Pith Number

pith:QWIGJSQN

pith:2026:QWIGJSQNTOJMAXZQWRDBTPSAPG

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Not All Proofs Are Equal: Evaluating LLM Proof Quality Beyond Correctness

Dimitar I. Dimitrov, Ivo Petrov, Jasper Dekoninck, Martin Vechev

LLM-generated proofs differ substantially in quality beyond mere correctness, with measurable trade-offs.

arxiv:2605.10379 v2 · 2026-05-11 · cs.CL

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Across models, we find substantial differences in proof quality that are not captured by correctness-only benchmarks. We also observe significant trade-offs between proof-quality metrics and correctness, suggesting that future evaluations of mathematical reasoning should measure how useful LLM-generated proofs are.

C2weakest assumption

That the five chosen proxies (conciseness, computational ease, cognitive simplicity, diversity, adaptivity) are scalable, objective enough to measure automatically, and genuinely reflect the aspects of proof quality that matter to human readers and downstream use.

C3one line summary

LLM proofs for hard math problems show large differences in quality metrics like conciseness and cognitive simplicity that correctness-only tests miss, along with trade-offs between quality and correctness.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-26T01:15:53.111753Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

859064ca0d9b92c05f30b44619be4079ba784772670d01fe8648dabe83b92b4a

Aliases

arxiv: 2605.10379 · arxiv_version: 2605.10379v2 · doi: 10.48550/arxiv.2605.10379 · pith_short_12: QWIGJSQNTOJM · pith_short_16: QWIGJSQNTOJMAXZQ · pith_short_8: QWIGJSQN

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QWIGJSQNTOJMAXZQWRDBTPSAPG \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 859064ca0d9b92c05f30b44619be4079ba784772670d01fe8648dabe83b92b4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d79407fe6c253eec7ab40bdb3729eefd4266fe0105ddaf41d61a35a0916aad9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CL",
    "submitted_at": "2026-05-11T11:23:36Z",
    "title_canon_sha256": "1b7f3f35c517047fae4eef1304aeec951765e7bb228216aeb258cf1aa64cb3bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10379",
    "kind": "arxiv",
    "version": 2
  }
}