{"id":"https://openalex.org/W7224365205","doi":"https://doi.org/10.5281/zenodo.23774684","title":"A Scoring Set That Covers the Statistic's Support Has Power Exactly Zero: A Pre-Data Screen, and the Null Distribution of a Ladder with a Free Exponent","display_name":"A Scoring Set That Covers the Statistic's Support Has Power Exactly Zero: A Pre-Data Screen, and the Null Distribution of a Ladder with a Free Exponent","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224365205","doi":"https://doi.org/10.5281/zenodo.23774684"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23774684","doi":"https://doi.org/10.5281/zenodo.23774684","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23774684","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","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23774684","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158879808","display_name":"Jason Almasy","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Almasy, Jason","raw_affiliation_strings":["Coheron Laboratory"],"raw_orcid":"https://orcid.org/0009-0006-8222-6688","affiliations":[{"raw_affiliation_string":"Coheron Laboratory","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5158879808"],"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":0.5526999831199646,"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":0.5526999831199646,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.17470000684261322,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.09030000120401382,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/null-distribution","display_name":"null distribution","score":0.7630000114440918},{"id":"https://openalex.org/keywords/digital-root","display_name":"digital root","score":0.7149999737739563},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.6909999847412109},{"id":"https://openalex.org/keywords/coverage-probability","display_name":"coverage probability","score":0.515999972820282},{"id":"https://openalex.org/keywords/hypothesis-testing","display_name":"hypothesis testing","score":0.5960000157356262},{"id":"https://openalex.org/keywords/p-values","display_name":"p-values","score":0.5609999895095825}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7901999950408936},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6330000162124634},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5928999781608582},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5412999987602234},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5217000246047974},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5212000012397766},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5139999985694885},{"id":"https://openalex.org/C2779832538","wikidata":"https://www.wikidata.org/wiki/Q2308809","display_name":"Coincidence","level":3,"score":0.4756999909877777},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4726000130176544},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.46889999508857727},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4287000000476837},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.42500001192092896},{"id":"https://openalex.org/C16757182","wikidata":"https://www.wikidata.org/wiki/Q33456","display_name":"Power function","level":2,"score":0.4185999929904938},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.41760000586509705},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.3873000144958496},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3573000133037567},{"id":"https://openalex.org/C191988596","wikidata":"https://www.wikidata.org/wiki/Q628374","display_name":"Null hypothesis","level":2,"score":0.33730000257492065},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3167000114917755},{"id":"https://openalex.org/C169857963","wikidata":"https://www.wikidata.org/wiki/Q1461038","display_name":"Test statistic","level":3,"score":0.3018999993801117},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C14367171","wikidata":"https://www.wikidata.org/wiki/Q173523","display_name":"Geometric progression","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C108882938","wikidata":"https://www.wikidata.org/wiki/Q274506","display_name":"Uniform distribution (continuous)","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C152636012","wikidata":"https://www.wikidata.org/wiki/Q817168","display_name":"Benford's law","level":2,"score":0.26170000433921814},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2565999925136566},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25429999828338623}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23774684","doi":"https://doi.org/10.5281/zenodo.23774684","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23774684","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.23774685","doi":"https://doi.org/10.5281/zenodo.23774685","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23774685","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.23774684","doi":"https://doi.org/10.5281/zenodo.23774684","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23774684","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2256509551","https://openalex.org/W2621272884","https://openalex.org/W7027791577","https://openalex.org/W2322430191","https://openalex.org/W6959563749","https://openalex.org/W7097576149","https://openalex.org/W2164177189","https://openalex.org/W7095636031","https://openalex.org/W1034852389","https://openalex.org/W2151868995"],"abstract_inverted_index":{"A":[0,65,129],"test":[1,10,66,130,300],"whose":[2],"scoring":[3,43,274],"set":[4,275],"covers":[5],"the":[6,39,42,47,95,110,114,120,123,143,212,239,243,247,254,273,278,289,294,298],"support":[7],"of":[8,20,78,103,119,146,182],"its":[9,281],"statistic":[11],"has":[12,125],"power":[13],"exactly":[14,21],"zero":[15],"and":[16,37,57,109,169,225,246,287],"returns":[17,301],"a":[18,69,76,117,133,163,170,175,217,222,226],"p-value":[19],"1,":[22,286],"whatever":[23],"figure":[24],"it":[25,33],"reports.":[26],"This":[27],"paper":[28],"states":[29],"that":[30,67,131,197],"rule,":[31],"proves":[32],"in":[34,151,160,231],"one":[35,55,79,230],"line,":[36],"gives":[38,242],"screen:":[40],"compute":[41],"set's":[44],"measure":[45,283],"under":[46],"null":[48,282,290],"before":[49,276],"reporting":[50],"any":[51,91],"result,":[52],"which":[53],"costs":[54],"loop":[56],"no":[58,126],"data.":[59],"Three":[60],"constructions":[61],"are":[62],"worked":[63],"through.":[64],"scores":[68],"word":[70,80,106,296],"count":[71,115],"n":[72],"against":[73,113,262],"\u03c6\u00b7round(n/\u03c6)":[74],"at":[75,250],"tolerance":[77,180],"cannot":[81,139],"fail,":[82],"because":[83],"|x":[84],"-":[85,190],"round(x)|":[86],"never":[87,97],"exceeds":[88,98],"1/2":[89],"for":[90,258,264],"real":[92,206],"x,":[93],"so":[94,122,204,238],"deviation":[96],"\u03c6/2":[99],"=":[100,195,252,260,266,303],"0.80902;":[101],"200,000":[102,104],"random":[105,176],"counts":[107],"pass,":[108],"quantity":[111],"compared":[112],"is":[116,158,215,221,229,256],"function":[118],"count,":[121],"comparison":[124],"second":[127],"argument.":[128],"assigns":[132],"meaning":[134],"to":[135,202],"each":[136],"digital":[137,144],"root":[138,145],"fail":[140],"either,":[141],"since":[142],"every":[147,205],"positive":[148],"integer":[149,172],"lies":[150],"{1,":[152],"...,":[153],"9}.":[154],"The":[155,268],"continuous":[156],"case":[157],"solved":[159],"closed":[161],"form:":[162],"geometric":[164],"ladder":[165],"with":[166,185],"ratio":[167,241],"b":[168,194,259,265],"free":[171],"exponent":[173],"places":[174],"target":[177,207],"within":[178],"relative":[179],"\u03c4":[181,251],"some":[183,210],"rung":[184],"probability":[186],"ln[(1":[187],"+":[188],"\u03c4)/(1":[189],"\u03c4)]/ln":[191],"b.":[192],"For":[193],"\u03c6":[196,261],"band":[198],"runs":[199],"from":[200],"-21.385%":[201],"+27.202%,":[203],"sits":[208],"near":[209],"rung,":[211],"median":[213],"miss":[214],"11.973%,":[216],"reported":[218],"2.2%":[219],"agreement":[220,228],"one-in-eleven":[223],"coincidence":[224],"3.01%":[227],"eight.":[232],"Coverage":[233],"scales":[234],"as":[235],"1/ln":[236],"b,":[237],"smallest":[240],"densest":[244],"rungs":[245],"weakest":[248],"test:":[249],"0.022":[253],"coverage":[255],"0.0915":[257],"0.0191":[263],"10.":[267],"corrected":[269,299],"procedure":[270],"follows:":[271],"fix":[272],"seeing":[277],"data,":[279],"keep":[280],"strictly":[284],"below":[285],"state":[288],"distribution.":[291],"Run":[292],"on":[293],"same":[295],"counts,":[297],"p":[302],"0.27.":[304]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-10-30T00:00:00"}