{"id":"https://openalex.org/W7225379291","doi":"https://doi.org/10.5281/zenodo.24023136","title":"Low-degree hardness of recovery below the Kesten\u2013Stigum threshold in planted 3-SAT","display_name":"Low-degree hardness of recovery below the Kesten\u2013Stigum threshold in planted 3-SAT","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225379291","doi":"https://doi.org/10.5281/zenodo.24023136"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24023136","doi":"https://doi.org/10.5281/zenodo.24023136","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24023136","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":"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24023136","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064867350","display_name":"Yan Ru Pei","orcid":"https://orcid.org/0000-0002-6999-3691","observed_orcids":["https://orcid.org/0000-0002-6999-3691"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pei, Yan Ru","raw_affiliation_strings":["University of California San Diego"],"raw_orcid":"https://orcid.org/0000-0002-6999-3691","affiliations":[{"raw_affiliation_string":"University of California San Diego","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064867350"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.7548999786376953,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.7548999786376953,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.015599999576807022,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10591","display_name":"Theoretical and Computational Physics","score":0.01510000042617321,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/weak-recovery","display_name":"weak recovery","score":0.8650000095367432},{"id":"https://openalex.org/keywords/mobius-inversion-formula","display_name":"M\u00f6bius inversion","score":0.6899999976158142},{"id":"https://openalex.org/keywords/spectral-algorithms","display_name":"spectral algorithms","score":0.4880000054836273},{"id":"https://openalex.org/keywords/information-theoretic-limits","display_name":"information-theoretic limits","score":0.5619999766349792}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8740000128746033},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5343000292778015},{"id":"https://openalex.org/C2780882242","wikidata":"https://www.wikidata.org/wiki/Q14235582","display_name":"Literal (mathematical logic)","level":2,"score":0.44690001010894775},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.44620001316070557},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44609999656677246},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4219000041484833},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4198000133037567},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.41110000014305115},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3824999928474426},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C96865113","wikidata":"https://www.wikidata.org/wiki/Q2946816","display_name":"Certificate","level":2,"score":0.35100001096725464},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3262999951839447},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.31869998574256897},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C40976572","wikidata":"https://www.wikidata.org/wiki/Q2330873","display_name":"Gauge (firearms)","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.2660999894142151}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24023136","doi":"https://doi.org/10.5281/zenodo.24023136","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24023136","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":"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"},{"id":"doi:10.5281/zenodo.24023137","doi":"https://doi.org/10.5281/zenodo.24023137","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24023137","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":"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"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24023136","doi":"https://doi.org/10.5281/zenodo.24023136","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24023136","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":"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225433734","https://openalex.org/W7099924211","https://openalex.org/W3047315550","https://openalex.org/W7163698207","https://openalex.org/W2404909759","https://openalex.org/W7164409179","https://openalex.org/W1823551964","https://openalex.org/W6891820876","https://openalex.org/W7109937352","https://openalex.org/W7097726200"],"abstract_inverted_index":{"In":[0],"planted":[1],"random":[2,6],"3-SAT":[3],"a":[4,34,61,81,149,175,179,188,196,211,218,226,268,276],"uniformly":[5],"assignment":[7],"x*":[8,17],"is":[9,172,232],"hidden":[10],"and":[11,51,67,163,221,282],"about":[12,28],"\u03b1n":[13],"clauses":[14],"satisfied":[15],"by":[16,38,88,174,273],"are":[18,104,251],"revealed.":[19],"When":[20],"the":[21,30,77,94,140,154,201,206,214,222,233,239,246,259,283,286],"literal":[22,44],"signs":[23,244],"carry":[24],"no":[25,146],"single-variable":[26],"information":[27],"x*,":[29],"exchangeable":[31],"plantings":[32],"form":[33,217],"one-parameter":[35],"family":[36],"constructed":[37],"Barthel":[39],"et":[40],"al.,":[41],"with":[42,126,178],"pairwise":[43],"correlation":[45,125],"\u03bb":[46],"=":[47,55,59],"(4p\u2080":[48],"\u2212":[49],"1)/3":[50],"Kesten\u2013Stigum":[52],"parameter":[53],"\u03ba":[54,58],"6\u03b1\u03bb\u00b2.":[56],"Above":[57],"1":[60],"spectral":[62],"algorithm":[63],"of":[64,76,83,117,198,238,285],"Liu,":[65],"Mohanty":[66],"Raghavendra":[68],"achieves":[69],"weak":[70,193],"recovery":[71,194],"in":[72,167,195],"an":[73],"ordered-triple":[74],"variant":[75],"model;":[78],"below":[79,200],"it,":[80],"result":[82],"Kunisky":[84],"rules":[85],"out":[86],"detection":[87],"low":[89],"coordinate-degree":[90],"functions.":[91],"We":[92],"prove":[93],"corresponding":[95],"statement":[96],"for":[97,135],"recovery.":[98],"For":[99,182],"p\u2080":[100,183],"<":[101],"1/4":[102],"there":[103],"\u03b4,":[105],"C":[106],">":[107,184],"0,":[108],"depending":[109,278],"only":[110,279],"on":[111,245,267,280],"|\u03bb|,":[112],"such":[113],"that":[114],"every":[115],"function":[116],"coordinate":[118],"degree":[119],"D":[120],"\u2264":[121],"n^\u03b4":[122],"has":[123,225],"squared":[124],"x\u2081*x\u2082*":[127],"at":[128],"most":[129],"(1/n)(1":[130],"+":[131],"C\u00b7D^C/n)":[132],"\u03a3_{t=1}^{D}":[133],"\u03ba^t,":[134],"all":[136],"large":[137],"n.":[138],"Below":[139],"threshold,":[141],"low-degree":[142],"estimators":[143],"thus":[144],"do":[145],"better":[147],"than":[148],"constant.":[150],"The":[151,203,248],"bound":[152],"covers":[153],"satisfiable":[155],"plantings,":[156],"whose":[157],"clause":[158],"laws":[159],"have":[160],"zero":[161,256],"entries,":[162],"their":[164],"noisy":[165],"versions,":[166],"which":[168],"each":[169,229,271],"truth":[170],"pattern":[171],"replaced":[173],"uniform":[176],"one":[177],"fixed":[180],"probability.":[181],"p_*":[185],"\u2248":[186],"0.12121,":[187],"first-moment":[189],"argument":[190],"gives":[191],"information-theoretic":[192],"window":[197],"densities":[199],"threshold.":[202],"proof":[204],"uses":[205],"Sohn\u2013Wein":[207],"certificate":[208,224,249],"method.":[209],"After":[210],"gauge":[212],"transformation":[213],"latent":[215],"variables":[216],"product":[219],"measure,":[220],"block":[223,230,260,287],"closed":[227],"form:":[228],"term":[231],"M\u00f6bius":[234],"increment,":[235],"over":[236],"sub-blocks,":[237],"posterior":[240],"means":[241],"E[x\u2081*x\u2082*":[242],"|":[243],"sub-block].":[247],"equations":[250],"therefore":[252],"solvable":[253],"even":[254],"when":[255],"entries":[257],"make":[258],"Gram":[261],"matrices":[262],"singular.":[263],"A":[264],"Cauchy":[265],"estimate":[266],"polydisc":[269],"bounds":[270],"increment":[272],"|\u03bb|^|B|":[274],"times":[275],"constant":[277],"|\u03bb|":[281],"excess":[284],"B.":[288]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-07T00:00:00"}