{"id":"https://openalex.org/W7157179236","doi":"https://doi.org/10.48550/arxiv.2604.23002","title":"FormalScience: Scalable Human-in-the-Loop Autoformalisation of Science with Agentic Code Generation in Lean","display_name":"FormalScience: Scalable Human-in-the-Loop Autoformalisation of Science with Agentic Code Generation in Lean","publication_year":2026,"publication_date":"2026-04-24","ids":{"openalex":"https://openalex.org/W7157179236","doi":"https://doi.org/10.48550/arxiv.2604.23002"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.23002","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23002","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.2604.23002","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134765086","display_name":"Jordan Meadows","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meadows, Jordan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134771057","display_name":"Lan Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Lan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134777039","display_name":"Andre Freitas","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Freitas, Andre","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":0.22050000727176666,"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":0.22050000727176666,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.13510000705718994,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.12430000305175781,"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":0.51910001039505},{"id":"https://openalex.org/keywords/formal-methods","display_name":"Formal methods","score":0.503600001335144},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5031999945640564},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5023000240325928},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.43700000643730164},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.42489999532699585},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.42260000109672546},{"id":"https://openalex.org/keywords/automated-reasoning","display_name":"Automated reasoning","score":0.4043000042438507},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.3792000114917755}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6973999738693237},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.51910001039505},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.5116999745368958},{"id":"https://openalex.org/C75606506","wikidata":"https://www.wikidata.org/wiki/Q1049183","display_name":"Formal methods","level":2,"score":0.503600001335144},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5031999945640564},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5023000240325928},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.43700000643730164},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.42489999532699585},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.42260000109672546},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.4043000042438507},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3799999952316284},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.3792000114917755},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.37119999527931213},{"id":"https://openalex.org/C102315432","wikidata":"https://www.wikidata.org/wiki/Q649732","display_name":"Formal system","level":2,"score":0.35249999165534973},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.34200000762939453},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.3343999981880188},{"id":"https://openalex.org/C116253237","wikidata":"https://www.wikidata.org/wiki/Q1437424","display_name":"Formal specification","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C146499914","wikidata":"https://www.wikidata.org/wiki/Q5469969","display_name":"Formal semantics (linguistics)","level":2,"score":0.3199999928474426},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3109999895095825},{"id":"https://openalex.org/C146072743","wikidata":"https://www.wikidata.org/wiki/Q192161","display_name":"Formal language","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C2522767166","wikidata":"https://www.wikidata.org/wiki/Q2374463","display_name":"Data science","level":1,"score":0.28130000829696655},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C135257023","wikidata":"https://www.wikidata.org/wiki/Q691358","display_name":"Domain-specific language","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C48859967","wikidata":"https://www.wikidata.org/wiki/Q6486712","display_name":"Language construct","level":2,"score":0.26249998807907104}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.23002","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23002","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.2604.23002","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.23002","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Formalising":[0],"informal":[1,78],"mathematical":[2],"reasoning":[3,79],"into":[4],"formally":[5],"verifiable":[6],"code":[7],"is":[8,197],"a":[9,52,59,91,136,151],"significant":[10],"challenge":[11],"for":[12,80],"large":[13],"language":[14,66,191],"models.":[15],"In":[16],"scientific":[17,47,217],"fields":[18],"such":[19,180],"as":[20,181],"physics,":[21,87],"domain-specific":[22],"machinery":[23],"(\\textit{e.g.}":[24],"Dirac":[25],"notation,":[26],"vector":[27],"calculus)":[28],"imposes":[29],"additional":[30],"formalisation":[31],"challenges":[32],"that":[33,57],"modern":[34,161],"LLMs":[35],"and":[36,72,99,104,123,132,150,156,184,213],"agentic":[37,55,154],"approaches":[38],"have":[39],"yet":[40],"to":[41,68,86,113],"tackle.":[42],"To":[43],"aid":[44],"autoformalisation":[45,138,158,175,212],"in":[46,160,173,176,216],"domains,":[48],"we":[49,88],"present":[50],"FormalScience;":[51],"domain-agnostic":[53],"human-in-the-loop":[54],"pipeline":[56],"enables":[58],"single":[60],"domain":[61],"expert":[62],"(without":[63],"deep":[64],"formal":[65,75,110,115,121,190],"experience)":[67],"produce":[69],"\\textit{syntactically":[70],"correct}":[71],"\\textit{semantically":[73],"aligned}":[74],"proofs":[76],"of":[77,93,170,178],"low":[81],"economic":[82],"cost.":[83],"Applying":[84],"FormalScience":[85,208],"construct":[89],"FormalPhysics,":[90],"dataset":[92,142],"200":[94],"university-level":[95],"(LaTeX)":[96],"physics":[97,174],"problems":[98],"solutions":[100],"(primarily":[101],"quantum":[102],"mechanics":[103],"electromagnetism),":[105],"along":[106],"with":[107,147,204],"their":[108],"Lean4":[109],"representations.":[111],"Compared":[112],"existing":[114],"math":[116],"benchmarks,":[117],"FormalPhysics":[118],"achieves":[119],"perfect":[120],"validity":[122],"exhibits":[124],"greater":[125],"statement":[126,137],"complexity.":[127],"We":[128,164,199],"evaluate":[129],"open-source":[130],"models":[131],"proprietary":[133],"systems":[134],"on":[135,140],"task":[139],"our":[141],"via":[143],"zero-shot":[144],"prompting,":[145],"self-refinement":[146],"error":[148],"feedback,":[149],"novel":[152],"multi-stage":[153],"approach,":[155],"explore":[157],"limitations":[159],"LLM-based":[162],"approaches.":[163],"provide":[165],"the":[166,201],"first":[167],"systematic":[168],"characterisation":[169],"semantic":[171,195],"drift":[172],"terms":[177],"concepts":[179],"notational":[182],"collapse":[183],"abstraction":[185],"elevation":[186],"which":[187,210],"reveals":[188],"what":[189],"verifies":[192],"when":[193],"full":[194],"preservation":[196],"unattainable.":[198],"release":[200],"codebase":[202],"together":[203],"an":[205],"interactive":[206],"UI-based":[207],"system":[209],"facilitates":[211],"theorem":[214],"proving":[215],"domains":[218],"beyond":[219],"physics.https://github.com/jmeadows17/formal-science":[220]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-29T00:00:00"}