{"id":"https://openalex.org/W7225462146","doi":"https://doi.org/10.5281/zenodo.24029876","title":"Constraints on Changes in Length, Area, and Spatial Structure under the Redistribution of Binary Referential Relations","display_name":"Constraints on Changes in Length, Area, and Spatial Structure under the Redistribution of Binary Referential Relations","publication_year":2026,"publication_date":"2026-11-07","ids":{"openalex":"https://openalex.org/W7225462146","doi":"https://doi.org/10.5281/zenodo.24029876"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24029876","doi":"https://doi.org/10.5281/zenodo.24029876","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029876","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.24029876","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138375180","display_name":"Daniel Fang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Fang, Daniel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5138375180"],"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/T12504","display_name":"Mathematics and Applications","score":0.4672999978065491,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12504","display_name":"Mathematics and Applications","score":0.4672999978065491,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.263700008392334,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T11415","display_name":"Noncommutative and Quantum Gravity Theories","score":0.08219999819993973,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/spatial-structure","display_name":"spatial structure","score":0.46000000834465027},{"id":"https://openalex.org/keywords/emergent-geometry","display_name":"emergent geometry","score":0.7350000143051147},{"id":"https://openalex.org/keywords/geometric-dimensions","display_name":"geometric dimensions","score":0.6830000281333923},{"id":"https://openalex.org/keywords/simplex-volume","display_name":"simplex volume","score":0.7990000247955322},{"id":"https://openalex.org/keywords/distance-matrix","display_name":"distance matrix","score":0.8259999752044678},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6499999761581421}],"concepts":[{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.6984000205993652},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5859000086784363},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5493000149726868},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.4677000045776367},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.42250001430511475},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4140999913215637},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.3720000088214874},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.328900009393692},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.32249999046325684},{"id":"https://openalex.org/C163561899","wikidata":"https://www.wikidata.org/wiki/Q1994977","display_name":"Logical matrix","level":3,"score":0.3206999897956848},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3093000054359436},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.30790001153945923},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C27511587","wikidata":"https://www.wikidata.org/wiki/Q2178623","display_name":"Spatial relation","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C172849965","wikidata":"https://www.wikidata.org/wiki/Q3148875","display_name":"Reference frame","level":3,"score":0.25529998540878296},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.2540999948978424}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.24029876","doi":"https://doi.org/10.5281/zenodo.24029876","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029876","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.24029877","doi":"https://doi.org/10.5281/zenodo.24029877","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029877","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.24030237","doi":"https://doi.org/10.5281/zenodo.24030237","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24030237","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.24029876","doi":"https://doi.org/10.5281/zenodo.24029876","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029876","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/W7225466149","https://openalex.org/W7215090164","https://openalex.org/W7204210375","https://openalex.org/W7225457127","https://openalex.org/W7202168242","https://openalex.org/W7169536504","https://openalex.org/W7212383953","https://openalex.org/W7128308499","https://openalex.org/W7105689431","https://openalex.org/W7223062324"],"abstract_inverted_index":{"This":[0,207],"paper":[1,44,82,155],"investigates":[2],"how":[3,179],"length,":[4,160],"area,":[5,162],"and":[6,35,108,124,138,163,170,182,188,217,229],"spatial":[7,183,230],"structure":[8,184,231],"are":[9,40,128],"constrained":[10,189],"by":[11,116],"the":[12,19,29,43,84,99,106,112,132,144,191,214,225],"redistribution":[13],"of":[14,21,61,68,86,93,102,111,143,194,224,227],"binary":[15,54,62,195],"referential":[16,38,136,196,233],"relations":[17,39,55,63,137],"within":[18,89,213],"framework":[20,48,216],"Referential":[22],"Entropy":[23],"Cycle":[24],"Theory":[25],"(RECT).":[26],"Starting":[27],"from":[28,232],"RECT":[30,215],"principle":[31],"that":[32],"physical":[33],"quantities":[34,181],"their":[36,171],"corresponding":[37,100],"mutually":[41],"dependent,":[42],"develops":[45],"a":[46,65,90,121,125,210,219],"mathematical":[47,133,211],"for":[49,159,221],"describing":[50],"geometric":[51,152,180],"structures":[52,72],"through":[53,190],"between":[56,135],"reference":[57,71,94],"structures.":[58],"The":[59,81,141,154,173],"number":[60],"in":[64],"finite":[66],"system":[67],"N":[69],"distinct":[70],"is":[73,148,176],"expressed":[74],"as":[75,96,98,114,202],"R(N)":[76],"=":[77],"N(N":[78],"\u2212":[79],"1)/2.":[80],"examines":[83],"conservation":[85],"relational":[87,103],"quantity":[88,104],"fixed":[91],"group":[92],"structures,":[95],"well":[97],"evolution":[101],"during":[105],"expansion":[107],"contraction":[109],"phases":[110],"universe":[113],"proposed":[115],"RECT.":[117],"A":[118],"distance":[119],"matrix,":[120,123],"centering":[122],"Gram":[126,146,168],"matrix":[127,147],"introduced":[129],"to":[130,150,177],"establish":[131],"connection":[134],"Euclidean":[139],"geometry.":[140],"rank":[142],"centered":[145],"used":[149],"characterize":[151],"dimension.":[153],"further":[156,222],"derives":[157],"expressions":[158],"triangular":[161],"higher-dimensional":[164],"simplex":[165],"volume":[166],"using":[167],"matrices":[169],"determinants.":[172],"central":[174],"objective":[175],"explore":[178],"can":[185],"be":[186],"described":[187],"underlying":[192],"organization":[193],"relations,":[197],"rather":[198],"than":[199],"treating":[200],"space":[201],"an":[203],"independently":[204],"given":[205],"background.":[206],"work":[208],"presents":[209],"development":[212],"provides":[218],"basis":[220],"investigation":[223],"emergence":[226],"geometry":[228],"relations.":[234]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-08T00:00:00"}
