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PROOF_EMB_README.md

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+# Proof embeddings — vector_behavior
+
+Vectors for the proofs, made with the same models and the same pooling as the statement
+spaces already in this repo, so the two are directly comparable.
+
+| directory | what one row is | rows | dim |
+|---|---|---|---|
+| `proof_emb/e5-large-v2_theorem/` | one theorem's whole tactic script | 61,542 | 1024 |
+| `proof_emb/e5-large-v2_step/` | one tactic invocation with its goal state | ~259,580 | 1024 |
+| `proof_emb/e5-mistral-7b-instruct_theorem/` | one theorem's whole tactic script | 61,542 | 4096 |
+
+Each directory holds `embeddings.npy`, `idx_to_name.json`, `meta.json`, and for the step
+granularity `step_meta.json.gz` with the theorem, step index and premises per row.
+
+## Lining a proof up with its statement
+
+Row `i` of a proof space is the theorem named at `idx_to_name.json[i]`. The statement
+spaces are keyed the same way, so going between them is a name lookup:
+
+```python
+import json, numpy as np
+
+P  = np.load("proof_emb/e5-large-v2_theorem/embeddings.npy")
+pn = json.load(open("proof_emb/e5-large-v2_theorem/idx_to_name.json"))
+S  = np.load("embeddings/e5_large/embeddings.npy")
+sn = json.load(open("embeddings/e5_large/idx_to_name.json"))
+
+si = {n: i for i, n in enumerate(sn)}
+both = [(i, si[n]) for i, n in enumerate(pn) if n in si]   # 56,467 theorems
+pi, sj = zip(*both)
+proof_vecs, stmt_vecs = P[list(pi)], S[list(sj)]
+```
+
+56,467 of the 61,542 proved theorems are also in the 99,552-theorem statement pool. The
+rest have proofs but no statement embedding.
+
+For step rows, `idx_to_name.json[i]` is `"<theorem>#<step index>"`; split on `#` to get
+back to the theorem.
+
+## Truncation
+
+Proofs are much longer than statements and everything is encoded at 512 tokens, so long
+tactic scripts are cut off. The exact count is in each directory's `meta.json` as
+`n_truncated` / `frac_truncated` — check it before drawing conclusions about long proofs.
+
+## Please read this before using them
+
+In the parent study proofs are **held back on purpose**. Every claim about discovered
+structure is checked by asking whether the grouped theorems share proof premises, and
+that check has force only because no encoder was ever shown a proof.
+
+These vectors break that. Any structure found with them cannot then be validated against
+proofs — that is confirming a finding with the thing that produced it. Validate with
+something else: human judgement, a held-out corpus, or the source organisation.
+
+The same applies to `real_pairs_verified.json.gz` in this repo, which is the answer key
+for the pairing step rather than the discovery step.