{"id":"https://openalex.org/W7162422167","doi":"https://doi.org/10.48550/arxiv.2605.25556","title":"Keep the Proof State Live: Snapshotting for Efficient Tactic Search in Lean 4","display_name":"Keep the Proof State Live: Snapshotting for Efficient Tactic Search in Lean 4","publication_year":2026,"publication_date":"2026-05-25","ids":{"openalex":"https://openalex.org/W7162422167","doi":"https://doi.org/10.48550/arxiv.2605.25556"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.25556","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.25556","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":"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.2605.25556","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080749862","display_name":"Austin Shen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shen, Austin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5079557370","display_name":"Yunong Shi","orcid":"https://orcid.org/0000-0002-0824-6107"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Yunong","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/T10126","display_name":"Logic, programming, and type systems","score":0.9089999794960022,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9089999794960022,"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/T10142","display_name":"Formal Methods in Verification","score":0.024900000542402267,"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/T11424","display_name":"Security and Verification in Computing","score":0.006200000178068876,"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/speedup","display_name":"Speedup","score":0.786300003528595},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5313000082969666},{"id":"https://openalex.org/keywords/proof-of-concept","display_name":"Proof of concept","score":0.5313000082969666},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.48660001158714294},{"id":"https://openalex.org/keywords/pipeline","display_name":"Pipeline (software)","score":0.42730000615119934},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4237000048160553},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.38940000534057617},{"id":"https://openalex.org/keywords/overhead","display_name":"Overhead (engineering)","score":0.37610000371932983}],"concepts":[{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.786300003528595},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6801999807357788},{"id":"https://openalex.org/C124978682","wikidata":"https://www.wikidata.org/wiki/Q1201019","display_name":"Proof of concept","level":2,"score":0.5313000082969666},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5313000082969666},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.48660001158714294},{"id":"https://openalex.org/C43521106","wikidata":"https://www.wikidata.org/wiki/Q2165493","display_name":"Pipeline (software)","level":2,"score":0.42730000615119934},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4237000048160553},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4169999957084656},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.37610000371932983},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3644999861717224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3612000048160553},{"id":"https://openalex.org/C91154448","wikidata":"https://www.wikidata.org/wiki/Q623818","display_name":"Binary search tree","level":3,"score":0.3458000123500824},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.3384999930858612},{"id":"https://openalex.org/C137335462","wikidata":"https://www.wikidata.org/wiki/Q380772","display_name":"Lean manufacturing","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C128896722","wikidata":"https://www.wikidata.org/wiki/Q1501387","display_name":"Transitive closure","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C2989134064","wikidata":"https://www.wikidata.org/wiki/Q288510","display_name":"Execution time","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.2572000026702881},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.2515000104904175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.25556","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.25556","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":"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.2605.25556","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.25556","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":"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":{"Automated":[0],"theorem":[1,72],"proving":[2],"systems":[3],"built":[4],"on":[5,10,83],"Lean":[6,45,158,206,218],"4":[7,46,159],"increasingly":[8],"rely":[9],"parallel":[11],"tactic":[12],"search":[13,30,97,115],"over":[14,181],"partially":[15],"specified":[16],"proofs,":[17],"such":[18],"as":[19,227],"those":[20],"generated":[21],"by":[22,36],"Draft-Sketch-Prove":[23],"(DSP)":[24],"pipelines.":[25],"In":[26,44],"current":[27],"systems,":[28],"each":[29],"branch":[31],"reconstructs":[32],"a":[33,108,153,177],"proof":[34,84,114,127,144,195],"state":[35,145],"re-running":[37],"elaboration,":[38,68],"leading":[39],"to":[40,75,156,201],"substantial":[41],"per-branch":[42,92],"overhead.":[43],"with":[47,191],"Mathlib,":[48],"this":[49,104],"cost":[50],"has":[51],"two":[52],"components:":[53],"(1)":[54],"import":[55,210],"loading,":[56],"which":[57,69,140,208],"deserializes":[58],"pre-compiled":[59],"libraries":[60],"(~60":[61],"s":[62,81],"per":[63],"branch);":[64],"and":[65,116,147,169,220],"(2)":[66],"theorem-body":[67,214],"re-checks":[70],"the":[71,76,111,142,157,182,192,221],"context":[73],"up":[74],"target":[77],"goal":[78],"(estimated":[79],"18-735":[80],"depending":[82],"complexity).":[85],"Together,":[86],"these":[87],"account":[88],"for":[89],">99%":[90],"of":[91,113,126,194],"wall":[93],"time,":[94],"making":[95],"portfolio-based":[96],"impractical":[98],"at":[99],"scale.":[100],"We":[101],"observe":[102],"that":[103],"overhead":[105],"arises":[106],"from":[107],"mismatch":[109],"between":[110],"structure":[112],"its":[117],"execution":[118],"model:":[119],"branching":[120],"is":[121,199],"implemented":[122],"via":[123,152],"repeated":[124],"reconstruction":[125],"states":[128],"rather":[129],"than":[130],"direct":[131],"reuse.":[132],"To":[133],"address":[134],"this,":[135],"we":[136],"introduce":[137],"proof-state":[138],"snapshotting,":[139],"captures":[141],"elaborated":[143],"once":[146],"reuses":[148],"it":[149],"across":[150],"branches":[151],"small":[154],"extension":[155],"language":[160],"server.":[161],"Across":[162],"48":[163],"miniF2F-v2":[164],"problems":[165],"(45":[166],"prove-phase":[167],"benchmarks":[168],"3":[170],"full":[171],"end-to-end":[172],"runs),":[173],"our":[174],"approach":[175],"achieves":[176],"5.6-50x":[178],"wall-time":[179],"speedup":[180],"standard":[183],"fallback":[184],"(average":[185],"14x,":[186],"median":[187],"9.7x).":[188],"Speedup":[189],"increases":[190],"number":[193],"branches.":[196],"Our":[197],"method":[198],"orthogonal":[200],"import-level":[202],"caching":[203],"(e.g.,":[204],"Kimina":[205],"Server),":[207],"avoids":[209],"loading":[211],"but":[212],"not":[213],"elaboration.":[215],"The":[216],"patched":[217],"binary":[219],"Snapshot-DSP":[222],"pipeline":[223],"will":[224],"be":[225],"released":[226],"open":[228],"source":[229],"upon":[230],"publication.":[231]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-27T00:00:00"}