You are an expert analyst. A cluster of similar propositions are shown below, followed by their supporting observations.

Your job is to produce a **final set** of propositions that is clear, non-redundant, and captures everything about the user.

To support information retrieval (e.g., with BM25), you must **explicitly identify and preserve all named entities** from the input wherever possible. These may include applications, websites, documents, people, organizations, tools, or any other specific proper nouns mentioned in the original propositions or their evidence.

You MAY:

- **Edit** a proposition for clarity, precision, or brevity.
- **Merge** propositions that convey the same meaning.
- **Split** a proposition that contains multiple distinct claims.
- **Add** a new proposition if a distinct idea is implied by the evidence but not yet stated.
- **Remove** propositions that become redundant after merging or splitting.

You should **liberally add new propositions** when useful to express distinct ideas that are otherwise implicit or entangled in broader statements—but never preserve duplicates.

When editing, **retain or introduce references to specific named entities** from the evidence wherever possible, as this improves clarity and retrieval fidelity.

Edge cases to handle:

- **Contradictions** – If two propositions conflict, keep the one with stronger supporting evidence, or merge them into a conditional statement. Lower the confidence score of weaker or uncertain claims.
- **No supporting observations** – Keep the proposition, but retain its original confidence and decay unless justified by new evidence.
- **Granularity mismatch** – If one proposition subsumes others, prefer the version that avoids redundancy while preserving all distinct ideas.
- **Confidence and decay recalibration** – After editing, merging, or splitting, update the confidence and decay scores based on the final form of the proposition and evidence.

General guidelines:

- Keep each proposition clear and concise (typically 1–2 sentences).
- Maintain all meaningful content from the originals.
- Provide a brief reasoning/evidence statement for each final proposition.
- Confidence and decay scores range from 1–10 (higher = stronger or longer-lasting).

## Evaluation Criteria

For each proposition you revise, evaluate its strength using two scales:

### 1. Confidence Scale

Rate your confidence in the proposition based on how directly and clearly it is supported by the evidence. Consider:

- **Direct Evidence**: Is the claim directly supported by clear, named interactions in the observations?
- **Relevance**: Is the evidence closely tied to the proposition?
- **Completeness**: Are key details present and unambiguous?
- **Engagement Level**: Does the user interact meaningfully with the named content?

Score: **1 (weak/assumed)** to **10 (explicitly demonstrated)**. High scores require direct and strong evidence from the observations.

### 2. Decay Scale

Rate how long the insight is likely to remain relevant. Consider:

- **Immediacy**: Is the activity time-sensitive?
- **Durability**: Will the proposition remain true over time?

Score: **1 (short-lived)** to **10 (long-term relevance or behavioral pattern)**.

# Input

{body}

# Output

Return **only** JSON in the following format:

{
  "propositions": [
    {
      "proposition": "<rewritten / merged / new proposition>",
      "reasoning":   "<revised reasoning including any named entities where applicable>",
      "confidence":  <integer 1-10>,
      "decay":       <integer 1-10>
    },
    ...
  ]
}
