{"id":"https://openalex.org/W7224135002","doi":"https://doi.org/10.5281/zenodo.23724053","title":"MERLIN SCIENCE \u2014 Plimpton 322 as Rank-3 Lattice of Reciprocal-Pair Pythagorean Triples \u2014 E8 Intelligence Research","display_name":"MERLIN SCIENCE \u2014 Plimpton 322 as Rank-3 Lattice of Reciprocal-Pair Pythagorean Triples \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-10-28","ids":{"openalex":"https://openalex.org/W7224135002","doi":"https://doi.org/10.5281/zenodo.23724053"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23724053","doi":"https://doi.org/10.5281/zenodo.23724053","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23724053","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.23724053","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158599967","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/A5158599967"],"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/T12170","display_name":"History and Theory of Mathematics","score":0.6161999702453613,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.6161999702453613,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12307","display_name":"Ancient Near East History","score":0.27810001373291016,"subfield":{"id":"https://openalex.org/subfields/1204","display_name":"Archeology (arts and humanities)"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13175","display_name":"Historical Astronomy and Related Studies","score":0.03139999881386757,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/plimpton-322","display_name":"Plimpton 322","score":1.0},{"id":"https://openalex.org/keywords/pythagorean-triples","display_name":"Pythagorean triples","score":0.9549999833106995},{"id":"https://openalex.org/keywords/reciprocal-pairs","display_name":"reciprocal pairs","score":0.75},{"id":"https://openalex.org/keywords/sexagesimal-numbers","display_name":"sexagesimal numbers","score":0.9259999990463257},{"id":"https://openalex.org/keywords/babylonian-mathematics","display_name":"Babylonian mathematics","score":0.9810000061988831},{"id":"https://openalex.org/keywords/e8","display_name":"E8","score":0.6190000176429749}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6902999877929688},{"id":"https://openalex.org/C80918210","wikidata":"https://www.wikidata.org/wiki/Q208225","display_name":"Pythagorean triple","level":3,"score":0.5546000003814697},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5192999839782715},{"id":"https://openalex.org/C100461760","wikidata":"https://www.wikidata.org/wiki/Q11518","display_name":"Pythagorean theorem","level":2,"score":0.49540001153945923},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.4341999888420105},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.42730000615119934},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4106999933719635},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.4018000066280365},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.3865000009536743},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3450999855995178},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C125257309","wikidata":"https://www.wikidata.org/wiki/Q131752","display_name":"Greatest common divisor","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23724053","doi":"https://doi.org/10.5281/zenodo.23724053","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23724053","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.23724054","doi":"https://doi.org/10.5281/zenodo.23724054","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23724054","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.23724053","doi":"https://doi.org/10.5281/zenodo.23724053","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23724053","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/W7220403224","https://openalex.org/W7223916827","https://openalex.org/W7219733990","https://openalex.org/W7223843621","https://openalex.org/W7206150707","https://openalex.org/W7170154486","https://openalex.org/W7220357547","https://openalex.org/W7171449370","https://openalex.org/W7169728026","https://openalex.org/W7169872445"],"abstract_inverted_index":{"The":[0,81],"finding":[1],"is":[2,22,54,76,105],"this:":[3],"Plimpton":[4,52],"322":[5,53],"encodes":[6],"fifteen":[7],"Pythagorean":[8],"triples":[9],"generated":[10],"by":[11],"reciprocal":[12],"pairs":[13],"of":[14,45,65,173],"regular":[15,116],"sexagesimal":[16,117],"numbers,":[17,118],"and":[18,93,108,120,130,150],"the":[19,32,43,49,77,94,106,133,142,151,174],"whole":[20],"tablet":[21],"best":[23],"understood":[24],"as":[25,57,136,144,154],"a":[26,58,62,69,91,161],"rank-three":[27],"lattice":[28],"problem":[29],"embedded":[30],"in":[31],"Babylonian":[33],"metrological":[34],"system.":[35],"If":[36],"you":[37,47,109],"work":[38],"with":[39],"number":[40],"theory":[41],"or":[42,61,68],"history":[44],"mathematics,":[46],"know":[48],"standard":[50],"reading.":[51],"usually":[55],"treated":[56],"trigonometric":[59],"table,":[60],"teacher's":[63],"list":[64],"solved":[66],"problems,":[67],"scratch":[70],"pad.":[71],"What":[72],"that":[73],"framing":[74],"misses":[75],"generative":[78],"structure":[79],"underneath.":[80],"scribes":[82],"weren't":[83],"listing":[84],"triples.":[85],"They":[86],"were":[87],"computing":[88],"them":[89],"from":[90],"parameterization,":[92],"parameters":[95],"they":[96,101],"chose":[97],"tell":[98],"us":[99],"what":[100],"actually":[102],"understood.":[103],"Here":[104],"mechanism,":[107],"can":[110],"check":[111],"every":[112],"step.":[113],"Take":[114],"two":[115],"p":[119,137,145],"q,":[121],"meaning":[122],"their":[123],"only":[124],"prime":[125],"factors":[126],"are":[127],"2,":[128],"3,":[129],"5.":[131],"Form":[132],"short":[134],"side":[135,153],"squared":[138,146],"minus":[139],"q":[140,148],"squared,":[141,149,162],"diagonal":[143],"plus":[147],"middle":[152],"2pq.":[155],"Column":[156],"one":[157],"tabulates":[158],"c":[159],"over":[160],"which":[163],"i":[164],"Author:":[165],"Andrew":[166],"Stewart":[167],"Caldin,":[168],"Independent":[169],"Researcher,":[170],"UK.":[171],"Part":[172],"E8":[175],"Intelligence":[176],"Research":[177],"series.":[178],"Platform:":[179],"e8intelligence.com":[180]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-29T00:00:00"}
