{"id":"https://openalex.org/W7225199100","doi":"https://doi.org/10.5281/zenodo.23921824","title":"Entropy contraction on complete bipartite graphs via reverse erasure: only the rarest symbol matters","display_name":"Entropy contraction on complete bipartite graphs via reverse erasure: only the rarest symbol matters","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7225199100","doi":"https://doi.org/10.5281/zenodo.23921824"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23921824","doi":"https://doi.org/10.5281/zenodo.23921824","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23921824","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23921824","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Anonymous","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Anonymous","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/T13500","display_name":"Probability and Statistical Research","score":0.3452000021934509,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.3452000021934509,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.23280000686645508,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.0869000032544136,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/complete-bipartite-graphs","display_name":"complete bipartite graphs","score":0.9620000123977661},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"spectral gap","score":0.8259999752044678},{"id":"https://openalex.org/keywords/mixing-time","display_name":"mixing time","score":0.6589999794960022},{"id":"https://openalex.org/keywords/markov-chains","display_name":"Markov chains","score":0.40799999237060547}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8219000101089478},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7160000205039978},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6736000180244446},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6407999992370605},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.527400016784668},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5108000040054321},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.47429999709129333},{"id":"https://openalex.org/C196083917","wikidata":"https://www.wikidata.org/wiki/Q17103874","display_name":"Min entropy","level":5,"score":0.4480000138282776},{"id":"https://openalex.org/C170320093","wikidata":"https://www.wikidata.org/wiki/Q1953457","display_name":"De Bruijn sequence","level":2,"score":0.44519999623298645},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.3926999866962433},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.351500004529953},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.3262999951839447},{"id":"https://openalex.org/C149862233","wikidata":"https://www.wikidata.org/wiki/Q864142","display_name":"Binary erasure channel","level":4,"score":0.3174999952316284},{"id":"https://openalex.org/C154547637","wikidata":"https://www.wikidata.org/wiki/Q776602","display_name":"Expander graph","level":3,"score":0.3158999979496002},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.30959999561309814},{"id":"https://openalex.org/C20218877","wikidata":"https://www.wikidata.org/wiki/Q3066095","display_name":"De Bruijn graph","level":3,"score":0.3001999855041504},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.28290000557899475},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.263700008392334},{"id":"https://openalex.org/C2778790127","wikidata":"https://www.wikidata.org/wiki/Q484885","display_name":"Erasure","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.25769999623298645},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.2551000118255615}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23921824","doi":"https://doi.org/10.5281/zenodo.23921824","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23921824","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23921825","doi":"https://doi.org/10.5281/zenodo.23921825","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23921825","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23921824","doi":"https://doi.org/10.5281/zenodo.23921824","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23921824","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1590505944","https://openalex.org/W1791650288","https://openalex.org/W2003776291","https://openalex.org/W2071462233","https://openalex.org/W2098392316","https://openalex.org/W2110051854","https://openalex.org/W2169691280","https://openalex.org/W2290247654","https://openalex.org/W2465286492","https://openalex.org/W2518476007","https://openalex.org/W2803741743","https://openalex.org/W2884296540","https://openalex.org/W2963423396","https://openalex.org/W3042492913","https://openalex.org/W3091482820","https://openalex.org/W4221151467","https://openalex.org/W4387804025","https://openalex.org/W4413042188","https://openalex.org/W7166196260"],"related_works":["https://openalex.org/W2744328542","https://openalex.org/W1621250739","https://openalex.org/W2139769859","https://openalex.org/W390216103","https://openalex.org/W7224600362","https://openalex.org/W1483924839","https://openalex.org/W7225006802","https://openalex.org/W2320724191","https://openalex.org/W1594177088","https://openalex.org/W7096989086"],"abstract_inverted_index":{"Unrefereed":[0],"research":[1],"candidate.":[2],"In":[3],"one":[4,61,132],"sentence:":[5],"for":[6,112,116,288,365,390],"the":[7,14,22,41,64,69,80,92,99,110,142,146,166,172,186,192,209,211,251,283,292,299,303,310,317,356],"Bayesian":[8],"reverse":[9],"of":[10,17,34,56,63,125,134,141,200,205,247,256,302],"an":[11],"erasure":[12],"channel,":[13],"worst-case":[15],"loss":[16],"relative":[18,75],"entropy":[19,76],"depends":[20,170],"on":[21,40,45,68,171,250,410],"prior":[23,161,173],"only":[24,93,174,399],"through":[25,175],"its":[26,176,320],"rarest":[27],"symbol,":[28],"and":[29,38,52,115,218,231,282,315,319,336,349,360,376,419],"this":[30,135,164],"settles":[31,243],"a":[32,156,160,198,201,236,244,254,268,368,411],"conjecture":[33,111],"Caputo,":[35,49],"Chen,":[36,50],"Gu":[37,51],"Polyanskiy":[39,53],"half-lazy":[42,65],"random":[43,66],"walk":[44,67,136,304],"complete":[46,70],"bipartite":[47,71,239],"graphs.":[48],"(Electronic":[54],"Journal":[55],"Probability,":[57],"2025)":[58],"conjectured":[59],"that":[60,131],"step":[62,133],"graph":[72],"Kn,n":[73],"shrinks":[74],"by":[77,155],"at":[78,180,271],"most":[79,272],"factor":[81],"log":[82,86],"n":[83,101],"/":[84,196],"(2":[85],"2n),":[87],"with":[88,104,118,149,270,333,340,344],"single":[89],"vertices":[90],"as":[91],"worst":[94,212],"starting":[95],"points;":[96],"they":[97],"proved":[98],"case":[100,227],"=":[102,120,190],"3":[103],"computer":[105],"assistance.":[106],"This":[107],"paper":[108],"proves":[109],"every":[113,181,366],"n,":[114],"Km,n":[117],"M":[119],"max(m,":[121],"n)":[122],"in":[123,347],"place":[124],"n.":[126],"The":[127,224,307],"key":[128],"observation":[129,246],"is":[130,194,222,228,295,305],"splits":[137],"into":[138],"two":[139,273],"copies":[140],"reverse-erasure":[143],"channel:":[144],"keep":[145],"current":[147],"symbol":[148],"probability":[150],"\u03b1,":[151],"otherwise":[152],"replace":[153],"it":[154],"fresh":[157],"draw":[158],"from":[159],"\u03c1.":[162],"For":[163],"channel":[165],"relative-entropy":[167],"contraction":[168],"coefficient":[169,193],"smallest":[177],"atom":[178],"q,":[179],"retention":[182],"probability.":[183],"Up":[184],"to":[185,267],"sharp":[187],"threshold":[188,210],"\u03b1":[189],"qq/(1-q)":[191],"log(1/q)":[195],"log(1/(\u03b1q)),":[197],"translation":[199],"weighted":[202,238],"mean":[203],"inequality":[204],"Gao":[206],"(credited);":[207],"above":[208],"inputs":[213],"become":[214],"full-support":[215],"exponential":[216],"tilts":[217],"no":[219,296],"closed":[220],"form":[221],"given.":[223],"uniform":[225],"binary":[226],"known":[229],"(Nair":[230],"Wang;":[232],"Zhao).":[233],"Further":[234],"consequences:":[235],"rank-one":[237],"extension,":[240],"which":[241],"also":[242],"numerical":[245,382],"Jadhav":[248],"(2026)":[249],"lazy":[252],"star;":[253],"reduction":[255],"any":[257],"block-reset":[258,337],"chain":[259,269],"(any":[260],"laziness,":[261],"all":[262],"powers,":[263],"stars,":[264],"multipartite":[265],"graphs)":[266],"states":[274],"per":[275],"block,":[276],"whose":[277],"values":[278,393],"are":[279,384,394],"computed":[280],"numerically;":[281],"exact":[284,353],"one-way":[285],"communication":[286],"rate":[287],"agreement":[289],"distillation":[290],"below":[291],"threshold.":[293],"There":[294],"mixing-time":[297],"improvement:":[298],"spectral":[300],"gap":[301],"1/2.":[306],"archive":[308],"contains":[309],"manuscript":[311],"(LaTeX":[312],"source,":[313],"bibliography":[314],"PDF),":[316],"figure":[318],"script,":[321],"four":[322],"verification":[323],"scripts":[324],"(random-sample":[325],"suite,":[326],"minimum-mass":[327],"diagnostics,":[328],"ten":[329],"must-fail":[330,342],"negative":[331],"controls":[332],"near-extremiser":[334],"families,":[335],"extension":[338],"checks":[339],"five":[341],"controls)":[343],"recorded":[345],"outputs":[346],"normal":[348],"optimised":[350],"Python":[351],"modes,":[352],"small-kernel":[354],"fingerprints,":[355],"dated":[357],"prior-art":[358],"gate":[359],"audit,":[361],"raw":[362],"registry":[363],"records":[364],"reference,":[367],"rating-free":[369],"internal":[370,396],"review":[371,398],"summary,":[372],"development":[373],"notes,":[374],"CI":[375],"SHA-256":[377],"sums.":[378],"Assurance:":[379],"written":[380],"proofs;":[381,387],"diagnostics":[383],"evidence,":[385],"not":[386],"point-optimality":[388],"windows":[389],"other":[391],"laziness":[392],"numerical;":[395],"AI-assisted":[397],"(not":[400],"peer":[401],"review,":[402],"independent":[403],"reproduction":[404],"or":[405],"formal":[406],"verification);":[407],"priority":[408],"rests":[409],"bounded":[412],"literature":[413],"search.":[414],"Creator:":[415],"Anonymous.":[416],"Text,":[417],"data":[418],"figures":[420],"CC0-1.0;":[421],"code":[422],"MIT.":[423]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-04T00:00:00"}
