Upload README.md

README.md

@@ -0,0 +1,156 @@
+# ChainMath Benchmark 🔗🧮
+
+> **Evaluating the reasoning chain integrity of large language models across multilingual arithmetic challenges.**
+
+---
+
+## What is ChainMath?
+
+**ChainMath** is a procedurally generated benchmark designed to stress-test a model's ability to:
+
+- **Track arithmetic state** across a sequence of dependent questions
+- **Follow instructions in multiple natural languages** (English, Spanish, French, German, Italian)
+- **Produce structured output** (JSON) reliably on the first attempt
+- **Handle distractors** — irrelevant information embedded to mislead the model
+- **Resolve cross-question references** using natural language anaphora
+
+Unlike benchmarks that evaluate questions in isolation, ChainMath questions are **interdependent**: the correct answer to question *N* is often a function of the answers to earlier questions. A model that loses track of the chain — even once — will propagate errors forward.
+
+---
+
+## Why ChainMath?
+
+Existing mathematical reasoning benchmarks (GSM8K, MATH, etc.) largely test **independent problems**. Real-world tasks, however, require models to maintain coherent state over long contexts.
+
+ChainMath was built on the hypothesis that **current large language models struggle with context-dependent arithmetic chains**, particularly when:
+
+- Questions switch between languages mid-sequence
+- Irrelevant numeric information is injected as noise
+- Conditional logic branches based on the parity or magnitude of a prior result
+- The chain spans more than 10 dependent steps
+
+> **Hypothesis:** Models that perform well on standard math benchmarks may significantly underperform on ChainMath due to poor chain-state tracking — regardless of raw computational ability.
+
+The first evaluation round supports this hypothesis. Two out of five models scored below 30%.
+
+---
+
+## Benchmark Format
+
+Each ChainMath instance consists of **200 questions** generated from a numeric **seed**. The seed deterministically reproduces the entire question set, ensuring reproducibility without exposing the answer key.
+
+Questions range across 5 difficulty levels:
+
+| Level | Description |
+|-------|-------------|
+| ★☆☆☆☆ | Simple arithmetic on a standalone value |
+| ★★☆☆☆ | Two-step chains, single language |
+| ★★★☆☆ | Multi-step chains, possible language switch |
+| ★★★★☆ | Conditional/comparison logic, anaphora, distractors |
+| ★★★★★ | Cross-language anaphora, inverse operations, high-depth chains |
+
+The score is **difficulty-weighted**: harder questions contribute more to the final score.
+
+---
+
+## Scoring
+
+ChainMath uses a transparent, multi-component scoring system:
+
+```
+Final Score = Weighted Correctness × (1 − Order Penalty) − JSON Penalty
+```
+
+| Component | Detail |
+|-----------|--------|
+| **Weighted Correctness** | Each correct answer earns points proportional to its difficulty weight |
+| **Correctness Tolerance** | ±0.01 absolute **or** ±0.1% relative — whichever is satisfied |
+| **Order Penalty** | Up to −15% for answers not returned sorted by question ID |
+| **JSON Format Penalty** | −10% flat if the model failed to produce valid JSON on the first attempt |
+| **Score Range** | Clamped to [0, 100] |
+
+---
+
+## Validated Results — Round 1 (October 2026)
+
+Five models were evaluated on the same benchmark seed.
+
+| Model | Provider | Thinking | Tools | Final Score |
+|-------|----------|----------|-------|-------------|
+| **Claude Haiku 5.5** | Anthropic | ✅ | ✅ | **84.29%** |
+| Gemini 3.6 Flash | Google | ✅ | ❌ | 75.36% |
+| DeepSeek V4.1 Flash | DeepSeek | ✅ | ✅ | 71.19% |
+| ChatGPT 5.6 Luna | OpenAI | ❌ | ✅ | 26.42% |
+| Qwen 3.8-Max | Alibaba | ✅ | ✅ | 10.56% |
+
+> **Note:** Scores reflect the combined effect of correctness, JSON discipline, and ordering compliance. Raw correctness percentages differ from final scores for models that incurred penalties. See [`validated_results.json`](./validated_results.json) for full breakdown.
+
+### Key Observations
+
+- **Thinking / extended reasoning mode** is a strong predictor of performance. The only model evaluated *without* thinking mode (ChatGPT 5.6 Luna) scored significantly below models with it — even when given tool access.
+- **JSON discipline matters.** Two models (ChatGPT 5.6 Luna, Qwen 3.8-Max) failed to produce valid JSON on the first attempt, incurring a −10% penalty. This is a real-world capability gap.
+- **Tool access is not sufficient.** All low-scoring models had tool access but still struggled with chain tracking — suggesting this is a reasoning problem, not a tool availability problem.
+- **High difficulty (★★★★★) is the main differentiator.** Most models performed reasonably at difficulty ★★★, but diverged sharply at ★★★★★.
+
+---
+
+## Evaluation Methodology
+
+Evaluation is fully automated via the provided comparator script. Steps:
+
+1. Generate a benchmark from a seed: produces `benchmark_<seed>.txt` (prompt) and `benchmark_<seed>.json` (answer key, not shared with the model).
+2. Send the `.txt` prompt to the model in a single turn (no mid-session hints).
+3. Record whether the model returned valid JSON **on the first attempt**.
+4. Run the comparator against the model's JSON output and the answer key.
+5. Record the full result including per-question breakdown.
+
+No human judgment is involved in scoring. All answers are numeric.
+
+---
+
+## Participating with Your Model
+
+We welcome submissions from AI labs, developers, and researchers. To have your model evaluated:
+
+1. **Contact us** via GitHub Issues on this repository.
+2. We will provide you with a **benchmark seed** (the question set is procedurally generated — each submission can use a different seed to prevent data contamination).
+3. You run the model against the prompt and share the JSON output.
+4. We run the comparator and publish the results with full transparency.
+
+> Results are published alongside methodology details. We do not publish the answer key or the generator source code in order to prevent benchmark gaming.
+
+---
+
+## Repository Structure
+
+```
+chainmath-benchmark/
+├── README.md                  ← This file (public)
+├── validated_results.json     ← Round 1 validated scores
+├── comparator.py              ← Public scoring script
+└── SUBMISSION_GUIDE.md        ← How to submit your model
+```
+
+> The **generator** is kept private to prevent answer contamination. Benchmark seeds are issued per-submission.
+
+---
+
+## Citation
+
+If you use ChainMath in your research or evaluation pipeline, please cite:
+
+```
+ChainMath Benchmark v1.0 (2026)
+Author: [Your Name / Organization]
+URL: https://github.com/[your-handle]/chainmath-benchmark
+```
+
+---
+
+## License
+
+This benchmark and its tooling are released under the **MIT License**. See `LICENSE` for details.
+
+---
+
+*ChainMath — Does your model know where it left off?*