# Belief data and label semantics

## What a row represents

`dataset/Belief/source/data.parquet` contains 1,810,609 wallet-market records. A row summarizes a wallet's held outcomes in one market and assigns a dominant outcome (`stance_outcome`) plus a position-derived score (`confidence`).

## Source columns

| Column | Meaning supported by the release |
|---|---|
| `wallet` | Pseudonymous wallet address. |
| `market_id` | Market identifier. |
| `question`, `market_slug`, `event_slug` | Human-readable market metadata. |
| `n_outcomes`, `positive_outcomes` | Outcome metadata. |
| `total_hold_amt` | Total held amount used by the label calculation. |
| `stance_outcome` | Outcome selected as the wallet's stance. |
| `stance_hold_amt` | Amount held on `stance_outcome`. |
| `second_hold_amt` | Amount held on the second side/outcome. |
| `confidence` | Position-derived normalized holding imbalance. |
| `label_status`, `label_status_v2` | Released label-status fields. |
| `stance_first_block`, `stance_last_block` | First and last block associated with the stance. |
| `stance_first_tx_hash`, `stance_last_tx_hash` | Corresponding transaction hashes. |


## Verified confidence formula

Direct numerical validation over all source rows gives:

\[
\text{confidence}=2\frac{\text{stance\_hold\_amt}}{\text{total\_hold\_amt}}-1.
\]

For a two-sided market, if `stance_hold_amt = H_max`, `second_hold_amt = H_min`, and `total_hold_amt = H_max + H_min`, this is equivalent to:

\[
\text{confidence}=\frac{H_{\max}-H_{\min}}{H_{\max}+H_{\min}}.
\]

Examples:

| Holdings | Confidence |
|---|---:|
| 50 / 50 | 0.0 |
| 60 / 40 | 0.2 |
| 75 / 25 | 0.5 |
| 90 / 10 | 0.8 |
| 100 / 0 | 1.0 |

This is best interpreted as **position-derived confidence** or **normalized position imbalance**. It is not a directly reported belief probability.

## Model-ready split columns

`dataset/Belief/splits/*.parquet` and `benchmark/Belief/direct/*.parquet` contain:

```text
sample_id, wallet, market_id, split, system_prompt, input_text,
label_choice, label_confidence, event_slug, question,
stance_first_block, stance_last_block
```

Profile adds `profile_generator_model` and `generated_profile`. Retrieval adds `retrieval_method` and `retrieved_support`.