{"id":"https://openalex.org/W7212373519","doi":"https://doi.org/10.5281/zenodo.22730434","title":"Elevation of Prime Gaps to Vector Topological Distances on Calabi-Yau Three-folds: A Discrete-Continuous Geometric Embedding Study Based on the PDSM-NT Framework","display_name":"Elevation of Prime Gaps to Vector Topological Distances on Calabi-Yau Three-folds: A Discrete-Continuous Geometric Embedding Study Based on the PDSM-NT Framework","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7212373519","doi":"https://doi.org/10.5281/zenodo.22730434"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22730434","doi":"https://doi.org/10.5281/zenodo.22730434","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22730434","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":"article-journal"},"volume":null,"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22730434","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133683835","display_name":"xiaogang shui","orcid":"https://orcid.org/0009-0000-0858-6489","observed_orcids":["https://orcid.org/0009-0000-0858-6489"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"shui, xiaogang","raw_affiliation_strings":["Shaanxi Mutian Computational Intelligence Technology Co., Ltd., Xi'an 710000, Shaanxi, China"],"raw_orcid":"https://orcid.org/0009-0000-0858-6489","affiliations":[{"raw_affiliation_string":"Shaanxi Mutian Computational Intelligence Technology Co., Ltd., Xi'an 710000, Shaanxi, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5133683835"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.87259315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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":0.5449000000953674,"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":0.5449000000953674,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.290800005197525,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.11710000038146973,"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":[{"id":"https://openalex.org/keywords/prime-gaps","display_name":"prime gaps","score":0.996999979019165},{"id":"https://openalex.org/keywords/calabi-yau-threefolds","display_name":"Calabi-Yau threefolds","score":0.9179999828338623},{"id":"https://openalex.org/keywords/prime-number-distribution","display_name":"prime number distribution","score":0.8320000171661377},{"id":"https://openalex.org/keywords/compact-kahler-manifolds","display_name":"compact K\u00e4hler manifolds","score":0.8529999852180481},{"id":"https://openalex.org/keywords/ricci-flatness","display_name":"Ricci flatness","score":0.8309999704360962}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7663000226020813},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.43369999527931213},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.3580999970436096},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3560999929904938},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35030001401901245},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3479999899864197},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C143330242","wikidata":"https://www.wikidata.org/wiki/Q849798","display_name":"Knot theory","level":3,"score":0.28540000319480896},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C116335209","wikidata":"https://www.wikidata.org/wiki/Q240651","display_name":"Prime element","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.25619998574256897},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22730434","doi":"https://doi.org/10.5281/zenodo.22730434","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22730434","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":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.22730435","doi":"https://doi.org/10.5281/zenodo.22730435","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22730435","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":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.22730434","doi":"https://doi.org/10.5281/zenodo.22730434","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22730434","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":"article-journal"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/9","score":0.4988344609737396,"display_name":"Industry, innovation and infrastructure"}],"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],"The":[1],"prime":[2,19,29,66,89,115,121,218,266],"gap":[3,122],"$$g_n=p_{n+1}-p_n$$":[4],"is":[5,123],"a":[6,110,256,294],"fundamental":[7,111,310],"physical":[8],"and":[9,73,84,102,153,172,190,212,226,246,268,288,306,320],"mathematical":[10],"quantity":[11],"that":[12,38],"characterizes":[13],"the":[14,41,80,94,118,134,146,165,176,199,204,213,222,241,251,261,269,279,313,321],"asymptotic":[15,215],"distribution":[16,67,263],"behavior":[17],"of":[18,59,88,136,148,180,208,217,229,250,265,273,316,324],"numbers":[20],"in":[21,159],"analytic":[22,71,285],"number":[23,90,99,116,286],"theory.":[24],"In":[25],"traditional":[26,119],"research":[27,68,277],"systems,":[28],"gaps":[30,267],"are":[31],"simply":[32],"defined":[33,132],"as":[34],"one-dimensional":[35],"discrete":[36,230,284],"scalars":[37],"only":[39],"reflect":[40],"numerical":[42],"difference":[43],"between":[44,203,260,283],"adjacent":[45],"primes,":[46],"without":[47],"carrying":[48],"inherent":[49,62],"topological":[50,130,201,270,322],"morphology,":[51],"geometric":[52,82,314],"structural":[53],"attributes":[54],"or":[55],"high-dimensional":[56,234],"evolutionary":[57,86],"degrees":[58],"freedom.":[60],"This":[61,276],"limitation":[63],"confines":[64],"existing":[65],"to":[69,78,126],"simple":[70],"estimation":[72],"empirical":[74],"statistical":[75,247,262],"fitting,":[76],"failing":[77],"explore":[79],"essential":[81],"origins":[83],"field-theoretic":[85],"mechanisms":[87],"distribution.":[91],"Based":[92],"on":[93,133,301],"original":[95,166,309],"PDSM-NT":[96],"primitive":[97],"vortex":[98],"theory":[100,287,326],"framework":[101,299],"wormhole":[103],"space":[104],"axiomatic":[105,178],"system,":[106,254],"this":[107,195],"study":[108,196],"proposes":[109],"paradigm":[112,311],"innovation":[113],"for":[114,312],"research:":[117],"scalar":[120],"strictly":[124,173],"elevated":[125],"an":[127,308],"intrinsic":[128,258],"vector":[129],"distance":[131],"ontology":[135],"pure":[137,289],"compact":[138,185,209],"Calabi-Yau":[139,290],"three-folds":[140],"$$CY_3$$,":[141],"thoroughly":[142],"breaking":[143],"away":[144],"from":[145],"limitations":[147],"extrinsic":[149],"cohomology":[150],"lattice":[151],"approximation":[152],"finite":[154],"field":[155],"truncation":[156],"models":[157],"adopted":[158],"previous":[160],"arithmetic-geometric":[161,297],"studies.":[162],"Supported":[163],"by":[164,175],"$$\\pi$$-eigen":[167],"conformal":[168],"phase":[169,271],"scaling":[170],"mechanism":[171],"abiding":[174],"complete":[177],"system":[179],"standard":[181,302],"$$CY_3$$":[182,274],"manifolds":[183,211],"(including":[184],"K\u00e4hler":[186],"property,":[187],"Ricci":[188],"flatness":[189],"vanishing":[191],"first":[192],"Chern":[193],"class),":[194],"fundamentally":[197],"resolves":[198],"classical":[200],"paradox":[202],"bounded":[205],"metric":[206],"constraint":[207],"complex":[210,236,291,303],"unbounded":[214],"growth":[216],"sequences.":[219],"It":[220],"realizes":[221],"smooth":[223],"homologous":[224],"embedding":[225,253],"synchronous":[227],"evolution":[228,272],"arithmetic":[231],"structures":[232],"into":[233],"holomorphic":[235],"manifolds.":[237,275],"Systematic":[238],"verification":[239],"confirms":[240],"well-posedness,":[242],"strict":[243],"order":[244],"preservation":[245],"ergodic":[248],"equivalence":[249],"proposed":[252],"establishing":[255],"rigorous":[257],"correspondence":[259],"law":[264],"eliminates":[278],"long-term":[280],"disciplinary":[281],"separation":[282],"geometry,":[292],"constructs":[293],"unified":[295],"self-consistent":[296],"theoretical":[298],"based":[300],"manifold":[304],"ontology,":[305],"provides":[307],"solution":[315],"classic":[317],"number-theoretic":[318],"problems":[319],"normalization":[323],"string":[325],"vacuum":[327],"structures.":[328]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-09-13T00:00:00"}
