{"id":"https://openalex.org/W7225575248","doi":"https://doi.org/10.5281/zenodo.24055302","title":"Relational Horizon Dynamics (RHD): Chronological Mathematical Research Master \u2014 Foundations, Singular Fusion, Modular Geometry, CAR Interactions, and the Five-Way Bottleneck (372 Pages)","display_name":"Relational Horizon Dynamics (RHD): Chronological Mathematical Research Master \u2014 Foundations, Singular Fusion, Modular Geometry, CAR Interactions, and the Five-Way Bottleneck (372 Pages)","publication_year":2026,"publication_date":"2026-11-07","ids":{"openalex":"https://openalex.org/W7225575248","doi":"https://doi.org/10.5281/zenodo.24055302"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24055302","doi":"https://doi.org/10.5281/zenodo.24055302","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055302","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","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.24055302","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136788930","display_name":"TODD SISCA","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"SISCA, TODD","raw_affiliation_strings":["Colorado State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Colorado State University","institution_ids":["https://openalex.org/I92446798"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5136788930"],"corresponding_institution_ids":["https://openalex.org/I92446798"],"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.8949999809265137,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.8949999809265137,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.017999999225139618,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.017400000244379044,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cohen-forcing","display_name":"Cohen forcing","score":0.7710000276565552},{"id":"https://openalex.org/keywords/operator-algebras","display_name":"operator algebras","score":0.8799999952316284},{"id":"https://openalex.org/keywords/modular-theory","display_name":"modular theory","score":0.9279999732971191},{"id":"https://openalex.org/keywords/singular-measures","display_name":"singular measures","score":0.7599999904632568},{"id":"https://openalex.org/keywords/car-algebra","display_name":"CAR algebra","score":0.9990000128746033},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"quantum entanglement","score":0.984000027179718},{"id":"https://openalex.org/keywords/de-branges-rovnyak-spaces","display_name":"de Branges-Rovnyak spaces","score":0.9459999799728394},{"id":"https://openalex.org/keywords/gauge-covariance","display_name":"gauge covariance","score":0.984000027179718},{"id":"https://openalex.org/keywords/gravitational-dynamics","display_name":"gravitational dynamics","score":0.5460000038146973}],"concepts":[{"id":"https://openalex.org/C2780513914","wikidata":"https://www.wikidata.org/wiki/Q18210350","display_name":"Bottleneck","level":2,"score":0.5184999704360962},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.516700029373169},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4503999948501587},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4422999918460846},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3828999996185303},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3824999928474426},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3562999963760376},{"id":"https://openalex.org/C159176650","wikidata":"https://www.wikidata.org/wiki/Q43261","display_name":"Horizon","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C2778692605","wikidata":"https://www.wikidata.org/wiki/Q4041866","display_name":"Joins","level":2,"score":0.3167000114917755},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C66783780","wikidata":"https://www.wikidata.org/wiki/Q1166625","display_name":"Mathematical problem","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28850001096725464},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.28519999980926514},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C47884741","wikidata":"https://www.wikidata.org/wiki/Q1166618","display_name":"Mathematical logic","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C134765980","wikidata":"https://www.wikidata.org/wiki/Q879126","display_name":"Bitwise operation","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24055302","doi":"https://doi.org/10.5281/zenodo.24055302","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055302","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24055303","doi":"https://doi.org/10.5281/zenodo.24055303","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055303","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24055302","doi":"https://doi.org/10.5281/zenodo.24055302","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055302","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","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":["https://openalex.org/W7225393871","https://openalex.org/W7225009377","https://openalex.org/W7223054067","https://openalex.org/W7162321099","https://openalex.org/W7225011471","https://openalex.org/W7225396730","https://openalex.org/W7223092593","https://openalex.org/W7223157463","https://openalex.org/W7220937972","https://openalex.org/W7162238615"],"abstract_inverted_index":{"Title:":[0],"Relational":[1,40,218],"Horizon":[2,41,219],"Dynamics":[3,42],"(RHD):":[4],"Chronological":[5],"Mathematical":[6],"Research":[7,183],"Master":[8],"\u2014":[9],"Foundations,":[10],"Singular":[11],"Fusion,":[12],"Modular":[13],"Geometry,":[14],"CAR":[15,149,232],"Interactions,":[16],"and":[17,73,89,97,121,134,153,161,169,201,204,215],"the":[18,37,50,64,145,179,190,193],"Five-Way":[19],"Bottleneck":[20],"(372":[21],"Pages)":[22],"Author:":[23],"Todd":[24,46,185],"M.":[25,47,186],"Sisca":[26],"Description":[27],"/":[28],"Abstract:":[29],"This":[30],"372-page":[31],"chronological":[32,167],"mathematical":[33,65,127,236],"research":[34,66],"compilation":[35],"presents":[36],"development":[38],"of":[39,192],"(RHD),":[43],"originated":[44],"by":[45],"Sisca,":[48],"from":[49],"earliest":[51],"included":[52],"October":[53],"2026":[54],"source":[55],"manuscripts":[56,160],"through":[57],"November":[58],"7,":[59],"2026.":[60],"The":[61,102,126],"dossier":[62],"preserves":[63],"record":[67],"in":[68,178,208],"historical":[69],"sequence,":[70],"including":[71],"Cohen":[72,222],"random":[74],"forcing,":[75],"operator-algebra":[76],"constructions,":[77,131],"dyadic":[78,230],"singular":[79,228],"measures,":[80],"horizon-seam":[81],"modular":[82,226,243],"theory,":[83],"de":[84,240],"Branges\u2013Rovnyak":[85,241],"kernel":[86],"geometry,":[87],"fused":[88],"unfused":[90],"tilings,":[91],"exact":[92],"resonance":[93],"identities,":[94],"recoverable":[95],"compression,":[96],"recursive":[98],"forcing":[99,238],"centrum":[100],"constructions.":[101],"later":[103],"investigations":[104],"develop":[105],"an":[106],"intrinsic":[107],"singular-inner-seam-to-CAR":[108],"interaction,":[109],"gauge-covariant":[110],"operator":[111,224],"families,":[112],"modular-state":[113],"compatibility":[114],"criteria,":[115],"representation":[116],"obstructions,":[117],"Feshbach":[118,245],"residual":[119],"dynamics,":[120,152],"a":[122],"five-route":[123],"bottleneck":[124],"analysis.":[125],"results":[128],"establish":[129],"explicit":[130],"conditional":[132],"theorems,":[133],"counterexamples":[135],"within":[136],"their":[137],"stated":[138],"hypotheses.":[139],"A":[140],"canonical":[141],"forcing-derived":[142],"correspondence":[143],"with":[144,166],"original":[146],"physical":[147],"horizon":[148],"representation,":[150],"gravitational":[151],"Standard":[154],"Model":[155],"realization":[156],"remain":[157],"open.":[158],"Original":[159],"archival":[162],"copies":[163],"are":[164,176],"preserved":[165],"indexing":[168],"source-page":[170],"traceability.":[171],"Explicit":[172],"FAP":[173],"audit":[174],"records":[175],"maintained":[177],"separate":[180],"companion":[181],"volume.":[182],"originator:":[184],"Sisca.":[187],"Technical":[188],"assistance:":[189],"author":[191],"framework":[194],"has":[195],"traumatic":[196],"brain":[197],"injuries,":[198],"trigeminal":[199],"neuralgia,":[200],"double":[202],"vision,":[203],"uses":[205],"Ai":[206],"reading/collaborative-assist:":[207],"this":[209],"case:":[210],"opus":[211],"5.5,":[212],"Fable":[213],"5.1,":[214],"GPT6.":[216],"Keywords:":[217],"Dynamics;":[220],"RHD;":[221],"forcing;":[223],"algebras;":[225],"theory;":[227],"measures;":[229],"tilings;":[231],"algebra;":[233],"quantum":[234],"entanglement;":[235],"physics;":[237],"centrum;":[239],"spaces;":[242],"resonance;":[244],"compression;":[246],"gauge":[247],"covariance.":[248],"Version:":[249],"v-Chrono-1.0":[250],"(Chronological":[251],"edition,":[252],"version":[253],"1.0)":[254],"#MightyMouse":[255]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}
