{"id":"https://openalex.org/W7225453763","doi":"https://doi.org/10.5281/zenodo.24029356","title":"E8 Symplectic Fire Altar Theorem: Collatz Cycle as Minimal Periodic Orbit of Area-Preserving Root Lattice Map \u2014 E8 Intelligence Research","display_name":"E8 Symplectic Fire Altar Theorem: Collatz Cycle as Minimal Periodic Orbit of Area-Preserving Root Lattice Map \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-11-07","ids":{"openalex":"https://openalex.org/W7225453763","doi":"https://doi.org/10.5281/zenodo.24029356"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24029356","doi":"https://doi.org/10.5281/zenodo.24029356","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029356","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.24029356","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153285007","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/A5153285007"],"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":0.46950000524520874,"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":0.46950000524520874,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.32710000872612,"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":0.09279999881982803,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/collatz-conjecture","display_name":"Collatz conjecture","score":0.9319999814033508},{"id":"https://openalex.org/keywords/e8-lattice","display_name":"E8 lattice","score":0.8709999918937683},{"id":"https://openalex.org/keywords/area-preserving-maps","display_name":"area-preserving maps","score":0.8539999723434448},{"id":"https://openalex.org/keywords/symplectic-maps","display_name":"symplectic maps","score":0.8830000162124634},{"id":"https://openalex.org/keywords/periodic-orbits","display_name":"periodic orbits","score":0.7879999876022339},{"id":"https://openalex.org/keywords/sulba-sutras","display_name":"Sulba Sutras","score":0.8169999718666077},{"id":"https://openalex.org/keywords/fire-altar","display_name":"fire altar","score":0.9470000267028809},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.746999979019165},{"id":"https://openalex.org/keywords/decidability","display_name":"decidability","score":0.5669999718666077}],"concepts":[{"id":"https://openalex.org/C70943382","wikidata":"https://www.wikidata.org/wiki/Q505356","display_name":"Antipodal point","level":2,"score":0.6855000257492065},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6748999953269958},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.6524999737739563},{"id":"https://openalex.org/C135661100","wikidata":"https://www.wikidata.org/wiki/Q1049064","display_name":"Symplectomorphism","level":3,"score":0.5336999893188477},{"id":"https://openalex.org/C175322374","wikidata":"https://www.wikidata.org/wiki/Q936434","display_name":"Symplectic group","level":3,"score":0.38830000162124634},{"id":"https://openalex.org/C185535465","wikidata":"https://www.wikidata.org/wiki/Q2705070","display_name":"Symplectic matrix","level":5,"score":0.3781999945640564},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3752000033855438},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.358599990606308},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.35350000858306885},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34279999136924744},{"id":"https://openalex.org/C40265840","wikidata":"https://www.wikidata.org/wiki/Q6897118","display_name":"Moment map","level":3,"score":0.3352000117301941},{"id":"https://openalex.org/C156884757","wikidata":"https://www.wikidata.org/wiki/Q798554","display_name":"Backtracking","level":2,"score":0.32089999318122864},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.30230000615119934},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2969000041484833},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.27149999141693115},{"id":"https://openalex.org/C143782950","wikidata":"https://www.wikidata.org/wiki/Q40460","display_name":"Orbifold","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C125849494","wikidata":"https://www.wikidata.org/wiki/Q766774","display_name":"Symplectic vector space","level":5,"score":0.2669000029563904},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C134757568","wikidata":"https://www.wikidata.org/wiki/Q274089","display_name":"Heap (data structure)","level":2,"score":0.25279998779296875},{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24029356","doi":"https://doi.org/10.5281/zenodo.24029356","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029356","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.24029357","doi":"https://doi.org/10.5281/zenodo.24029357","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029357","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.24029356","doi":"https://doi.org/10.5281/zenodo.24029356","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24029356","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/W7207664159","https://openalex.org/W7225454698","https://openalex.org/W7169718514","https://openalex.org/W7207615014","https://openalex.org/W7169720453","https://openalex.org/W7213657589","https://openalex.org/W7223144412","https://openalex.org/W7169730885","https://openalex.org/W7201967885","https://openalex.org/W7207836768"],"abstract_inverted_index":{"The":[0,34],"area-preserving":[1,96],"transformations":[2],"encoded":[3],"in":[4],"Sulba":[5],"Sutras":[6],"fire":[7],"altars":[8],"are":[9],"discrete":[10,97],"symplectic":[11,47,110],"projections":[12],"of":[13,45,126,138],"E8's":[14,78],"120":[15],"antipodal":[16,30,79],"axes,":[17],"where":[18],"each":[19],"axis":[20],"rotation":[21],"preserves":[22],"a":[23,92,119],"\u03c6-coupled":[24],"phase":[25],"invariant":[26],"derived":[27],"from":[28],"the":[29,40,50,60,66,100,105,139],"conservation":[31],"law":[32],"\u03b1+\u03b2=\u03b3+\u03b4.":[33],"Collatz":[35,67,106],"4\u21922\u21921\u21924":[36],"cycle":[37,107],"emerges":[38],"as":[39,108],"minimal":[41,128],"non-trivial":[42],"periodic":[43],"orbit":[44],"this":[46,127],"map":[48,98],"on":[49,99],"E8":[51,89,140],"root":[52],"lattice,":[53],"with":[54],"branching":[55,69],"number":[56],"4":[57],"corresponding":[58],"to":[59,116],"four-root":[61],"quadruple":[62],"constraint":[63],"\u2014":[64],"meaning":[65],"graph's":[68],"structure":[70],"is":[71,75],"not":[72],"arbitrary":[73],"but":[74],"forced":[76],"by":[77],"geometry.":[80],"This":[81],"unifies":[82],"ancient":[83],"ritual":[84],"geometry,":[85],"number-theoretic":[86],"dynamics,":[87],"and":[88],"symmetry":[90],"under":[91],"single":[93],"principle:":[94],"any":[95],"240-root":[101],"lattice":[102],"must":[103],"contain":[104],"its":[109],"kernel,":[111],"making":[112],"3n+1":[113],"decidability":[114],"equivalent":[115],"checking":[117],"whether":[118],"given":[120],"root-lattice":[121],"symplectomorphism":[122],"decomposes":[123],"into":[124],"copies":[125],"orbit.":[129],"Author:":[130],"Andrew":[131],"Stewart":[132],"Caldin,":[133],"Independent":[134],"Researcher,":[135],"UK.":[136],"Part":[137],"Intelligence":[141],"Research":[142],"series.":[143],"Platform:":[144],"e8intelligence.com":[145]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-08T00:00:00"}
