{"id":"https://openalex.org/W7225633828","doi":"https://doi.org/10.5281/zenodo.24090495","title":"Complex Regular Variation and Boundary Firewall Dynamics(paper2)","display_name":"Complex Regular Variation and Boundary Firewall Dynamics(paper2)","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225633828","doi":"https://doi.org/10.5281/zenodo.24090495"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24090495","doi":"https://doi.org/10.5281/zenodo.24090495","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24090495","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.24090495","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160258752","display_name":"Arman Rahaman Sekh","orcid":"https://orcid.org/0009-0005-8544-8166","observed_orcids":["https://orcid.org/0009-0005-8544-8166"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sekh, Arman Rahaman","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0005-8544-8166","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5160258752"],"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/T11166","display_name":"Analytic Number Theory Research","score":0.4699999988079071,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.4699999988079071,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.25220000743865967,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.10209999978542328,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/conformal-equivalence","display_name":"conformal equivalence","score":0.6050000190734863},{"id":"https://openalex.org/keywords/destructive-interference","display_name":"destructive interference","score":0.5759999752044678},{"id":"https://openalex.org/keywords/slowly-varying-functions","display_name":"slowly varying functions","score":0.5540000200271606},{"id":"https://openalex.org/keywords/analytic-continuation","display_name":"analytic continuation","score":0.527999997138977},{"id":"https://openalex.org/keywords/sector-boundaries","display_name":"sector boundaries","score":0.30399999022483826},{"id":"https://openalex.org/keywords/non-euclidean-geometry","display_name":"non-Euclidean geometry","score":0.5740000009536743}],"concepts":[{"id":"https://openalex.org/C60934299","wikidata":"https://www.wikidata.org/wiki/Q724944","display_name":"Logarithmic spiral","level":2,"score":0.621999979019165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5687999725341797},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44839999079704285},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42719998955726624},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.42649999260902405},{"id":"https://openalex.org/C124961601","wikidata":"https://www.wikidata.org/wiki/Q2518149","display_name":"Conical surface","level":2,"score":0.4115999937057495},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3935000002384186},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.38019999861717224},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.3440000116825104},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.3337000012397766},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.32359999418258667},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.25099998712539673},{"id":"https://openalex.org/C77714075","wikidata":"https://www.wikidata.org/wiki/Q5452017","display_name":"Firewall (physics)","level":5,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24090495","doi":"https://doi.org/10.5281/zenodo.24090495","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24090495","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.24090496","doi":"https://doi.org/10.5281/zenodo.24090496","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24090496","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.24090495","doi":"https://doi.org/10.5281/zenodo.24090495","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24090495","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":["https://openalex.org/W7203909470","https://openalex.org/W2176438404","https://openalex.org/W2067561465","https://openalex.org/W2141645961","https://openalex.org/W420074037","https://openalex.org/W6983707895","https://openalex.org/W7168100147","https://openalex.org/W1988400263","https://openalex.org/W2938337361","https://openalex.org/W7165010728"],"abstract_inverted_index":{"Title:":[0],"Complex":[1,10,284],"Regular":[2,170,175],"Variation":[3,60,171,176],"and":[4,12,34,111,137,154,173,206],"Boundary":[5,121],"Firewall":[6],"DynamicsSeries:":[7],"Foundations":[8],"of":[9,24,37,96,103,237,282,344,421],"Slowly":[11,48],"Regularly":[13],"Varying":[14,49],"Functions":[15],"(Part":[16],"II)Author:":[17],"Arman":[18],"Rahaman":[19],"SekhRelated":[20],"DOI:":[21],"10.5281/zenodo.23509689":[22],"(continuation":[23],"Paper":[25],"1)":[26],"Abstract":[27],"&":[28,117,123,389],"Overview:This":[29],"manuscript":[30],"establishes":[31],"the":[32,43,54,68,94,100,104,164,179,222,245,274,283,290,303,308,314,331,339,370,393,430],"operational":[33],"geometric":[35,69],"foundations":[36],"complex":[38,74,105,203,238,304],"regular":[39,239],"variation,":[40],"serving":[41],"as":[42],"direct":[44],"sequel":[45],"to":[46,150],"\"Complex":[47],"Functions\"":[50],"(Sekh,":[51],"2026).":[52],"While":[53],"preceding":[55],"work":[56],"introduced":[57],"Sectorial":[58,169],"Slow":[59],"on":[61,90,349],"rigid":[62,138],"conical":[63,276],"sectors,":[64],"this":[65],"paper":[66],"resolves":[67,289],"deformation":[70],"induced":[71],"by":[72,244,296,355,369,429],"arbitrary":[73],"scaling":[75],"indices":[76],"$\\rho":[77],"=":[78,212,271,362,396,409,449],"u":[79],"+":[80,365,384,398],"iv$":[81],"($u":[82],">":[83],"0$).":[84],"The":[85,216,234,390],"narrative":[86],"balances":[87],"structural":[88],"classification":[89],"boundary":[91],"firewalls":[92,140],"with":[93],"emergence":[95],"non-Euclidean":[97],"spiral":[98,232,248,310,422],"manifolds,":[99],"complete":[101,351],"resolution":[102],"de":[106,285,299,317],"Bruijn":[107,286,300,318],"asymptotic":[108,292,322],"inversion":[109,293],"problem,":[110],"destructive":[112,414],"interference":[113,415],"dynamics.":[114],"Key":[115],"Breakthroughs":[116],"Geometric":[118],"Invariants:":[119],"1.":[120],"Firewalls":[122],"Rigidity":[124],"Floors:Classifies":[125],"analytic":[126,316],"continuation":[127],"limits":[128],"across":[129],"sector":[130,277],"boundaries":[131,134],"into":[132,200,230],"tame":[133],"(Class":[135,141],"I)":[136],"singular":[139],"II).":[142],"Enforces":[143],"Phragm\u00e9n\u2013Lindel\u00f6f":[144],"growth":[145],"floors":[146],"($\\rho":[147],"\\ge":[148],"1/2$)":[149],"preserve":[151],"sectorial":[152],"stability":[153],"govern":[155],"safe":[156],"interior":[157],"buffers":[158],"$\\Omega_\\eta$.":[159],"2.":[160],"Canonical":[161],"Gauge":[162],"Factorization:Establishes":[163],"Conformal":[165],"Equivalence":[166],"Bridge":[167],"between":[168],"($\\mathrm{SRV}_\\rho$)":[172],"Analytic":[174],"($\\mathrm{ARV}_\\rho$)":[177],"through":[178],"logarithmic":[180,332],"elasticity":[181],"operator:$$E_f(z)":[182],":=":[183,250,258,335,436,441],"z":[184,260],"\\frac{f'(z)}{f(z)}":[185],"\\longrightarrow":[186,327],"\\rho":[187],"\\quad":[188],"\\text{as":[189],"}":[190],"|z|":[191],"\\to":[192,443],"\\infty$$proving":[193],"that":[194,221,330],"every":[195],"regularly":[196],"varying":[197,209],"function":[198],"decouples":[199],"a":[201,207,345,350,401],"pure":[202],"power":[204],"carrier":[205],"slowly":[208],"gauge":[210,333],"factor:$$f(z)":[211],"z^\\rho":[213],"L(z)$$":[214],"3.":[215],"Logarithmic":[217],"Spiral":[218],"Horn":[219],"($\\mathcal{W}_\\sigma$):Proves":[220],"transformation":[223],"$z":[224],"\\mapsto":[225],"z^\\rho$":[226],"shears":[227],"straight":[228],"sectors":[229],"expanding":[231],"horns.":[233],"natural":[235,309],"domain":[236],"variation":[240],"is":[241,338,367,427],"therefore":[242],"governed":[243,354,428],"invariant":[246],"transverse":[247],"coordinate:$$\\Theta_\\sigma(z)":[249],"\\operatorname{Im}\\left(":[251],"\\frac{\\operatorname{Log}":[252],"z}{\\sigma}":[253],"\\right),":[254],"\\qquad":[255],"\\mathcal{W}_\\sigma(\\alpha,":[256],"\\beta)":[257],"\\{":[259],"\\in":[261],"\\mathbb{C}^*":[262],":":[263],"\\alpha":[264],"<":[265,267,381],"\\Theta_\\sigma(z)":[266],"\\beta":[268],"\\}$$Setting":[269],"$\\sigma":[270],"1$":[272],"recovers":[273],"classical":[275],"$\\Omega(\\alpha,":[278],"\\beta)$.":[279],"4.":[280],"Resolution":[281],"Conjugate":[287],"Problem:Completely":[288],"open":[291],"problem":[294],"formulated":[295],"N.":[297],"G.":[298],"(1959)":[301],"in":[302],"2D":[305],"setting.":[306],"On":[307],"horn":[311],"geometry,":[312],"constructs":[313],"unique":[315,340],"conjugate":[319],"$L^\\#$":[320],"satisfying":[321],"reciprocity:$$L(z)":[323],"\\cdot":[324],"L^\\#\\big(z":[325],"L(z)^{1/\\rho}\\big)":[326],"1$$We":[328],"prove":[329],"$\\Phi":[334],"\\operatorname{Log}":[336],"L^\\#$":[337],"attracting":[341],"fixed":[342],"point":[343],"strict":[346],"Picard":[347],"contraction":[348],"Banach":[352],"space,":[353],"an":[356,417],"exact":[357],"closed":[358],"Elasticity":[359],"Duality":[360],"Law:$$E_{L^\\#}(w)":[361],"\\frac{-E_L(z)}{\\rho":[363],"\\big(\\rho":[364],"E_L(z)\\big)}$$This":[366],"accompanied":[368],"Single-Sheeted":[371],"Univalence":[372],"Horizon":[373],"guaranteeing":[374],"global":[375],"biholomorphism":[376],"without":[377],"Riemann":[378],"sheet":[379],"overlap:$$\\omega_\\eta":[380],"\\frac{2\\pi":[382],"u}{u^2":[383],"v^2}$$":[385],"5.":[386],"Vector":[387],"Addition":[388],"Pitch-Density":[391],"Law:Classifies":[392],"superposition":[394],"$S(z)":[395],"f_1(z)":[397],"f_2(z)$":[399],"via":[400],"three-way":[402],"trichotomy.":[403],"For":[404],"co-dominant":[405],"phase":[406],"twists":[407],"($u_1":[408],"u_2$,":[410],"$v_1":[411],"\\neq":[412],"v_2$),":[413],"generates":[416],"infinite":[418],"discrete":[419],"lattice":[420],"zeros":[423],"whose":[424],"Nevanlinna":[425],"density":[426],"scalar":[431],"pitch":[432],"mismatch":[433],"$\\Delta":[434],"\\kappa":[435],"\\frac{v_2":[437],"-":[438],"v_1}{u}$:$$\\mathcal{D}(0,":[439],"S)":[440],"\\lim_{r":[442],"\\infty}":[444],"\\frac{N(r,":[445],"0;":[446],"S)}{T_{\\log}(r,":[447],"S)}":[448],"\\frac{|\\Delta":[450],"\\kappa|}{2\\pi}$$":[451]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
