{"id":"https://openalex.org/W7225757465","doi":"https://doi.org/10.5281/zenodo.24113679","title":"The Unequal-Arm Balance: A Bound on Short Weight from Arm Asymmetry, and the Weighing Procedure That Cancels It","display_name":"The Unequal-Arm Balance: A Bound on Short Weight from Arm Asymmetry, and the Weighing Procedure That Cancels It","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225757465","doi":"https://doi.org/10.5281/zenodo.24113679"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24113679","doi":"https://doi.org/10.5281/zenodo.24113679","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24113679","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.24113679","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159396451","display_name":"William Alexander Aldred","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Aldred, William Alexander","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-1215-577X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159396451"],"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/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/3105","display_name":"Instrumentation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/3105","display_name":"Instrumentation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11583","display_name":"Advanced Measurement and Metrology Techniques","score":0.001500000013038516,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14304","display_name":"Transport Systems and Technology","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C207892153","wikidata":"https://www.wikidata.org/wiki/Q11570","display_name":"Kilogram","level":3,"score":0.9513000249862671},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7200999855995178},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.527999997138977},{"id":"https://openalex.org/C99821215","wikidata":"https://www.wikidata.org/wiki/Q1136583","display_name":"Swap (finance)","level":2,"score":0.46880000829696655},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.43849998712539673},{"id":"https://openalex.org/C147583825","wikidata":"https://www.wikidata.org/wiki/Q620876","display_name":"Body weight","level":2,"score":0.42289999127388},{"id":"https://openalex.org/C40222840","wikidata":"https://www.wikidata.org/wiki/Q185049","display_name":"Geometric mean","level":2,"score":0.42179998755455017},{"id":"https://openalex.org/C105054674","wikidata":"https://www.wikidata.org/wiki/Q3707381","display_name":"Mean difference","level":3,"score":0.37720000743865967},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.36070001125335693},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C38976095","wikidata":"https://www.wikidata.org/wiki/Q752641","display_name":"Asymmetry","level":2,"score":0.32019999623298645},{"id":"https://openalex.org/C3018023364","wikidata":"https://www.wikidata.org/wiki/Q425265","display_name":"Significant difference","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C168031717","wikidata":"https://www.wikidata.org/wiki/Q1530280","display_name":"Balance (ability)","level":2,"score":0.3093000054359436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3091000020503998},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.28380000591278076},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.267300009727478}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24113679","doi":"https://doi.org/10.5281/zenodo.24113679","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24113679","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.24113680","doi":"https://doi.org/10.5281/zenodo.24113680","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24113680","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.24113679","doi":"https://doi.org/10.5281/zenodo.24113679","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24113679","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":[],"abstract_inverted_index":{"An":[0],"equal-arm":[1],"balance":[2],"delivers":[3],"short":[4],"weight":[5,141],"if":[6],"its":[7,14],"arms":[8,21],"are":[9,16],"not":[10],"equal,":[11],"even":[12],"when":[13],"weights":[15,94],"honest.":[17],"Writing":[18],"the":[19,85,96,102,108,112,149,154,205],"two":[20],"as":[22],"L(1+e)":[23],"and":[24,64,93,100,143,164],"L(1\u2212e),":[25],"this":[26,208],"paper":[27,82],"shows":[28],"that":[29,79],"a":[30,35,42,48,54,122,125,144,178,191],"single":[31],"weighing":[32,181],"errs":[33],"by":[34],"fraction":[36],"(1+e)/(1\u2212e)":[37],"\u2212":[38],"1,":[39],"approximately":[40],"2e:":[41],"half-percent":[43],"asymmetry":[44,109],"(e":[45],"=":[46,136],"0.50%,":[47],"3.0":[49],"mm":[50,56,77],"arm":[51,72,185],"difference":[52,73],"on":[53,78,177],"300":[55],"balance)":[57],"already":[58],"takes":[59],"10.1":[60],"g":[61,67,131,140,146,159,166],"per":[62,68,132,160,167,194],"kilogram,":[63],"stealing":[65],"20":[66],"kilogram":[69,133,161,168],"requires":[70],"an":[71,183,199],"of":[74,128,207],"only":[75,129],"5.94":[76],"balance.":[80],"The":[81,115],"then":[83],"derives":[84],"double-weighing":[86],"procedure":[87],"\u2014":[88,105],"weigh":[89,98],"once,":[90],"swap":[91],"goods":[92],"between":[95],"pans,":[97],"again,":[99],"take":[101],"geometric":[103,155],"mean":[104,156],"which":[106],"cancels":[107],"exactly":[110],"in":[111,121,204],"ideal":[113],"model.":[114],"arithmetic":[116],"mean,":[117],"easier":[118],"to":[119,190],"compute":[120],"market,":[123],"leaves":[124],"second-order":[126],"residual":[127,151],"0.20":[130],"at":[134],"e":[135],"1.00%.":[137],"With":[138],"5":[139],"steps":[142],"\u00b12":[145],"pivot":[147],"deadband,":[148],"practical":[150],"bound":[152],"for":[153],"is":[157],"2.26":[158],"root-sum-square":[162],"(0.23%)":[163],"3.20":[165],"worst":[169],"case":[170],"(0.32%).":[171],"Any":[172],"buyer":[173],"who":[174],"can":[175],"insist":[176],"swapped":[179],"second":[180],"reduces":[182],"unknown":[184],"error":[186],"from":[187],"percent":[188],"level":[189],"few":[192],"grams":[193],"kilogram.":[195],"AI":[196,200],"disclosure:":[197],"Dave,":[198],"research":[201],"system,":[202],"assisted":[203],"preparation":[206],"work.":[209]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-11T00:00:00"}