{"id":"https://openalex.org/W7225316099","doi":"https://doi.org/10.5281/zenodo.23977550","title":"Three-electron Hylleraas integrals with two inverse-square distances: exact reduction and high-precision evaluation for the fine structure of lithium","display_name":"Three-electron Hylleraas integrals with two inverse-square distances: exact reduction and high-precision evaluation for the fine structure of lithium","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225316099","doi":"https://doi.org/10.5281/zenodo.23977550"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23977550","doi":"https://doi.org/10.5281/zenodo.23977550","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23977550","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.23977550","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151883138","display_name":"Jonas Matuzas","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I173212132","display_name":"Vilnius University","ror":"https://ror.org/03nadee84","country_code":"LT","type":"education","lineage":["https://openalex.org/I173212132"]}],"countries":["LT"],"is_corresponding":true,"raw_author_name":"Matuzas, Jonas","raw_affiliation_strings":["Vilnius University"],"raw_orcid":"https://orcid.org/0009-0008-0266-0498","affiliations":[{"raw_affiliation_string":"Vilnius University","institution_ids":["https://openalex.org/I173212132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5151883138"],"corresponding_institution_ids":["https://openalex.org/I173212132"],"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/T10523","display_name":"Atomic and Molecular Physics","score":0.9672999978065491,"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/T10523","display_name":"Atomic and Molecular Physics","score":0.9672999978065491,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.010400000028312206,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10002","display_name":"Advanced Chemical Physics Studies","score":0.005799999926239252,"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/coulomb-field","display_name":"Coulomb field","score":0.5059999823570251},{"id":"https://openalex.org/keywords/integration-by-parts","display_name":"integration by parts","score":0.6539999842643738},{"id":"https://openalex.org/keywords/polylogarithms","display_name":"polylogarithms","score":0.8799999952316284},{"id":"https://openalex.org/keywords/high-precision-numerical-evaluation","display_name":"high-precision numerical evaluation","score":0.6639999747276306},{"id":"https://openalex.org/keywords/exact-reduction","display_name":"exact reduction","score":0.4449999928474426},{"id":"https://openalex.org/keywords/qed-corrections","display_name":"QED corrections","score":0.5759999752044678},{"id":"https://openalex.org/keywords/numerical-verification","display_name":"numerical verification","score":0.32499998807907104},{"id":"https://openalex.org/keywords/error-bounds","display_name":"error bounds","score":0.4970000088214874},{"id":"https://openalex.org/keywords/master-integrals","display_name":"master integrals","score":0.31200000643730164}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5748000144958496},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5576000213623047},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4749000072479248},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46639999747276306},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.387800008058548},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.36629998683929443},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.35359999537467957},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.3499999940395355},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3346000015735626},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3158999979496002},{"id":"https://openalex.org/C9342510","wikidata":"https://www.wikidata.org/wiki/Q25406","display_name":"Coulomb","level":3,"score":0.310699999332428},{"id":"https://openalex.org/C41054515","wikidata":"https://www.wikidata.org/wiki/Q2000912","display_name":"Standard basis","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29750001430511475},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.2969000041484833},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.2937000095844269},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.28780001401901245},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.2793000042438507},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.2653999924659729},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23977550","doi":"https://doi.org/10.5281/zenodo.23977550","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23977550","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.23977551","doi":"https://doi.org/10.5281/zenodo.23977551","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23977551","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.23977550","doi":"https://doi.org/10.5281/zenodo.23977550","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23977550","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/W2011394387","https://openalex.org/W2072762458","https://openalex.org/W1987883940","https://openalex.org/W3151519774","https://openalex.org/W2063658009","https://openalex.org/W1978138294","https://openalex.org/W2079156052","https://openalex.org/W2038564291","https://openalex.org/W1992744339","https://openalex.org/W2021565568"],"abstract_inverted_index":{"Abstract.":[0],"Two":[1,16],"Coulomb":[2],"fields":[3],"produce":[4],"singular":[5,289],"three-electron":[6,65,290],"integrals":[7,188],"that":[8],"limited":[9],"Hylleraas":[10,291],"evaluations":[11],"of":[12,54,98,130,142,147,244,287,305,339,351],"lithium":[13],"fine-structure":[14],"operators.":[15],"integrations":[17],"by":[18,150,250,390],"parts":[19,304],"reduce":[20],"the":[21,79,99,173,185,199,207,215,225,234,238,242,245,252,264,268,272,275,279,288,315,327,340,359,367,370,386],"eight":[22],"relevant":[23],"operators":[24],"to":[25,92,153,230,262],"two":[26,151],"inverse-square":[27],"families":[28,164],"and":[29,42,85,125,144,184,213,233,241,257,266,296,308,322,343,349,357,362,369,405],"previously":[30],"treated":[31],"integrals.":[32],"We":[33],"give":[34],"one-dimensional":[35],"representations":[36],"for":[37,278,319,346,366],"their":[38],"masters":[39,77,91],"T\u2082,":[40],"T\u2083,":[41],"alternative":[43],"cube\u2013square":[44],"anchors":[45],"C\u2082,":[46],"C\u2083;":[47],"C\u2083":[48],"is":[49,274,396],"expressed":[50],"in":[51,189,303,313],"classical":[52],"polylogarithms":[53],"weight":[55],"at":[56,78,107,172],"most":[57],"three.":[58],"Parity":[59],"separates":[60],"decoupled":[61,132],"sectors":[62],"from":[63,227],"genuinely":[64],"sectors.":[66],"Exact":[67,96],"rational":[68],"reductions":[69],"through":[70,134],"index":[71,135],"sum":[72,136],"32":[73],"use":[74,113],"twelve":[75],"sufficient":[76],"tested":[80,109],"exponent":[81,170],"sets.":[82],"Double":[83],"screening":[84],"Gaussian":[86],"coordinate":[87],"integration":[88],"determine":[89],"these":[90],"sixty":[93],"significant":[94],"digits.":[95,155],"collection":[97],"source":[100,212,232],"functions":[101],"controls":[102],"cancellation":[103],"near":[104],"equal":[105,111],"exponents":[106,112],"four":[108],"separations;":[110],"a":[114,331],"separate":[115],"exact":[116,223],"reduction.":[117],"Numerical":[118],"comparisons":[119],"cover":[120],"104":[121],"pre-specified":[122],"recursive":[123],"members":[124,133],"an":[126],"independent":[127,347],"direct":[128],"sample":[129],"136":[131],"32.":[137],"Production-size":[138],"basis":[139],"matrix":[140,192],"elements":[141,193],"P\u2084":[143],"one":[145,157],"component":[146],"P\u2081":[148],"agree":[149],"methods":[152],"41\u201345":[154],"On":[156],"Intel":[158],"Xeon":[159],"Silver":[160],"4410Y":[161],"machine,":[162],"both":[163],"require":[165],"5.85\u20136.99":[166],"CPU":[167],"hours":[168],"per":[169],"set":[171],"stated":[174],"64-digit":[175],"output":[176],"precision.":[177],"Uniform":[178],"error":[179],"bounds,":[180],"minimal":[181],"master":[182],"sets,":[183],"uncovered":[186],"lower":[187],"some":[190],"class-2":[191],"remain":[194],"open.":[195],"This":[196],"record":[197],"holds":[198],"manuscript":[200],"(version":[201],"11,":[202],"revision":[203],"4;":[204],"38":[205],"pages),":[206],"verification":[208,217],"bundle":[209,273],"LITHIUM_QED_MASTER_P2_v11.zip":[210],"(LaTeX":[211],"PDF,":[214],"supplementary":[216],"package":[218],"with":[219],"reference":[220],"values,":[221],"kernels,":[222],"identities,":[224],"map":[226],"every":[228,352],"statement":[229],"its":[231],"replay":[235],"script":[236],"run_checks.py,":[237],"claims":[239],"ledger":[240],"provenance":[243],"manuscript;":[246],"3,050":[247],"files,":[248],"checked":[249],"manifest.sha256),":[251],"clean":[253],"arXiv":[254],"LaTeX":[255],"source,":[256],"SHA256SUMS.txt.":[258],"README.md":[259],"explains":[260],"how":[261],"verify":[263],"files":[265],"run":[267],"checks;":[269],"PAPER2_VERIFICATION/README.md":[270],"inside":[271],"entry":[276],"point":[277],"replay.":[280],"Companion":[281],"article:":[282],"J.":[283],"Matuzas,":[284],"Elliptic":[285],"structure":[286],"integrals,":[292],"doi:10.5281/zenodo.23858519.":[293],"Generative-AI":[294],"disclosure":[295],"author":[297,355],"responsibility.":[298],"ChatGPT-6":[299],"Pro":[300,302,312],"(ChatGPT-5.6":[301],"rounds":[306],"10":[307],"12;":[309],"GPT-6":[310],"Astra":[311],"writing":[314],"manuscript)":[316],"was":[317,344,388],"used":[318,345],"derivations,":[320],"computations,":[321],"drafting;":[323],"OpenAI":[324],"Codex":[325],"ran":[326],"production":[328],"computations":[329],"on":[330],"local":[332],"server;":[333],"Claude":[334],"Opus":[335],"5.5":[336],"proposed":[337],"several":[338],"reduction":[341],"steps":[342],"re-derivation":[348],"audit":[350],"increment.":[353],"The":[354],"directed":[356],"audited":[358],"work":[360,387],"throughout":[361],"takes":[363],"full":[364,401],"responsibility":[365],"mathematics":[368],"final":[371],"text.":[372],"2020":[373],"Mathematics":[374],"Subject":[375],"Classification.":[376],"Primary":[377],"81V45;":[378],"Secondary":[379],"65D30,":[380],"65F35,":[381],"33B30,":[382],"33E05,":[383],"81-08.":[384],"All":[385],"done":[389],"AI.":[391],"Preprint.":[392],"External":[393],"peer":[394],"review":[395],"not":[397],"claimed.":[398],"Website":[399],"companion,":[400],"text,":[402],"reading":[403],"guide":[404],"citation":[406],"files:":[407],"https://jonas-matuzas-research.matuzas77.chatgpt.site/papers/2026-three-electron-hylleraas-integrals-two-inverse-square-distances-23977551/":[408],"ResearchGate":[409,411],"preprint:":[410],"publication":[412],"417503397.":[413]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-11-06T00:00:00"}