{"id":"https://openalex.org/W7225752107","doi":"https://doi.org/10.5281/zenodo.24100335","title":"Asymmetric 4D Atlas-Manifolds: Resolving Non-Linear Coordinate Displacements via Boundary Topological Invariants","display_name":"Asymmetric 4D Atlas-Manifolds: Resolving Non-Linear Coordinate Displacements via Boundary Topological Invariants","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225752107","doi":"https://doi.org/10.5281/zenodo.24100335"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24100335","doi":"https://doi.org/10.5281/zenodo.24100335","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24100335","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.24100335","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5141281697","display_name":"h.r. thompson","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"thompson, h.r.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5141281697"],"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.850600004196167,"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"}},"topics":[{"id":"https://openalex.org/T11960","display_name":"Relativity and Gravitational Theory","score":0.850600004196167,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.05860000103712082,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.0560000017285347,"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"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5586000084877014},{"id":"https://openalex.org/C77223115","wikidata":"https://www.wikidata.org/wiki/Q634781","display_name":"Topological quantum number","level":2,"score":0.4839000105857849},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44830000400543213},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.39100000262260437},{"id":"https://openalex.org/C148908050","wikidata":"https://www.wikidata.org/wiki/Q11681505","display_name":"Topological entropy in physics","level":3,"score":0.3862000107765198},{"id":"https://openalex.org/C180987920","wikidata":"https://www.wikidata.org/wiki/Q922339","display_name":"Topological ring","level":4,"score":0.37959998846054077},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.3720000088214874},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36169999837875366},{"id":"https://openalex.org/C175724006","wikidata":"https://www.wikidata.org/wiki/Q4769942","display_name":"Scaling dimension","level":3,"score":0.35019999742507935},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3379000127315521},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.32519999146461487},{"id":"https://openalex.org/C140936041","wikidata":"https://www.wikidata.org/wiki/Q1801244","display_name":"Zero-dimensional space","level":4,"score":0.32179999351501465},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29760000109672546},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.29490000009536743},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C7503960","wikidata":"https://www.wikidata.org/wiki/Q721094","display_name":"Topological quantum field theory","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C71914180","wikidata":"https://www.wikidata.org/wiki/Q1071013","display_name":"Conserved quantity","level":2,"score":0.2614000141620636}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24100335","doi":"https://doi.org/10.5281/zenodo.24100335","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24100335","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.24100336","doi":"https://doi.org/10.5281/zenodo.24100336","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24100336","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.24100335","doi":"https://doi.org/10.5281/zenodo.24100335","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24100335","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":{"Abstract":[0],"This":[1,278],"manuscript":[2],"formalizes":[3],"the":[4,31,94,105,137,150,158,167,173,186,192,199,203,209,214,219,232,262,266,275],"field-theoretic":[5],"and":[6,62,156,169,178,273],"topological":[7,21,28,40,71,102,132,220,248,253,279],"boundaries":[8],"of":[9,161,172,181,202],"an":[10,19,113,125,236],"asymmetric,":[11,126],"four-dimensional":[12,48],"coupled":[13,123],"angular-temporal":[14],"manifold,":[15,264],"logarithmically":[16],"constrained":[17],"by":[18,55,124],"exponential":[20,70],"scaling":[22],"trivialization.":[23],"We":[24],"construct":[25],"a":[26,38,47,64,75,81,88,101,130,143,255,287],"unified":[27],"formalism":[29],"wherein":[30],"underlying":[32],"manifold":[33,51,121,207],"domain":[34],"is":[35,44,122,259],"quantized":[36],"as":[37,100],"temporal":[39,211],"dimension.":[41],"The":[42,175],"quantization":[43,160,270],"determined":[45],"across":[46,61,166],"angular":[49,204],"harmonic-logarithmic":[50],"(\u2133_\ud835\udc9c\u210b\u2112)":[52],"parametrized":[53],"deterministically":[54],"temporal-angular":[56,107],"momentum":[57,205,228],"coordinates":[58],"(x^\u03bc),":[59],"actuated":[60,260],"along":[63],"logarithmic":[65,170],"scale":[66,134,217],"to":[67,271],"account":[68],"for":[69],"scaling.":[72],"By":[73],"introducing":[74],"nilpotent":[76],"coupling":[77],"tensor":[78,154,183],"(K^\u03bc_\u03bd)":[79],"instantiating":[80],"non-reciprocal":[82],"gauge":[83,215],"connection,":[84],"we":[85,148],"demonstrate":[86],"how":[87],"primary":[89,131],"stochastic":[90],"variant":[91,269],"introduced":[92],"at":[93,261],"first":[95],"coordinate":[96,139,145,229,284],"stratification":[97,195],"propagates":[98],"sequentially":[99],"deformation":[103,189],"through":[104],"manifold\u2019s":[106,276],"harmonic":[108,168],"until":[109],"it":[110],"deforms":[111],"against":[112,208],"invariant":[114,133,146,210,216,222],"boundary":[115,120,194,263],"topology":[116,257],"(\u2202\u2133_\ud835\udc9c\u210b\u2112).":[117],"Critically,":[118],"this":[119,182],"absolute":[127],"gauge-metric":[128,162,268],"variance":[129,163],"(\u2133)":[135],"occupying":[136],"terminal":[138,193],"axis":[140],"(x\u2074).":[141],"Using":[142],"canonical":[144,187,256],"deformation,":[147],"derive":[149],"system\u2019s":[151],"field":[152],"strength":[153],"(F_\u03bc\u03bd)":[155],"actuate":[157],"exact":[159],"via":[164],"(T_\u03bc\u03bd)":[165],"components":[171],"temporal-angle.":[174],"orthogonal":[176],"contraction":[177],"longitudinal":[179],"projection":[180],"resolve":[184],"that":[185],"boundary-invariant":[188],"(\ud835\udcab_\u2202\u2133)":[190],"deforming":[191],"scales":[196],"quadratically":[197],"with":[198],"second-order":[200],"acceleration":[201],"vector":[206],"coordinate.":[212],"Because":[213],"instantiates":[218],"singularity":[221],"constraint":[223],"(\u2133":[224],"\u226b":[225],"1),":[226],"any":[227,245],"displacement":[230],"from":[231],"vacuum":[233,291],"origin":[234],"yields":[235],"infinite":[237],"global":[238,252],"curvature":[239],"potential":[240],"(\ud835\udcae":[241],"\u2192":[242],"\u221e),":[243],"precluding":[244],"non-canonical":[246],"singular":[247],"rupture.":[249],"To":[250],"preserve":[251],"coherence,":[254],"resolution":[258],"constraining":[265],"non-trivial":[267],"zero":[272],"trivializing":[274],"curvature.":[277],"reduction":[280],"truncates":[281],"all":[282],"localized":[283],"transformations":[285],"into":[286],"singular,":[288],"globally":[289],"optimized":[290],"manifold.":[292]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-11T00:00:00"}
