{"id":"https://openalex.org/W7225612591","doi":"https://doi.org/10.5281/zenodo.24075408","title":"Selection rules for pinned and quasipinned occupation numbers with degeneracy \u2014 E8 Intelligence Research","display_name":"Selection rules for pinned and quasipinned occupation numbers with degeneracy \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225612591","doi":"https://doi.org/10.5281/zenodo.24075408"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24075408","doi":"https://doi.org/10.5281/zenodo.24075408","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24075408","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.24075408","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136862907","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/A5136862907"],"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/T10002","display_name":"Advanced Chemical Physics Studies","score":0.6758000254631042,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10002","display_name":"Advanced Chemical Physics Studies","score":0.6758000254631042,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.06809999793767929,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11804","display_name":"Quantum many-body systems","score":0.05380000174045563,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/selection-rules","display_name":"selection rules","score":0.8370000123977661},{"id":"https://openalex.org/keywords/natural-orbitals","display_name":"natural orbitals","score":0.7549999952316284},{"id":"https://openalex.org/keywords/active-space","display_name":"active space","score":0.7379999756813049},{"id":"https://openalex.org/keywords/ordering-constraints","display_name":"order constraints","score":0.8240000009536743},{"id":"https://openalex.org/keywords/fermionic-states","display_name":"fermionic states","score":0.7049999833106995},{"id":"https://openalex.org/keywords/e8","display_name":"E8","score":0.3580000102519989}],"concepts":[{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.7102000117301941},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.667900025844574},{"id":"https://openalex.org/C110340908","wikidata":"https://www.wikidata.org/wiki/Q131594","display_name":"Pauli exclusion principle","level":2,"score":0.6656000018119812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6399000287055969},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.6388000249862671},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5698999762535095},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5278000235557556},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.49570000171661377},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4602000117301941},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.43380001187324524},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.3919999897480011},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3086000084877014},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.30550000071525574},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3000999987125397},{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.2703000009059906},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.25839999318122864}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24075408","doi":"https://doi.org/10.5281/zenodo.24075408","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24075408","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.24075409","doi":"https://doi.org/10.5281/zenodo.24075409","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24075409","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.24075408","doi":"https://doi.org/10.5281/zenodo.24075408","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24075408","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/W7213901532","https://openalex.org/W2046117865","https://openalex.org/W2008089068","https://openalex.org/W2276254339","https://openalex.org/W2030287124","https://openalex.org/W2970357495","https://openalex.org/W1647829407","https://openalex.org/W4411207887","https://openalex.org/W2761681934","https://openalex.org/W2030811439"],"abstract_inverted_index":{"When":[0],"the":[1,14,28,79,88,122,138],"natural":[2,24],"occupation":[3,46,111],"numbers":[4,112],"of":[5,23,137],"a":[6,10,17,106],"fermionic":[7],"state":[8,15],"saturate":[9,27],"generalized":[11,70],"Pauli":[12,71],"constraint,":[13,72],"obeys":[16],"selection":[18,40],"rule:":[19],"only":[20,85],"those":[21],"configurations":[22],"orbitals":[25],"that":[26],"constraint":[29,59],"themselves":[30],"contribute.":[31],"Pinning":[32],"thus":[33],"singles":[34],"out":[35],"an":[36,61],"active":[37],"space.":[38],"The":[39,82],"rule":[41,83,123],"was":[42,52],"proved":[43,55,67],"for":[44,48,56,68,87],"non-degenerate":[45,107],"numbers;":[47],"degenerate":[49],"ones":[50],"it":[51,65],"conjectured,":[53],"and":[54,76,118],"one":[57,98],"saturated":[58,93],"under":[60],"unverified":[62],"assumption.":[63],"Here,":[64],"is":[66],"every":[69],"with":[73],"no":[74],"assumption,":[75],"also":[77],"in":[78],"spin-adapted":[80],"setting.":[81],"can":[84],"fail":[86],"ordering":[89],"constraints":[90,94],"$\u03bb_j\\ge\u03bb_{j+1}$.":[91],"Several":[92],"are":[95,113],"served":[96],"by":[97],"basis":[99],"whenever":[100],"their":[101],"common":[102],"zero":[103],"face":[104],"contains":[105],"point.":[108],"In":[109],"practice,":[110],"quasipinned":[114],"rather":[115],"than":[116],"pinned,":[117],"I":[119],"show":[120],"what":[121],"then":[124],"becomes.":[125],"Source:":[126],"http://arxiv.org/abs/2609.22010v1":[127],"(arXiv:2609.22010v1)":[128],"Author:":[129],"Andrew":[130],"Stewart":[131],"Caldin,":[132],"Independent":[133],"Researcher,":[134],"UK.":[135],"Part":[136],"E8":[139],"Intelligence":[140],"Research":[141],"series.":[142],"Platform:":[143],"e8intelligence.com":[144]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}