{"id":"https://openalex.org/W7166814893","doi":"https://doi.org/10.48550/arxiv.2606.31002","title":"Beyond Compilation: Evaluating Faithful Natural-Language-to-Lean Statement Formalization","display_name":"Beyond Compilation: Evaluating Faithful Natural-Language-to-Lean Statement Formalization","publication_year":2026,"publication_date":"2026-06-30","ids":{"openalex":"https://openalex.org/W7166814893","doi":"https://doi.org/10.48550/arxiv.2606.31002"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.31002","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.31002","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.31002","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139741885","display_name":"Ke Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Ke","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139830319","display_name":"Patricio Gallardo Candela","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Candela, Patricio Gallardo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028869576","display_name":"Sudhir Murthy","orcid":"https://orcid.org/0000-0003-0316-9023"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Murthy, Sudhir","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139736904","display_name":"Yi Xie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xie, Yi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139768291","display_name":"Zhi Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Zhi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5012536010","display_name":"Maziar Raissi","orcid":"https://orcid.org/0000-0002-8467-4568"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raissi, Maziar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11986","display_name":"Scientific Computing and Data Management","score":0.12319999933242798,"subfield":{"id":"https://openalex.org/subfields/1802","display_name":"Information Systems and Management"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11986","display_name":"Scientific Computing and Data Management","score":0.12319999933242798,"subfield":{"id":"https://openalex.org/subfields/1802","display_name":"Information Systems and Management"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.11649999767541885,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.07410000264644623,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.6498000025749207},{"id":"https://openalex.org/keywords/declaration","display_name":"Declaration","score":0.5274999737739563},{"id":"https://openalex.org/keywords/elaboration","display_name":"Elaboration","score":0.44679999351501465},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.41600000858306885},{"id":"https://openalex.org/keywords/audit","display_name":"Audit","score":0.4092000126838684},{"id":"https://openalex.org/keywords/rework","display_name":"Rework","score":0.34139999747276306},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.33230000734329224},{"id":"https://openalex.org/keywords/expert-system","display_name":"Expert system","score":0.32280001044273376}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.685699999332428},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.6498000025749207},{"id":"https://openalex.org/C138147947","wikidata":"https://www.wikidata.org/wiki/Q1183659","display_name":"Declaration","level":2,"score":0.5274999737739563},{"id":"https://openalex.org/C2779192218","wikidata":"https://www.wikidata.org/wiki/Q16944486","display_name":"Elaboration","level":2,"score":0.44679999351501465},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.426800012588501},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.41600000858306885},{"id":"https://openalex.org/C199521495","wikidata":"https://www.wikidata.org/wiki/Q181487","display_name":"Audit","level":2,"score":0.4092000126838684},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.35179999470710754},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.35010001063346863},{"id":"https://openalex.org/C2776543023","wikidata":"https://www.wikidata.org/wiki/Q2147046","display_name":"Rework","level":2,"score":0.34139999747276306},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.33230000734329224},{"id":"https://openalex.org/C58328972","wikidata":"https://www.wikidata.org/wiki/Q184609","display_name":"Expert system","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.3192000091075897},{"id":"https://openalex.org/C75606506","wikidata":"https://www.wikidata.org/wiki/Q1049183","display_name":"Formal methods","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C116253237","wikidata":"https://www.wikidata.org/wiki/Q1437424","display_name":"Formal specification","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C2780385302","wikidata":"https://www.wikidata.org/wiki/Q367158","display_name":"Protocol (science)","level":3,"score":0.27639999985694885},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C2780876879","wikidata":"https://www.wikidata.org/wiki/Q3054749","display_name":"Meaning (existential)","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.2574999928474426}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.31002","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.31002","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.31002","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.31002","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7524245381355286,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Theorem-proving":[0],"benchmarks":[1],"evaluate":[2],"proof":[3],"search":[4,209],"against":[5],"fixed":[6],"formal":[7,15,155],"statements,":[8],"but":[9,96,105,200],"natural-language-to-Lean":[10],"formalization":[11,46,182],"must":[12],"generate":[13],"the":[14,112,196],"statement":[16,45,162],"itself.":[17],"In":[18],"this":[19,141,222],"setting,":[20],"compilation":[21,95],"is":[22,84,195,218],"only":[23,97],"a":[24,27,39,53,57,89,102,115,171,204],"validity":[25,198],"check:":[26],"Lean":[28,72,149,158,190],"declaration":[29],"may":[30],"type-check":[31],"while":[32,130],"omitting":[33],"hypotheses,":[34],"changing":[35],"domains,":[36],"or":[37],"expressing":[38],"vacuous":[40],"claim.":[41],"We":[42,168],"study":[43],"faithful":[44,161],"as":[47,114],"both":[48],"an":[49],"evaluation":[50],"problem":[51],"and":[52,67,77,147,160,189,213,215,227],"bottleneck-attribution":[54],"problem.":[55],"On":[56],"400-entry":[58],"graduate-level":[59],"benchmark":[60],"spanning":[61],"real":[62],"analysis,":[63,65],"complex":[64],"topology,":[66],"algebra,":[68],"our":[69],"protocol":[70],"combines":[71],"compilation,":[73],"cross-model":[74],"semantic":[75,138],"judging,":[76],"human":[78,109],"expert":[79,185],"calibration.":[80],"The":[81],"resulting":[82],"picture":[83],"different":[85],"from":[86],"compile-rate":[87],"evaluation:":[88],"full":[90,172],"tool-augmented":[91],"agent":[92],"reaches":[93],"89.5%":[94],"60.5%":[98],"consensus":[99],"faithfulness,":[100],"exposing":[101],"29.0-point":[103],"compile-pass":[104,133,206],"consensus-unfaithful":[106],"gap.":[107],"Targeted":[108],"audits":[110],"support":[111],"metric":[113],"conservative":[116],"decision":[117],"boundary:":[118],"across":[119],"available":[120],"case-level":[121],"audits,":[122],"96.0%":[123],"of":[124,132],"consensus-positive":[125],"outputs":[126,135],"are":[127,136,229],"human-confirmed":[128,137],"faithful,":[129],"82.4%":[131],"consensus-negative":[134],"failures.":[139],"Under":[140],"metric,":[142],"existing":[143],"one-shot":[144],"formalizer":[145],"models":[146,150],"prover-oriented":[148],"remain":[151],"low,":[152],"suggesting":[153],"that":[154],"validity,":[156],"proof-oriented":[157],"competence,":[159],"generation":[163],"should":[164],"be":[165],"reported":[166],"separately.":[167],"then":[169],"use":[170],"$2^3$":[173],"factorial":[174],"design":[175],"to":[176],"decompose":[177],"three":[178],"recurring":[179],"interventions":[180],"in":[181,221],"pipelines:":[183],"parametric":[184],"drafting,":[186],"Mathlib/context":[187],"search,":[188],"elaboration":[191],"feedback.":[192],"Elaboration":[193],"feedback":[194,226],"largest":[197],"intervention,":[199],"it":[201],"also":[202],"exposes":[203],"larger":[205],"semantic-failure":[207],"bucket;":[208],"mainly":[210],"improves":[211],"grounding":[212,228],"selectivity;":[214],"fine-tuned":[216],"drafting":[217],"largely":[219],"substitutable":[220],"tool":[223],"stack":[224],"once":[225],"available.":[230]},"counts_by_year":[],"updated_date":"2026-07-02T06:18:51.028212","created_date":"2026-07-02T00:00:00"}
