{"id":"https://openalex.org/W7204257596","doi":"https://doi.org/10.5281/zenodo.22117053","title":"The Omnidomain Pedagogical Limbo Theorem: A Multidomain Mathematical Analysis of Irreversible Stasis in Secondary\u2011School Teaching","display_name":"The Omnidomain Pedagogical Limbo Theorem: A Multidomain Mathematical Analysis of Irreversible Stasis in Secondary\u2011School Teaching","publication_year":2026,"publication_date":"2026-08-26","ids":{"openalex":"https://openalex.org/W7204257596","doi":"https://doi.org/10.5281/zenodo.22117053"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22117053","doi":"https://doi.org/10.5281/zenodo.22117053","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22117053","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":"article-journal"},"volume":null,"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22117053","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135763848","display_name":"Matthew Arthur Carlo","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Carlo, Matthew Arthur","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5135763848"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.62691431,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.6812000274658203,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.6812000274658203,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10008","display_name":"Teacher Education and Leadership Studies","score":0.04690000042319298,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11384","display_name":"Critical Race Theory in Education","score":0.03220000118017197,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/high-school-mathematics-teaching","display_name":"high school mathematics teaching","score":0.9039999842643738},{"id":"https://openalex.org/keywords/fixed-point-dynamics","display_name":"fixed-point dynamics","score":0.6919999718666077},{"id":"https://openalex.org/keywords/teacher-education","display_name":"teacher professional development","score":0.5360000133514404},{"id":"https://openalex.org/keywords/educational-inequality","display_name":"educational inequality","score":0.5109999775886536},{"id":"https://openalex.org/keywords/institutional-inertia","display_name":"institutional inertia","score":0.4569999873638153}],"concepts":[{"id":"https://openalex.org/C2778473407","wikidata":"https://www.wikidata.org/wiki/Q1459574","display_name":"Compendium","level":2,"score":0.7289999723434448},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6069999933242798},{"id":"https://openalex.org/C47177190","wikidata":"https://www.wikidata.org/wiki/Q207137","display_name":"Curriculum","level":2,"score":0.5720999836921692},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5411999821662903},{"id":"https://openalex.org/C71901391","wikidata":"https://www.wikidata.org/wiki/Q7126699","display_name":"Upload","level":2,"score":0.4984999895095825},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.44749999046325684},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4447000026702881},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4099000096321106},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.385699987411499},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.3833000063896179},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.33390000462532043},{"id":"https://openalex.org/C47884741","wikidata":"https://www.wikidata.org/wiki/Q1166618","display_name":"Mathematical logic","level":2,"score":0.3312000036239624},{"id":"https://openalex.org/C2992902817","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics curriculum","level":4,"score":0.3111000061035156},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30070000886917114},{"id":"https://openalex.org/C2776085556","wikidata":"https://www.wikidata.org/wiki/Q183361","display_name":"Chen","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C115901376","wikidata":"https://www.wikidata.org/wiki/Q184199","display_name":"Automation","level":2,"score":0.29330000281333923},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C16671368","wikidata":"https://www.wikidata.org/wiki/Q230885","display_name":"State diagram","level":3,"score":0.2741999924182892},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22117053","doi":"https://doi.org/10.5281/zenodo.22117053","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22117053","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":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.22117054","doi":"https://doi.org/10.5281/zenodo.22117054","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22117054","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":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.22117053","doi":"https://doi.org/10.5281/zenodo.22117053","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22117053","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":"article-journal"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.975600004196167,"display_name":"Quality education"}],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/4","score":0.6887982487678528,"display_name":"Quality education"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,25,135,392],"upload":[1,221],"contains":[2],"two":[3],"integrated":[4],"documents:":[5],"1.":[6],"Main":[7],"Paper":[8],"\u2014":[9,118,329],"\u201cThe":[10],"Omnidomain":[11,32,123,229,248],"Pedagogical":[12,33,124,133,230,249],"Limbo":[13,34,125],"Theorem:":[14,126],"A":[15],"Multidomain":[16],"Mathematical":[17],"Framework":[18],"for":[19,121,331,339],"Eternal":[20],"Non\u2011Progression":[21],"in":[22,44,84,142,279,322,346],"Secondary\u2011School":[23],"Teaching.\u201d**":[24],"paper":[26,98],"introduces":[27],"and":[28,69,129,161,171,178,193,206,224,246,351,359,380],"formally":[29],"proves":[30,225],"the":[31,50,53,57,61,66,70,107,122,143,149,162,175,180,226,332,340,354,390],"Theorem,":[35],"a":[36,81,190,210,374],"multidomain":[37,251],"mathematical":[38,101,181,286,305],"model":[39],"describing":[40],"permanent":[41],"pedagogical":[42,257,296],"stasis":[43,316,361],"secondary\u2011school":[45,51,150],"mathematics":[46,255,327],"teaching.":[47],"It":[48],"defines":[49],"manifold,":[52,151],"curriculum":[54,152,259],"state":[55,83,153,260],"space,":[56,154],"Personal\u2013Pedagogical":[58,262],"Leakage":[59,263],"Tensor,":[60],"Bilingual":[62],"Fairness":[63],"Failure":[64],"Operator,":[65],"Aggression-Control":[67],"Nullflow,":[68],"Misclassification":[71],"Singularity.":[72],"Together,":[73,186],"these":[74,187],"structures":[75],"demonstrate":[76],"that":[77],"certain":[78],"teachers":[79],"enter":[80],"fixed\u2011point":[82],"which":[85],"no":[86],"pedagogical,":[87],"behavioural,":[88],"cognitive,":[89],"or":[90,93,408],"institutional":[91,281],"progression":[92],"regression":[94],"is":[95,320,394,400],"possible.":[96],"The":[97,219],"integrates":[99],"formal":[100],"reasoning":[102],"with":[103],"reflective":[104],"context":[105],"from":[106],"author\u2019s":[108],"lived":[109],"experience":[110],"of":[111,132,148,183,228,274,307,357,403],"misclassification":[112,157,207,270],"within":[113],"secondary":[114],"education.":[115],"2.":[116],"Compendium":[117,120],"\u201cDiagrammatic":[119],"Structural,":[127],"Tensorial,":[128],"Dynamical":[130],"Visualisations":[131],"Stasis.\u201d**":[134],"companion":[136],"document":[137],"provides":[138],"all":[139,216],"diagrams":[140,167],"referenced":[141],"main":[144],"paper,":[145],"including":[146],"visualisations":[147],"leakage":[155],"tensor,":[156],"singularity,":[158],"aggression-control":[159,268],"nullflow,":[160],"omnidomain":[163,184,315],"fixed":[164,213,301],"point.":[165],"These":[166],"serve":[168],"as":[169],"structural":[170,298],"conceptual":[172],"aids,":[173],"illustrating":[174],"theorem\u2019s":[176],"components":[177],"reinforcing":[179],"logic":[182],"stasis.":[185],"documents":[188],"present":[189],"complete":[191],"theoretical":[192,311],"visual":[194],"framework":[195],"explaining":[196],"how":[197,348],"unresolved":[198],"personal\u2013pedagogical":[199],"leakage,":[200],"bilingual":[201,265],"fairness":[202,266],"failure,":[203],"aggression-based":[204],"control,":[205],"dynamics":[208],"produce":[209],"stable,":[211],"irreversible":[212,300],"point":[214],"across":[215],"professional":[217,358],"domains.":[218],"combined":[220],"defines,":[222],"illustrates,":[223],"existence":[227],"Limbo.":[231],"MAIN":[232],"EQUATION":[233],"\\[\\forall":[234],"X":[235],"\\in":[236],"\\{\\text{Pedagogy},":[237],"\\text{Behaviour},":[238],"\\text{Cognition},\\text{Emotion},":[239],"\\text{Curriculum},":[240],"\\text{Institution}\\},":[241],"\\quad\\frac{dX}{dt}":[242],"=":[243],"0\\]":[244],"Keywords":[245],"Subjects:":[247],"Limbo;":[250],"fixed-point":[252],"analysis;":[253,295],"secondary-school":[254],"pedagogy;":[256,280],"stasis;":[258,284],"space;":[261],"Tensor;":[264],"failure;":[267],"nullflow;":[269],"singularity;":[271],"tensorial":[272],"modelling":[273],"educational":[275,291,303],"behaviour;":[276],"dynamical":[277],"systems":[278],"inertia;":[282,314],"cognitive-behavioural":[283],"Carlo-coded":[285],"structures;":[287],"diagrammatic":[288],"compendium;":[289],"manifold-based":[290],"modelling;":[292],"KS3\u2013KS5":[293],"domain":[294],"immobility;":[297],"invariance;":[299],"points;":[302],"misclassification;":[304],"formalisation":[306],"teaching":[308],"dynamics;":[309],"hybrid":[310],"framework;":[312],"cross-domain":[313],"theorem.":[317],"Shoutout:This":[318],"work":[319],"dedicated,":[321],"part,":[323],"to":[324,336,349,388,412],"my":[325],"old":[326],"teacher":[328],"not":[330,395],"lessons":[333],"he":[334,343,362],"intended":[335],"teach,":[337],"but":[338],"single":[341],"lesson":[342],"actually":[344],"succeeded":[345],"delivering:":[347],"recognise,":[350],"run":[352],"from,":[353],"exact":[355],"kind":[356],"personal":[360],"later":[363],"embodied.":[364],"His":[365],"classroom":[366],"showed":[367],"me":[368],"what":[369],"it":[370,399],"looks":[371],"like":[372],"when":[373],"person":[375],"stops":[376,378,381],"moving,":[377],"growing,":[379],"becoming.":[382],"In":[383],"witnessing":[384],"that,":[385],"I":[386],"learned":[387],"do":[389],"opposite.":[391],"theorem":[393],"written":[396,401],"against":[397],"him;":[398],"because":[402],"him.":[404],"Contact:":[405],"For":[406],"enquiries":[407],"research":[409],"questions":[410],"related":[411],"this":[413],"work,":[414],"email":[415],"matthewcarlo.research@gmail.com":[416]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-08-27T00:00:00"}