{"id":"https://openalex.org/W7223666176","doi":"https://doi.org/10.5281/zenodo.23666366","title":"Asymmetric Singular Coordinate System (ASCS): A Structural Reformulation of the Number Line via Boundary Singularity and Non-Linear Asymptotics","display_name":"Asymmetric Singular Coordinate System (ASCS): A Structural Reformulation of the Number Line via Boundary Singularity and Non-Linear Asymptotics","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W7223666176","doi":"https://doi.org/10.5281/zenodo.23666366"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23666366","doi":"https://doi.org/10.5281/zenodo.23666366","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23666366","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","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23666366","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159625163","display_name":"HOANG ANH DONG PHAM","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"DONG PHAM, HOANG ANH","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159625163"],"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.5849999785423279,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.5849999785423279,"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/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.10970000177621841,"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/T13806","display_name":"Mathematical and Computational Methods","score":0.09640000015497208,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/boundary-singularities","display_name":"boundary singularities","score":0.9269999861717224},{"id":"https://openalex.org/keywords/number-line","display_name":"number line","score":0.5019999742507935},{"id":"https://openalex.org/keywords/phase-discontinuity","display_name":"phase discontinuity","score":0.7689999938011169},{"id":"https://openalex.org/keywords/activation-functions","display_name":"activation functions","score":0.5929999947547913},{"id":"https://openalex.org/keywords/neural-network","display_name":"artificial neural networks","score":0.8560000061988831}],"concepts":[{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.7773000001907349},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.6920999884605408},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.6444000005722046},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6258999705314636},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5843999981880188},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5623999834060669},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.5568000078201294},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5364999771118164},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43639999628067017},{"id":"https://openalex.org/C162291796","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Coordinate space","level":2,"score":0.3995000123977661},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.39820000529289246},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.35839998722076416},{"id":"https://openalex.org/C71383303","wikidata":"https://www.wikidata.org/wiki/Q1876526","display_name":"Essential singularity","level":3,"score":0.33329999446868896},{"id":"https://openalex.org/C108172862","wikidata":"https://www.wikidata.org/wiki/Q1332432","display_name":"Elliptic coordinate system","level":3,"score":0.3273000121116638},{"id":"https://openalex.org/C207769094","wikidata":"https://www.wikidata.org/wiki/Q4245771","display_name":"Singularity theory","level":3,"score":0.30709999799728394},{"id":"https://openalex.org/C126990412","wikidata":"https://www.wikidata.org/wiki/Q203218","display_name":"Spherical coordinate system","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.296999990940094},{"id":"https://openalex.org/C185579658","wikidata":"https://www.wikidata.org/wiki/Q3554813","display_name":"Affine variety","level":3,"score":0.2953999936580658},{"id":"https://openalex.org/C68589394","wikidata":"https://www.wikidata.org/wiki/Q1332363","display_name":"Ellipsoidal coordinates","level":3,"score":0.2912999987602234},{"id":"https://openalex.org/C98343798","wikidata":"https://www.wikidata.org/wiki/Q1790208","display_name":"Curvilinear coordinates","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C40069579","wikidata":"https://www.wikidata.org/wiki/Q62494","display_name":"Polar coordinate system","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.25450000166893005},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.25450000166893005}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.5281/zenodo.23666366","doi":"https://doi.org/10.5281/zenodo.23666366","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23666366","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.23666367","doi":"https://doi.org/10.5281/zenodo.23666367","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23666367","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.23688358","doi":"https://doi.org/10.5281/zenodo.23688358","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23688358","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.23797314","doi":"https://doi.org/10.5281/zenodo.23797314","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23797314","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.23798369","doi":"https://doi.org/10.5281/zenodo.23798369","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23798369","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.23991457","doi":"https://doi.org/10.5281/zenodo.23991457","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23991457","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.23666366","doi":"https://doi.org/10.5281/zenodo.23666366","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23666366","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2780724162","https://openalex.org/W7130695932","https://openalex.org/W3012178710","https://openalex.org/W6980090613","https://openalex.org/W7047482645","https://openalex.org/W962517667","https://openalex.org/W2018351422","https://openalex.org/W3014706649","https://openalex.org/W2291034980","https://openalex.org/W6945783770"],"abstract_inverted_index":{"The":[0,69],"traditional":[1],"Cartesian":[2],"coordinate":[3],"system":[4],"exhibits":[5],"limitations":[6],"when":[7],"modeling":[8],"systems":[9],"with":[10],"phase":[11],"discontinuities":[12],"or":[13],"boundary":[14,34,56],"shocks.":[15],"This":[16],"paper":[17],"proposes":[18],"the":[19,29,38,46,55],"Asymmetric":[20],"Singular":[21],"Coordinate":[22],"System":[23],"(ASCS)":[24],"featuring":[25],"three":[26],"core":[27],"characteristics:":[28],"origin":[30],"acts":[31],"as":[32,82],"a":[33,63,83],"singularity":[35],"severing":[36],"symmetry,":[37],"positive":[39],"domain":[40,48],"expands":[41],"linearly":[42],"toward":[43],"infinity,":[44],"and":[45,78],"negative":[47,51],"initiates":[49],"from":[50],"infinity":[52],"adjacent":[53],"to":[54,60],"before":[57],"increasing":[58],"non-linearly":[59],"asymptotically":[61],"approach":[62],"saturation":[64],"bound":[65],"at":[66],"extreme":[67],"distances.":[68],"study":[70],"establishes":[71],"custom":[72],"algebraic":[73],"operations,":[74],"analyzes":[75],"differential":[76],"behaviors,":[77],"demonstrates":[79],"its":[80],"application":[81],"threshold-sensitive":[84],"activation":[85],"function":[86],"for":[87],"artificial":[88],"neural":[89],"networks.":[90]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-27T00:00:00"}