{"id":"https://openalex.org/W7225824661","doi":"https://doi.org/10.5281/zenodo.24139233","title":"Gradient Differentials - Relational Differentials, the 25-Node Kinetic Span, and the Structural Morphism of Change - Paper GD-II: The Axiom of Relationality in Full Derived from the Internal Contradiction of Nothing and the Co-Primacy Field","display_name":"Gradient Differentials - Relational Differentials, the 25-Node Kinetic Span, and the Structural Morphism of Change - Paper GD-II: The Axiom of Relationality in Full Derived from the Internal Contradiction of Nothing and the Co-Primacy Field","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225824661","doi":"https://doi.org/10.5281/zenodo.24139233"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24139233","doi":"https://doi.org/10.5281/zenodo.24139233","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24139233","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.24139233","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103553168","display_name":"Eugene B. Pretorius","orcid":"https://orcid.org/0009-0009-5458-6717","observed_orcids":["https://orcid.org/0009-0009-5458-6717"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pretorius, Eugene","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0009-5458-6717","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5103553168"],"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/T14299","display_name":"Complex Systems and Dynamics","score":0.43380001187324524,"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"}},"topics":[{"id":"https://openalex.org/T14299","display_name":"Complex Systems and Dynamics","score":0.43380001187324524,"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"}},{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.32199999690055847,"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"}},{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.03849999979138374,"subfield":{"id":"https://openalex.org/subfields/1211","display_name":"Philosophy"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7056999802589417},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5097000002861023},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.4871000051498413},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4683000147342682},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4602000117301941},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.45829999446868896},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.39489999413490295},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3564000129699707},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.352400004863739},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3483000099658966},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.3395000100135803},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3287000060081482},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.3005000054836273},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.25600001215934753}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24139233","doi":"https://doi.org/10.5281/zenodo.24139233","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24139233","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.24139234","doi":"https://doi.org/10.5281/zenodo.24139234","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24139234","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.24139233","doi":"https://doi.org/10.5281/zenodo.24139233","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24139233","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":{"Essay":[0],"II":[1],"of":[2,10,99,127],"the":[3,8,21,26,32,37,43,56,66,73,91,97,103,123,128,140,149,180,224,262],"Gradient":[4],"Differentials":[5],"suite":[6],"derives":[7,206],"Axiom":[9],"Relationality":[11],"(T.GD.REL)":[12],"in":[13,243,248],"full":[14,189],"and":[15,42,148,212,238],"produces":[16],"its":[17,76,80,131],"five":[18],"principal":[19],"theorems:":[20],"Relational":[22,44,281],"Differential":[23,282],"Theorem":[24,40,46,297],"(T.GD.RDJ),":[25],"25-Node":[27,286],"Kinetic":[28,301],"Span":[29],"Identity":[30,35],"(T.GD.KSP),":[31],"SVB-Span":[33],"Co-Constitutive":[34],"(T.GD.SVB),":[36],"Structural":[38,293],"Morphism":[39],"(T.GD.MOR),":[41],"Self-Knowledge":[45,296],"(T.GD.RSK).":[47],"Three":[48],"paradigm":[49],"shifts":[50],"are":[51,164],"established.":[52],"Paradigm":[53,94,221],"Shift":[54,95,222],"1:":[55],"relational":[57,225],"differential":[58,87,137,264],"is":[59,72,88,232,252],"not":[60,107,247,254],"a":[61,176,201],"difference":[62],"operator":[63],"applied":[64,260],"to":[65,109,261],"gradient":[67,74],"from":[68,90,209,258],"outside":[69],"\u2014":[70,114],"it":[71,256],"computing":[75],"own":[77,81],"change":[78],"using":[79],"kinetic":[82,125,136,170,195],"state":[83],"as":[84],"input.":[85],"The":[86,135,169],"self-referential":[89],"ground":[92],"up.":[93],"2:":[96],"sum":[98,138,171,182],"25":[100,141],"node-differentials":[101],"around":[102],"Level-1":[104],"loxodrome":[105],"does":[106],"evaluate":[108],"zero,":[110],"but":[111],"equals":[112],"\u22127/58":[113],"an":[115],"exact":[116],"Class":[117],"R":[118],"locked":[119],"constant":[120],"that":[121],"encodes":[122],"total":[124],"displacement":[126,174,196],"HoH":[129],"across":[130,139,175,187,235],"25-node":[132],"horizontal":[133,173],"extent.":[134],"discrete":[142,263],"nodes":[143],"(\u2211_{j=1}^{25}":[144],"dG/dj":[145],"=":[146,155,192,219,230],"\u22127/58)":[147],"topological":[150,181,198],"winding":[151],"zero-sum":[152],"(\u2211":[153],"dw/dj":[154],"1":[156,160],"\u2261":[157],"0":[158],"mod":[159],"over":[161],"75":[162],"steps)":[163],"two":[165],"fundamentally":[166],"distinct":[167],"invariants.":[168],"measures":[172,183],"single":[177],"traversal,":[178],"whereas":[179],"periodic":[184],"phase":[185],"closure":[186,199],"three":[188],"revolutions":[190],"(w":[191],"1/3).":[193],"Conflating":[194],"with":[197],"constitutes":[200],"category":[202],"error.":[203],"This":[204,250],"essay":[205],"both":[207],"invariants":[208],"first":[210],"principles":[211],"demonstrates":[213],"their":[214],"co-constitutive":[215],"dependence":[216],"on":[217],"SVB":[218],"1.":[220],"3:":[223],"differential's":[226],"functional":[227],"form":[228],"dG/dj(\u03c1)":[229],"\u2212G_raw/[(1+\u03c1)(1+\u03c1+1/90)]":[231],"structurally":[233],"isomorphic":[234],"all":[236,239],"scales":[237],"substrates,":[240],"changing":[241],"only":[242],"value":[244],"(through":[245],"\u03c1_j)":[246],"form.":[249],"isomorphism":[251],"derived,":[253],"postulated:":[255],"follows":[257],"T.GF.CPR":[259],"operator.":[265],"Keywords:":[266],"T.GD.REL":[267],"\u00b7":[268,270,272,274,276,278,280,283,285,288,292,295,298],"T.GD.RDJ":[269],"T.GD.KSP":[271],"T.GD.SVB":[273],"T.GD.MOR":[275],"T.GD.RSK":[277],"T.GD.NSD":[279],"dG/dj=\u22127/1210":[284],"Span=\u22127/58":[287],"SVB=1":[289],"forces":[290],"span":[291],"Isomorphism":[294],"Topological":[299],"vs":[300],"Zero-Sum":[302]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}
