Update README.md

README.md

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 # Long Horizon Execution
 
-This project contains the dataset accompanying the paper "The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs" to evaluate Long Horizon Execution capabilities of LLMs.
+This project contains the dataset accompanying the paper "[The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs](https://arxiv.org/abs/2509.09677)"
 
-### File Structure
-`config.json` contains metadata about out dataset.
+**GitHub:** [https://github.com/long-horizon-execution/measuring-execution/](https://github.com/long-horizon-execution/measuring-execution/)
 
-`dictionary.json` contains the key-value dictionary. 
+## Description
+![Our task.](task_overview.png)
 
-`test.jsonl` contains the individual samples with ground truth outputs.
+This dataset is a synthetic benchmark designed to measure the pure execution capability of LLMs over long horizons. The core task is **key-value dictionary addition**. A fixed, in-context dictionary mapping five-letter English words (keys) to integer values is provided in `dictionary.json`. The model's goal is to maintain a running sum. In each turn, it receives one or more keys (defined by the turn complexity, `K`), retrieves their corresponding values from the dictionary, adds them to the running sum, and outputs the new sum. The primary metric for evaluation is the **task length**: the number of steps a model can execute before its accuracy drops below a certain threshold.
 
-### Setup
-![Our task.](task_overview.png)
+The dataset is designed to be programmatically generated and thus contamination-free. We only provide 100 samples here for ease of access, but more can be generated using the script [here](https://github.com/long-horizon-execution/measuring-execution/blob/main/generate_dataset_json.py).
+
+## Using the dataset
+`test.jsonl` contains the individual samples that can be used to prompt the LLM.
+- _"input"_: contains the keys to be processed.
+- _"values"_: contains the values mapped to the corresponding keys as described in `dictionary.json`.
+- _"output"_: contains the expected running sum answers.
+
+The provided dataset is configured with a turn complexity of `K=1` (one key per turn). To evaluate models on a higher turn complexity, such as `K=N`, you can post-process the data by grouping every `N` consecutive turns:
+- _"input"_: Concatenate every `N` items into a single comma-separated string.
+- _"output"_: The new running sum for the grouped turn is simply the **last** running sum from the original group of `N` turns.
 
-### Benchmark of Frontier Models
+## Benchmark
 ![Benchmark of Frontier models.](benchmark.png)
 
-### Citation
+## Citation
 Find out more about our work at https://arxiv.org/abs/2509.09677. Consider citing us if you use our dataset.
 ```
 @misc{