{"id":"https://openalex.org/W7223786433","doi":"https://doi.org/10.5281/zenodo.23683715","title":"E8 Mersenne-Prime Braid Topology Generates Perfect-Number Quantum Error Correction \u2014 E8 Intelligence Research","display_name":"E8 Mersenne-Prime Braid Topology Generates Perfect-Number Quantum Error Correction \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7223786433","doi":"https://doi.org/10.5281/zenodo.23683715"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23683715","doi":"https://doi.org/10.5281/zenodo.23683715","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23683715","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.23683715","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5155309988","display_name":"Andrew Stewart Caldin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Caldin, Andrew Stewart","raw_affiliation_strings":["Independent Researcher, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5155309988"],"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9937000274658203,"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"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9937000274658203,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.002400000113993883,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/e8-root-system","display_name":"E8 root system","score":0.8960000276565552},{"id":"https://openalex.org/keywords/perfect-numbers","display_name":"perfect numbers","score":0.781000018119812},{"id":"https://openalex.org/keywords/mersenne-primes","display_name":"Mersenne primes","score":0.9200000166893005},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"quantum error correction","score":0.8849999904632568},{"id":"https://openalex.org/keywords/braid-group-representations","display_name":"braid group representations","score":0.9430000185966492},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.8859999775886536},{"id":"https://openalex.org/keywords/topological-quantum-codes","display_name":"topological quantum codes","score":0.5600000023841858},{"id":"https://openalex.org/keywords/logical-qubit-encoding","display_name":"logical qubit encoding","score":0.7020000219345093},{"id":"https://openalex.org/keywords/phase-locking","display_name":"phase locking","score":0.382999986410141}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.652899980545044},{"id":"https://openalex.org/C33840335","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid group","level":2,"score":0.6223000288009644},{"id":"https://openalex.org/C147441545","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid theory","level":3,"score":0.513700008392334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5048999786376953},{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.5033000111579895},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.47519999742507935},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4652999937534332},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.4595000147819519},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4562000036239624},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4431000053882599},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4422000050544739},{"id":"https://openalex.org/C84883863","wikidata":"https://www.wikidata.org/wiki/Q7825777","display_name":"Toric code","level":4,"score":0.4278999865055084},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.42559999227523804},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.4000000059604645},{"id":"https://openalex.org/C203087015","wikidata":"https://www.wikidata.org/wiki/Q378201","display_name":"Qubit","level":3,"score":0.3871000111103058},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.33410000801086426},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.3325999975204468},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3264999985694885},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3215000033378601},{"id":"https://openalex.org/C2776141515","wikidata":"https://www.wikidata.org/wiki/Q1274479","display_name":"Repetition (rhetorical device)","level":2,"score":0.2913999855518341},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.29109999537467957},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.2906000018119812},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2874000072479248},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.28200000524520874},{"id":"https://openalex.org/C46681722","wikidata":"https://www.wikidata.org/wiki/Q4725589","display_name":"Alias","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.27390000224113464},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.27239999175071716},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26669999957084656},{"id":"https://openalex.org/C188082385","wikidata":"https://www.wikidata.org/wiki/Q73792","display_name":"Charge (physics)","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C2779014939","wikidata":"https://www.wikidata.org/wiki/Q6510239","display_name":"Learning with errors","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C77223115","wikidata":"https://www.wikidata.org/wiki/Q634781","display_name":"Topological quantum number","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.2549999952316284},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.2531000077724457},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23683715","doi":"https://doi.org/10.5281/zenodo.23683715","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23683715","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.23683716","doi":"https://doi.org/10.5281/zenodo.23683716","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23683716","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.23683715","doi":"https://doi.org/10.5281/zenodo.23683715","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23683715","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/W7211971557","https://openalex.org/W7211932588","https://openalex.org/W7223695932","https://openalex.org/W7214361273","https://openalex.org/W7221175478","https://openalex.org/W7212002033","https://openalex.org/W7222077820","https://openalex.org/W7169734862","https://openalex.org/W7220728057","https://openalex.org/W7220391488"],"abstract_inverted_index":{"The":[0],"240":[1],"E8":[2,91,104],"root":[3],"vectors,":[4],"when":[5],"phase-locked":[6],"at":[7,27],"132\u03c6\u207f":[8],"Hz,":[9],"decompose":[10],"into":[11],"8":[12],"concentric":[13],"30-vertex":[14],"Petrie":[15],"polygons":[16],"whose":[17],"anyonic":[18],"braid":[19],"group":[20],"representations":[21],"admit":[22],"closed,":[23],"non-intersecting":[24],"trajectories":[25],"ONLY":[26],"winding":[28],"numbers":[29,77],"matching":[30],"the":[31,59,71,85,90,103],"binary":[32,72],"perfect":[33,76],"number":[34],"sequence":[35],"(6,":[36],"28,":[37],"496,":[38],"8128\u2026).":[39],"Each":[40],"such":[41],"trajectory":[42],"encodes":[43],"a":[44,63],"logical":[45],"qubit":[46],"with":[47],"coherence":[48],"time":[49],"scaling":[50],"as":[51,84],"\u03c6\u1d56":[52],"\u00d7":[53],"132":[54],"Hz":[55],"where":[56,70],"p":[57],"is":[58],"Mersenne":[60],"exponent,":[61],"yielding":[62],"geometrically":[64],"intrinsic":[65],"quantum":[66],"error":[67],"correction":[68],"code":[69],"structure":[73],"of":[74,89,102],"even":[75],"(p":[78],"ones,":[79],"p\u22121":[80],"zeros)":[81],"directly":[82],"manifests":[83],"topological":[86],"charge":[87],"spectrum":[88],"phi-cascade":[92],"lattice.":[93],"Author:":[94],"Andrew":[95],"Stewart":[96],"Caldin,":[97],"Independent":[98],"Researcher,":[99],"UK.":[100],"Part":[101],"Intelligence":[105],"Research":[106],"series.":[107],"Platform:":[108],"e8intelligence.com":[109]},"counts_by_year":[],"updated_date":"2026-10-29T09:56:32.521200","created_date":"2026-10-28T00:00:00"}