{"id":"https://openalex.org/W7172330379","doi":"https://doi.org/10.48550/arxiv.2607.29549","title":"AMTFV: Agentic Mathematical Tool-Flow Verification for LLM Self-Correction","display_name":"AMTFV: Agentic Mathematical Tool-Flow Verification for LLM Self-Correction","publication_year":2026,"publication_date":"2026-07-31","ids":{"openalex":"https://openalex.org/W7172330379","doi":"https://doi.org/10.48550/arxiv.2607.29549"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.29549","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.29549","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"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.2607.29549","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5144251721","display_name":"Rui Zou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zou, Rui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144267931","display_name":"Yutao Zhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Yutao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144295829","display_name":"Mengqi Wei","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wei, Mengqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5144250714","display_name":"Ji-Rong Wen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wen, Ji-Rong","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/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.45739999413490295,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.45739999413490295,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11450","display_name":"Model-Driven Software Engineering Techniques","score":0.05990000069141388,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T10028","display_name":"Topic Modeling","score":0.04410000145435333,"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/executable","display_name":"Executable","score":0.7670999765396118},{"id":"https://openalex.org/keywords/toolbox","display_name":"Toolbox","score":0.7483000159263611},{"id":"https://openalex.org/keywords/mathematical-model","display_name":"Mathematical model","score":0.5755000114440918},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.46480000019073486},{"id":"https://openalex.org/keywords/formal-verification","display_name":"Formal verification","score":0.40389999747276306},{"id":"https://openalex.org/keywords/mathematical-theory","display_name":"Mathematical theory","score":0.3921999931335449},{"id":"https://openalex.org/keywords/baseline","display_name":"Baseline (sea)","score":0.3817000091075897},{"id":"https://openalex.org/keywords/automated-reasoning","display_name":"Automated reasoning","score":0.36059999465942383},{"id":"https://openalex.org/keywords/software-verification","display_name":"Software verification","score":0.34450000524520874}],"concepts":[{"id":"https://openalex.org/C160145156","wikidata":"https://www.wikidata.org/wiki/Q778586","display_name":"Executable","level":2,"score":0.7670999765396118},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7554000020027161},{"id":"https://openalex.org/C2777655017","wikidata":"https://www.wikidata.org/wiki/Q1501161","display_name":"Toolbox","level":2,"score":0.7483000159263611},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.5755000114440918},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.5077000260353088},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.46480000019073486},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4239000082015991},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.40389999747276306},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C12725497","wikidata":"https://www.wikidata.org/wiki/Q810247","display_name":"Baseline (sea)","level":2,"score":0.3817000091075897},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3790999948978424},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.36059999465942383},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.34790000319480896},{"id":"https://openalex.org/C33054407","wikidata":"https://www.wikidata.org/wiki/Q6504747","display_name":"Software verification","level":5,"score":0.34450000524520874},{"id":"https://openalex.org/C66024118","wikidata":"https://www.wikidata.org/wiki/Q1122506","display_name":"Computational model","level":2,"score":0.33899998664855957},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3292999863624573},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.323199987411499},{"id":"https://openalex.org/C126433048","wikidata":"https://www.wikidata.org/wiki/Q7921324","display_name":"Verification and validation of computer simulation models","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C168065819","wikidata":"https://www.wikidata.org/wiki/Q845566","display_name":"Debugging","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C62460635","wikidata":"https://www.wikidata.org/wiki/Q5508853","display_name":"Functional verification","level":3,"score":0.29249998927116394},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C172347087","wikidata":"https://www.wikidata.org/wiki/Q3217196","display_name":"Language of mathematics","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C202973057","wikidata":"https://www.wikidata.org/wiki/Q7380130","display_name":"Runtime verification","level":3,"score":0.263700008392334},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.25769999623298645},{"id":"https://openalex.org/C176248197","wikidata":"https://www.wikidata.org/wiki/Q458526","display_name":"Probably approximately correct learning","level":4,"score":0.2574999928474426},{"id":"https://openalex.org/C75606506","wikidata":"https://www.wikidata.org/wiki/Q1049183","display_name":"Formal methods","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.2533999979496002}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.29549","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.29549","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.29549","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.29549","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"license_id":null,"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":{"Large":[0],"language":[1],"models":[2],"have":[3],"demonstrated":[4],"strong":[5],"mathematical":[6,47,82,95,112,149],"problem-solving":[7],"capabilities,":[8],"yet":[9],"reliably":[10,38],"verifying":[11],"their":[12],"candidate":[13],"answers":[14],"remains":[15],"challenging.":[16],"Existing":[17],"representative":[18,168],"methods":[19],"mainly":[20],"revise":[21],"outputs":[22,133],"through":[23,80],"natural-language":[24],"reflection":[25],"or":[26],"assist":[27],"verification":[28,32,71,86,91,203],"by":[29,188],"directly":[30],"generating":[31],"programs;":[33],"the":[34,43,85,94,111,118,127,167,185],"former":[35],"may":[36],"not":[37],"support":[39,135],"exact":[40,78,130],"computation,":[41],"whereas":[42],"latter":[44,116],"prematurely":[45],"couples":[46],"modeling":[48,72],"with":[49,152,194],"low-level":[50],"implementation.":[51],"We":[52,143],"propose":[53],"AMTFV":[54,69,145,165],"(Agentic":[55],"Mathematical":[56,61],"Tool-Flow":[57],"Verification).":[58],"By":[59],"introducing":[60],"Tool":[62,132],"Flow":[63],"(MTF)":[64],"as":[65],"an":[66,104,176],"interrupt--execute--resume":[67],"interface,":[68],"decouples":[70],"from":[73,156],"concrete":[74],"execution":[75,102],"and":[76,97,107,123,140,159,201],"supports":[77],"computation":[79],"a":[81,90],"toolbox.":[83],"Specifically,":[84],"agent":[87],"first":[88],"constructs":[89],"workflow,":[92],"encodes":[93],"objects":[96],"computational":[98],"intent":[99],"requiring":[100],"reliable":[101],"in":[103,171],"MTF":[105],"request,":[106,119],"sends":[108],"it":[109,180],"to":[110,126,190],"toolbox":[113],"agent.":[114],"The":[115],"parses":[117],"generates":[120],"executable":[121],"calls,":[122],"dispatches":[124],"them":[125],"backend":[128],"for":[129],"computation.":[131],"then":[134],"candidate-answer":[136],"adjudication,":[137],"answer":[138],"revision,":[139],"verification-workflow":[141],"revision.":[142],"evaluate":[144],"on":[146,197],"five":[147],"challenging":[148],"reasoning":[150],"datasets":[151],"seven":[153],"model":[154,178],"configurations":[155],"DeepSeek,":[157],"GPT,":[158],"Gemini.":[160],"Experimental":[161],"results":[162],"show":[163],"that":[164],"outperforms":[166],"baselines":[169],"evaluated":[170],"this":[172],"study":[173],"overall;":[174],"under":[175],"individual":[177],"configuration,":[179],"improves":[181],"average":[182],"accuracy":[183],"over":[184],"strongest":[186],"baseline":[187],"up":[189],"8.3":[191],"percentage":[192],"points,":[193],"larger":[195],"gains":[196],"samples":[198],"of":[199],"medium":[200],"high":[202],"complexity.":[204]},"counts_by_year":[],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2026-08-04T00:00:00"}
