 100% parse success |
+| Top-level field completeness | 100% |
+| Exact prompt duplicates | 0 |
+| Average problem length | 63.1 words |
+| Median problem length | 62 words |
+| Average solution content | 88.5 words |
+| Average reconciliation content | 68.1 words |
+| Average solution paths per item | 2.04 |
+| Items with 2 solution paths | 19,298 |
+| Items with 3 solution paths | 702 |
+| Average error entries per item | 2.88 |
+
+## Schema
+
+```json
+{
+  "id": "math-000001",
+  "topic": "Elementary Algebra: Linear Equations — Inverse Operations",
+  "difficulty": 1,
+  "problem_statement": "...",
+  "solution_paths": [
+    {
+      "method_name": "Inverse Operations",
+      "approach": "...",
+      "steps": ["...", "..."],
+      "final_answer": "..."
+    }
+  ],
+  "reconciliation": {
+    "consistency_check": "...",
+    "robustness_analysis": "..."
+  },
+  "error_catalogue": [
+    {
+      "error_description": "...",
+      "why_plausible": "...",
+      "why_wrong": "...",
+      "which_method_catches_it": "..."
+    }
+  ],
+  "conceptual_takeaway": "..."
+}
+
+Intended use
+
+This dataset is suitable for:
+
+supervised fine-tuning on step-by-step mathematical reasoning
+
+multi-solution reasoning behavior
+
+answer verification and self-check training
+
+error detection and correction tasks
+
+curriculum-style difficulty experiments
+
+
+Notes
+
+The dataset is synthetic and intentionally structured for reasoning quality.
+
+Most examples contain more than one solution path to support comparison and verification.
+
+The error catalogue is designed to model common student and model mistakes.
+
+The prompts are intentionally consistent in style to make reasoning supervision easier.
+
+
+Limitations
+
+The dataset is not a collection of real-world student work.
+
+The writing style is intentionally template-like, which may reduce natural-language diversity.
+
+The dataset focuses on mathematical reasoning and does not aim to cover general open-domain QA.
+
+
+Citation
+
+If you use this dataset, please cite it as:
+
+Math-HQ-20k. Synthetic JSONL dataset for supervised mathematical reasoning and verification.