Datasets:

ai4he
/

procedural-math-reasoning-robustness

model_id string	condition_id string	opaque_public_id string	hidden_label string	terminal_status string	decision string	theorem_exact int64	route_exact int64	joint_exact int64	positive_accept int64	false_positive int64	true_negative int64	prompt_leak_flags float64	schema_errors string	predicted_ops_json string	gold_ops_json string	gold_theorem_name string	predicted_theorem_name string
gemma-4-31b	C0_BASE	rcd2_6516fa8d135e2ec9	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_6516fa8d135e2ec9	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_6516fa8d135e2ec9	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_6516fa8d135e2ec9	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C0_BASE	rcd2_aa5f64b267e35265	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING", "DENORMALIZE_RELATION"]	Siegel's lemma	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_aa5f64b267e35265	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["REMOVE_WITNESS_ENCODING"]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING", "DENORMALIZE_RELATION"]	Siegel's lemma	Siegel's lemma
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_aa5f64b267e35265	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING", "DENORMALIZE_RELATION"]	Siegel's lemma	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_aa5f64b267e35265	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["REMOVE_WITNESS_ENCODING"]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING", "DENORMALIZE_RELATION"]	Siegel's lemma	Siegel's lemma
gemma-4-31b	C0_BASE	rcd2_45f5f15dbf2d1e10	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_45f5f15dbf2d1e10	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_45f5f15dbf2d1e10	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_45f5f15dbf2d1e10	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C0_BASE	rcd2_271c8e25fc8f8de7	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_DISTANCE_ENCODING"]	Monotone convergence theorem	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_271c8e25fc8f8de7	positive	OK	ACCEPT	1	1	1	1	0	0	null	null	["REMOVE_DISTANCE_ENCODING"]	["REMOVE_DISTANCE_ENCODING"]	Monotone convergence theorem	Monotone convergence theorem
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_271c8e25fc8f8de7	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_DISTANCE_ENCODING"]	Monotone convergence theorem	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_271c8e25fc8f8de7	positive	OK	ACCEPT	1	1	1	1	0	0	null	null	["REMOVE_DISTANCE_ENCODING"]	["REMOVE_DISTANCE_ENCODING"]	Monotone convergence theorem	Monotone convergence theorem
gemma-4-31b	C0_BASE	rcd2_2f1807533f51cdb2	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING", "DENORMALIZE_RELATION"]	Isoperimetric inequality	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_2f1807533f51cdb2	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING", "DENORMALIZE_RELATION"]	Isoperimetric inequality	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_2f1807533f51cdb2	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING", "DENORMALIZE_RELATION"]	Isoperimetric inequality	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_2f1807533f51cdb2	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING", "DENORMALIZE_RELATION"]	Isoperimetric inequality	null
gemma-4-31b	C0_BASE	rcd2_178f41df361fb3f1	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_178f41df361fb3f1	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_178f41df361fb3f1	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_178f41df361fb3f1	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C0_BASE	rcd2_88fbe406628dae53	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_ARGMIN_ENCODING"]	Hawkins–Simon condition	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_88fbe406628dae53	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_ARGMIN_ENCODING"]	Hawkins–Simon condition	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_88fbe406628dae53	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_ARGMIN_ENCODING"]	Hawkins–Simon condition	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_88fbe406628dae53	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_ARGMIN_ENCODING"]	Hawkins–Simon condition	null
gemma-4-31b	C0_BASE	rcd2_0a5c01f4782cae7e	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_OPTIMIZATION_ENCODING"]	Levinson's theorem	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_0a5c01f4782cae7e	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["REMOVE_DISTANCE_ENCODING", "REMOVE_OPTIMIZATION_ENCODING"]	["REMOVE_OPTIMIZATION_ENCODING"]	Levinson's theorem	Levinson's theorem
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_0a5c01f4782cae7e	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_OPTIMIZATION_ENCODING"]	Levinson's theorem	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_0a5c01f4782cae7e	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["REMOVE_QUANTIFIER_ENCODING", "REMOVE_DISTANCE_ENCODING"]	["REMOVE_OPTIMIZATION_ENCODING"]	Levinson's theorem	Levinson's theorem
gemma-4-31b	C0_BASE	rcd2_582c2e1f928a5b30	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_DISTANCE_ENCODING"]	Boué–Dupuis formula	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_582c2e1f928a5b30	positive	OK	ACCEPT	1	1	1	1	0	0	null	null	["REMOVE_DISTANCE_ENCODING"]	["REMOVE_DISTANCE_ENCODING"]	Boué–Dupuis formula	Boué–Dupuis formula
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_582c2e1f928a5b30	positive	OK	ACCEPT	1	1	1	1	0	0	null	null	["REMOVE_DISTANCE_ENCODING"]	["REMOVE_DISTANCE_ENCODING"]	Boué–Dupuis formula	Boué-Dupuis Formula
gemma-4-31b	C3_HYBRID_RAG	rcd2_582c2e1f928a5b30	positive	OK	ACCEPT	1	1	1	1	0	0	null	null	["REMOVE_DISTANCE_ENCODING"]	["REMOVE_DISTANCE_ENCODING"]	Boué–Dupuis formula	Boué–Dupuis formula
gemma-4-31b	C0_BASE	rcd2_2c516c5d7d51b60a	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_2c516c5d7d51b60a	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_2c516c5d7d51b60a	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_2c516c5d7d51b60a	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C0_BASE	rcd2_a6a5ee31b8f4014c	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_DISTANCE_ENCODING"]	Cayley–Hamilton theorem	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_a6a5ee31b8f4014c	positive	OK	ACCEPT	1	1	1	1	0	0	null	null	["REMOVE_DISTANCE_ENCODING"]	["REMOVE_DISTANCE_ENCODING"]	Cayley–Hamilton theorem	Cayley–Hamilton theorem
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_a6a5ee31b8f4014c	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_DISTANCE_ENCODING"]	Cayley–Hamilton theorem	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_a6a5ee31b8f4014c	positive	OK	ACCEPT	1	1	1	1	0	0	null	null	["REMOVE_DISTANCE_ENCODING"]	["REMOVE_DISTANCE_ENCODING"]	Cayley–Hamilton theorem	Cayley–Hamilton theorem
gemma-4-31b	C0_BASE	rcd2_c14d4eb07dcb7c30	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_WITNESS_ENCODING"]	Fundamental lemma	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_c14d4eb07dcb7c30	positive	OK	ACCEPT	1	1	1	1	0	0	null	null	["REMOVE_WITNESS_ENCODING"]	["REMOVE_WITNESS_ENCODING"]	Fundamental lemma	Fundamental lemma
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_c14d4eb07dcb7c30	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_WITNESS_ENCODING"]	Fundamental lemma	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_c14d4eb07dcb7c30	positive	OK	ACCEPT	1	1	1	1	0	0	null	null	["REMOVE_WITNESS_ENCODING"]	["REMOVE_WITNESS_ENCODING"]	Fundamental lemma	Fundamental lemma
gemma-4-31b	C0_BASE	rcd2_685215e73ac45625	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_685215e73ac45625	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_685215e73ac45625	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_685215e73ac45625	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C0_BASE	rcd2_78c107bfca939729	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_78c107bfca939729	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_78c107bfca939729	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_78c107bfca939729	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C0_BASE	rcd2_b9311af87fb01e96	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_CONTAINMENT_ENCODING"]	Erdős–Szekeres theorem	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_b9311af87fb01e96	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_CONTAINMENT_ENCODING"]	Erdős–Szekeres theorem	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_b9311af87fb01e96	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_CONTAINMENT_ENCODING"]	Erdős–Szekeres theorem	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_b9311af87fb01e96	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_CONTAINMENT_ENCODING"]	Erdős–Szekeres theorem	null
gemma-4-31b	C0_BASE	rcd2_2bb1f082ed232f6d	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_2bb1f082ed232f6d	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_2bb1f082ed232f6d	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_2bb1f082ed232f6d	negative	OK	ACCEPT	0	0	0	0	1	0	null	null	["REMOVE_QUANTIFIER_ENCODING"]	[]	null	Andreotti–Grauert theorem
gemma-4-31b	C0_BASE	rcd2_38a018c29468b21c	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["OTHER"]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING"]	q-Vandermonde identity	q-Vandermonde Identity
gemma-4-31b	C1_THEOREM_RAG	rcd2_38a018c29468b21c	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["OTHER"]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING"]	q-Vandermonde identity	q-Vandermonde identity
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_38a018c29468b21c	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["OTHER"]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING"]	q-Vandermonde identity	q-Vandermonde Identity
gemma-4-31b	C3_HYBRID_RAG	rcd2_38a018c29468b21c	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["OTHER"]	["EXPAND_ABBREVIATIONS", "REMOVE_SET_MEMBERSHIP_ENCODING"]	q-Vandermonde identity	q-Vandermonde identity
gemma-4-31b	C0_BASE	rcd2_789110b6998162ad	positive	OK	ABSTAIN	0	0	0	0	0	0	null	null	[]	["REMOVE_QUANTIFIER_ENCODING"]	Fundamental theorem of algebra	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_789110b6998162ad	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["REMOVE_QUANTIFIER_ENCODING", "REMOVE_SET_MEMBERSHIP_ENCODING"]	["REMOVE_QUANTIFIER_ENCODING"]	Fundamental theorem of algebra	Fundamental theorem of algebra
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_789110b6998162ad	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_QUANTIFIER_ENCODING"]	Fundamental theorem of algebra	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_789110b6998162ad	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["OTHER", "REMOVE_SET_MEMBERSHIP_ENCODING", "OTHER"]	["REMOVE_QUANTIFIER_ENCODING"]	Fundamental theorem of algebra	Fundamental theorem of algebra
gemma-4-31b	C0_BASE	rcd2_73b688347bf5f292	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_73b688347bf5f292	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_73b688347bf5f292	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_73b688347bf5f292	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C0_BASE	rcd2_a93169124a661949	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_a93169124a661949	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_a93169124a661949	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_a93169124a661949	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C0_BASE	rcd2_9e87ce0a616d2b0c	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_ARGMIN_ENCODING"]	Routh–Hurwitz theorem	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_9e87ce0a616d2b0c	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["REMOVE_OPTIMIZATION_ENCODING"]	["REMOVE_ARGMIN_ENCODING"]	Routh–Hurwitz theorem	Routh–Hurwitz theorem
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_9e87ce0a616d2b0c	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_ARGMIN_ENCODING"]	Routh–Hurwitz theorem	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_9e87ce0a616d2b0c	positive	OK	ACCEPT	1	1	1	1	0	0	null	null	["REMOVE_ARGMIN_ENCODING"]	["REMOVE_ARGMIN_ENCODING"]	Routh–Hurwitz theorem	Routh–Hurwitz theorem
gemma-4-31b	C0_BASE	rcd2_f0e754c9afa94ce8	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_DISTANCE_ENCODING"]	Sylvester's law of inertia	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_f0e754c9afa94ce8	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["OTHER"]	["EXPAND_ABBREVIATIONS", "REMOVE_DISTANCE_ENCODING"]	Sylvester's law of inertia	Sylvester's law of inertia
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_f0e754c9afa94ce8	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["EXPAND_ABBREVIATIONS", "REMOVE_DISTANCE_ENCODING"]	Sylvester's law of inertia	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_f0e754c9afa94ce8	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["DENORMALIZE_RELATION"]	["EXPAND_ABBREVIATIONS", "REMOVE_DISTANCE_ENCODING"]	Sylvester's law of inertia	Sylvester's law of inertia
gemma-4-31b	C0_BASE	rcd2_59770635374ce268	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_59770635374ce268	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_59770635374ce268	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_59770635374ce268	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C0_BASE	rcd2_c587f0569d461171	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_c587f0569d461171	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_c587f0569d461171	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_c587f0569d461171	negative	OK	REJECT	0	0	0	0	0	1	null	null	[]	[]	null	null
gemma-4-31b	C0_BASE	rcd2_90fb5ad3a64575c2	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_ARGMIN_ENCODING"]	Cayley–Hamilton theorem	null
gemma-4-31b	C1_THEOREM_RAG	rcd2_90fb5ad3a64575c2	positive	OK	ACCEPT	1	0	0	1	0	0	null	null	["REMOVE_ARGMIN_ENCODING", "REMOVE_DISTANCE_ENCODING"]	["REMOVE_ARGMIN_ENCODING"]	Cayley–Hamilton theorem	Cayley–Hamilton theorem
gemma-4-31b	C2_TRANSFORM_RAG	rcd2_90fb5ad3a64575c2	positive	OK	REJECT	0	0	0	0	0	0	null	null	[]	["REMOVE_ARGMIN_ENCODING"]	Cayley–Hamilton theorem	null
gemma-4-31b	C3_HYBRID_RAG	rcd2_90fb5ad3a64575c2	positive	OK	ACCEPT	1	1	1	1	0	0	null	null	["REMOVE_ARGMIN_ENCODING"]	["REMOVE_ARGMIN_ENCODING"]	Cayley–Hamilton theorem	Cayley–Hamilton theorem

End of preview. Expand in Data Studio

Procedural Math Reasoning Robustness

Dataset accompanying the paper From Recognition to Reconstruction: Towards Robust Procedural Mathematical Reasoning (4th Workshop on Mathematical Natural Language Processing (MathNLP 2026), EMNLP 2026).

A procedural-robustness panel of 2,800 mathematical statements (1,400 equivalent reformulations of named theorems and 1,400 constructed contrasts) with reference theorem labels and ordered transformation sequences, 44,800 scored outputs from four open-weight models under four conditions (closed-book and retrieval-augmented), the retrieval corpora (306 theorem cards, 17 operation cards) and the full protocol (prompts, output schema, operation vocabulary and run settings).


Paper	From Recognition to Reconstruction: Towards Robust Procedural Mathematical Reasoning
Venue	4th Workshop on Mathematical Natural Language Processing (MathNLP 2026), EMNLP 2026
Authors	Fateme Mazdarani, Carlos Toxtli
License	Creative Commons Attribution-ShareAlike 4.0 International (`cc-by-sa-4.0`)
Dataset DOI	10.5281/zenodo.24179015
Version	1.0.0
Maintainer	Human-AI Empowerment Lab, Clemson University

Paper abstract

Mathematical reasoning systems should be consistent when the same concept is expressed in equivalent forms. This requires not only recognizing shared mathematical meaning but also identifying the representation changes and reconstructing a traceable route between forms. We study this problem through mathematical theorems, whose equivalent formulations preserve the same underlying result while differing substantially in representation. In this setting, theorem recognition is only the first step: a robust system must also identify the intervening transformations and recover their order. We introduce an evaluation of robust procedural mathematical reasoning with three components: theorem identification, transformation identification, and ordered reconstruction. Using validated theorem–representation pairs from an existing corpus, we build a procedural-robustness dataset with typed operations, reference procedures, and matched contrasts that distinguish valid reformulations from invalid ones. We first measure closed-book performance of four open-weight models to establish a baseline, then evaluate retrieval-augmented generation (RAG) as support mechanism for the same task. Models identify theorem identity more reliably than they recover the transformations and ordered routes connecting equivalent representations. RAG improves every stage, but procedural reconstruction remains the main bottleneck. The framework supports more consistent and traceable mathematical systems, with potential applications in mathematical search, tutoring, autoformalization, and scientific discovery.

Dataset structure

Path	Format	Size	Records
`README.txt`	txt	1.9 KB
`annotations.jsonl`	jsonl	3.4 MB	2,800
`items.jsonl`	jsonl	645.2 KB	2,800
`results.csv`	csv	5.8 MB	44,800
`protocol/decoder_output_schema.json`	json	6.7 KB
`protocol/decoder_system_prompt.txt`	txt	1.3 KB
`protocol/decoder_user_template.txt`	txt	2.2 KB
`protocol/executed_experiment_conditions.yaml`	yaml	1.1 KB
`protocol/operation_vocabulary.json`	json	2.6 KB
`retrieval/operation_cards.jsonl`	jsonl	27.3 KB	17
`retrieval/theorem_cards.jsonl`	jsonl	299.8 KB	306

11 files, 10.2 MB in total (metadata files excluded). Records are rows for CSV/TSV/JSONL files and list length for JSON arrays.

Loading the data

from datasets import load_dataset

ds = load_dataset("ai4he/procedural-math-reasoning-robustness", "results")

Available subsets: results, annotations, items, theorem_cards, operation_cards. All other files can be downloaded with huggingface_hub.snapshot_download or from the Zenodo record.

Known limitations

Reference routes come from corpus metadata, not machine-checked proofs.
Contrasts were scored as negatives; their invalidity has not been independently established.
Results are unchanged from the original experiment, including 1,045 invalid outputs; raw generations and retry logs are not included.

Personal and sensitive information

None.

License

The data and documentation are released under the Creative Commons Attribution-ShareAlike 4.0 International. Theorem statements derive from the TREAT corpus, which is built from English Wikipedia (CC BY-SA 4.0); share-alike therefore applies.

Citation

If you use this dataset, please cite the paper:

@inproceedings{Mazdarani2026Recognition,
 title = {From Recognition to Reconstruction: Towards Robust Procedural Mathematical Reasoning},
 author = {Mazdarani, Fateme and Toxtli, Carlos},
 booktitle = {Proceedings of the 4th Workshop on Mathematical Natural Language Processing (MathNLP 2026)},
 address = {Budapest, Hungary},
 publisher = {Association for Computational Linguistics},
 year = {2026},
 month = October,
 note = {Forthcoming},
 url = {https://sites.google.com/view/mathnlp2026}
}

and the dataset:

@dataset{Mazdarani2026ProceduralMathReasoningRData,
  author = {Mazdarani, Fateme and Toxtli, Carlos},
  title = {{Procedural Math Reasoning Robustness}: Dataset for ``From Recognition to Reconstruction: Towards Robust Procedural Mathematical Reasoning''},
  year = {2026},
  version = {1.0.0},
  publisher = {Zenodo},
  doi = {10.5281/zenodo.24179015},
  url = {https://doi.org/10.5281/zenodo.24179015}
}

Notes from the original README.txt

From Recognition to Reconstruction
MathNLP 2026 data and results

Fateme Mazdarani and Carlos Toxtli
From Recognition to Reconstruction: Towards Robust Procedural Mathematical
Reasoning. MathNLP 2026, pp. 42-56.

Contents
  items.jsonl          2,800 statements, paired IDs and inference order
  annotations.jsonl    Reference theorem labels and transformation sequences
  results.csv          44,800 scored outputs from four models and four conditions
  retrieval/           306 theorem cards and 17 operation-card entries
  protocol/            Prompts, output schema, operation vocabulary and settings

JSONL files contain one JSON record per line and use UTF-8. Join the statement
and annotation files on item_id. The results column opaque_public_id refers to
the same ID; pair_id links each reformulation to its constructed contrast.
reference_operations gives the ordered operation labels, and reference_route
contains the source expressions and steps. Empty references for a contrast
mean that no theorem match was supplied, not that non-equivalence was proved.

The panel has 1,400 source reformulations and 1,400 constructed contrasts.
Reference routes come from corpus metadata, not machine-checked proofs.
The contrasts were scored as negative in the experiment; their invalidity
and absence of another matching theorem have not been independently established.
Some theorem assumptions are abbreviated in the source. The annotations and
results should be interpreted with these limitations.

Results are unchanged from the original experiment, including 1,045 invalid
outputs. hidden_label records the original positive/negative class. Accuracy
fields are binary indicators; compare positive examples and contrasts separately.
Raw generations and retry logs are not included.

Please cite the paper when using these materials. Existing rights and any
third-party terms still apply; this archive grants no additional reuse license.

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