mjbommar/openlemma-v0.1-eval

OpenLemma v0.1: evaluation

Probes and held-out items. Never in the training data.

• Copy-rate probes are multiple-choice k-shot prompts. In record, copy_index marks the option that copies the previous demonstration's answer, and prev_answer_is_gold marks when copying happens to be right (base rate). Score accuracy, copy rate and anti-copy rate.
• Held-out items come from held-out seeds, task types or headwords.

Config	Rows
constructs-1-heldout	10,783
gloss-probes	3,716
gloss-run2	12,633
gloss-run3	0
gloss-run4	63,214
lemma-v1-heldout	23,734
lemma-v1-probes	4,677

Provenance and verification

Every row comes from OpenLemma (code: MIT; the documentation in docs/ covers every source).

• Generation: procedural generators and gpt-6-luna (OpenAI, flex, reasoning effort low). Some upstream retrieval material was written by gpt-5.4-mini.
• Auditing only: gpt-6-sol.
• Checks:
  • verified: an independent checker, solver (axeyum), CAS route or truth table recomputed the answer;
  • constructed: the label is fixed by how the item was built (planted values, code corruptions, the sense a sentence was written for);
  • agreed: a model-proposed label that independent blind model checks agreed with, in a family whose gpt-6-sol audit is >= 95% (default) or 80-95% (extended, with audit_accuracy on every row);
  • prose: model-written explanatory text about verified facts.

Anti-copy packing. k-shot documents (k in {0, 1, 3, 8}) never reward copying the previous answer:

• open answers are pairwise distinct;
• label answers repeat the last demonstration's label only at the base rate 1/n, with labels balanced over the demonstrations;
• copy traps and symbol labels appear on 10% of documents each.

Batches v0/v1 were originally packed so that "any label but the last one" was always right; this release repacks those families.

Plain text. Documents in default/extended contain no control tokens. ALEA-style <|start|>/<|end|> boundaries are added at tokenization. Reasoning glyphs (① ∴ ∵ ⊢ ● ⚠ …) are ordinary characters. The special_tokens config keeps the original ALEA control-token renderings for replication.

Token counts use the ALEA tokenizer alea-p1-prefix-16k.

Licence and attribution

CC-BY-4.0. Attribute OpenLemma (https://github.com/mjbommar/openlemma). Upstream sources:

• axeyum (MIT OR Apache-2.0): curriculum, facts, scenarios, CAS and solver checks;
• OpenGloss v2.4 (CC-BY-4.0): lexical seeds and grounding;
• WordNet 3.0: rows derived from WordNet senses carry the WordNet licence, included as LICENSE-WordNet.txt;
• alea-quality-model: the 93 foundational reasoning constructs.

Generated text was produced with OpenAI models and is subject to the provider's terms.

Known limitations

• agreed labels are model-checked, not proven; read audit_accuracy and the per-family audits in the repository docs.
• OpenGloss v2.4 has known defects (about 10% of common senses invalid, unreliable etymologies). Etymology tasks are excluded, and seed senses were validity-checked for the newer runs.
• Two deontic constructs are thin (Permission Operator, Prohibition Operator).
• This release was published before any model was trained on it. It makes no claim about downstream gains.

Citation

@misc{openlemma2026,
  title  = {OpenLemma: verified, bottom-up synthetic data for logic, reasoning, algorithms and language},
  author = {Bommarito, Michael J.},
  year   = {2026},
  note   = {Version 0.1},
  url    = {https://github.com/mjbommar/openlemma}
}