CORPUS_README.md

Corpus and verified pairs — vector_behavior

Companion to the theorem/embedding/proof bundle already in this repo.

file	contents
corpus.jsonl.gz	all 180,907 Mathlib declarations with source code, one JSON object per file: {path, imports, premises:[{full_name, code, start, end, kind}]}
real_pairs_verified.json.gz	7,731 verified pairs over 1,666 substitutions, plus per-relation precision for the old name-matched pairs
llm_judge.json	blinded LLM verdicts on discovered groups, with decoy floors
pca_view.json	2,761 arrows projected on the duality and strictness axes, and on PCA
verified_relations.json	every relation re-measured on verified pairs vs all pairs
strictness_axis.json	the strictness-axis test with bootstrap intervals
ablation_relations*.json	name-stripping ablation, e5-large and e5-mistral
normalisation.json	preprocessing study with a pre-registered decision rule

The pairs

import gzip, json
vp = json.load(gzip.open("real_pairs_verified.json.gz", "rt"))

for a, b, from_tok, to_tok in vp["pairs"][:5]:
    print(f"{from_tok} -> {to_tok}:  {a}  |  {b}")

vp["top_substitutions"][:10]   # the substitutions Mathlib actually attests
vp["rule_precision"]           # how good the old name-matched pairs were

A pair is here if one token can be substituted throughout A's statement to give B's, with nothing else changed and declaration names deleted before matching. No embedding and no proof was consulted, so the set is usable as ground truth for either.

Precision is a lower bound on relatedness: a pair can be genuine without being a one-substitution match, since statements also differ in binders and add→mul usually travels with zero→one. Trust the ranking, not the level.

The corpus

import gzip, json
for line in gzip.open("corpus.jsonl.gz", "rt"):
    f = json.loads(line)
    for p in f["premises"]:
        if "@[to_additive" in p["code"]:
            print(p["full_name"])

180,907 declarations against the bundle's 99,552 theorem statements — the extra ~81,000 are definitions, instances and structures. Note that @[to_additive] twins are generated by the compiler and are not separate declarations here: of 9,602 marked declarations only 157 have a resolvable partner in the corpus and 12 have both halves embedded. That route to ground-truth pairs is a dead end, which is why the substitution matcher above exists.

Please read this before using either file

Both are answer keys, and the study they come from depends on their being held back.

Proofs validate discovery because no encoder ever saw one. The verified pairs validate the pairing step because they were not used to build it. Use either to find structure and then confirm with the same thing, and you have proved nothing. Validate with something else: human judgement, a held-out corpus, or the source organisation.