{"id":"https://openalex.org/W7225274482","doi":"https://doi.org/10.5281/zenodo.23936685","title":"Monomials Beyond the Far Standard: The Quartic Arrives at \u03c6_i = 2.0761 \u2014 and It Is Not Alone","display_name":"Monomials Beyond the Far Standard: The Quartic Arrives at \u03c6_i = 2.0761 \u2014 and It Is Not Alone","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7225274482","doi":"https://doi.org/10.5281/zenodo.23936685"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23936685","doi":"https://doi.org/10.5281/zenodo.23936685","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23936685","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.23936685","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159396451","display_name":"William Alexander Aldred","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Aldred, William Alexander","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-1215-577X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159396451"],"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":0.9990000128746033,"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":0.9990000128746033,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.0003000000142492354,"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"}},{"id":"https://openalex.org/T13806","display_name":"Mathematical and Computational Methods","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/quartic-potential","display_name":"quartic potential","score":0.5820000171661377},{"id":"https://openalex.org/keywords/sextic-potential","display_name":"sextic potential","score":0.7570000290870667},{"id":"https://openalex.org/keywords/vacuum-energy-density","display_name":"vacuum energy density","score":0.5680000185966492},{"id":"https://openalex.org/keywords/higher-degree-polynomials","display_name":"higher-degree polynomials","score":0.5059999823570251},{"id":"https://openalex.org/keywords/quantum-gravity","display_name":"quantum gravity","score":0.6370000243186951},{"id":"https://openalex.org/keywords/cosmological-constant-problem","display_name":"cosmological constant problem","score":0.703000009059906},{"id":"https://openalex.org/keywords/cosmological-constant","display_name":"cosmological constant","score":0.47699999809265137}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7131999731063843},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.6992999911308289},{"id":"https://openalex.org/C91528185","wikidata":"https://www.wikidata.org/wiki/Q520952","display_name":"Maxima","level":3,"score":0.6452000141143799},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5734999775886536},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.524399995803833},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.49540001153945923},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.48590001463890076},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4611999988555908},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.44690001010894775},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.42410001158714294},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36739999055862427},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3596999943256378},{"id":"https://openalex.org/C133769200","wikidata":"https://www.wikidata.org/wiki/Q174565","display_name":"Bracket","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C117139701","wikidata":"https://www.wikidata.org/wiki/Q7269363","display_name":"Quartic surface","level":3,"score":0.3361000120639801},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3206000030040741},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.2921999990940094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28870001435279846},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2721000015735626},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25699999928474426}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23936685","doi":"https://doi.org/10.5281/zenodo.23936685","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23936685","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.23936686","doi":"https://doi.org/10.5281/zenodo.23936686","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23936686","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.23936685","doi":"https://doi.org/10.5281/zenodo.23936685","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23936685","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/W7225264198","https://openalex.org/W7225269151","https://openalex.org/W7225250345","https://openalex.org/W7225259650","https://openalex.org/W7225238377","https://openalex.org/W7225227828","https://openalex.org/W7225274730","https://openalex.org/W7095417560","https://openalex.org/W3016459883","https://openalex.org/W2503545173"],"abstract_inverted_index":{"The":[0,109],"monomial":[1],"rolling-field":[2],"class":[3,110],"is":[4,82],"computed":[5],"beyond":[6],"the":[7,12,17,21,35,45,61,70,75,80,86,95,124],"far":[8],"standard":[9,96],"and":[10,34,52,74,101],"below":[11],"standard:":[13],"gated":[14],"digit-for-digit":[15],"on":[16,123],"far-standard":[18],"packet's":[19,37],"rows,":[20],"parent's":[22,125],"standard-condition":[23],"maxima":[24,41],"(0.1815":[25],"/":[26,28,30,32,43],"0.0620":[27],"0.0319":[29],"0.0190":[31],"0.0128),":[33],"interval":[36],"own":[38],"exhibits":[39],"(quartic":[40],"0.2283":[42],"0.4442,":[44],"quadratic":[46],"row":[47],"at":[48,65,72,77,85],"phi_i":[49,90,105],"=":[50,67,91],"1.25,":[51],"both":[53],"ends":[54],"of":[55,116],"its":[56],"threshold":[57],"bracket":[58],"[1.20349,":[59],"1.20361]),":[60],"quartic's":[62],"surface":[63],"begins":[64],"phi_i*":[66],"2.0761":[68],"(bisected),":[69],"sextic's":[71],"2.8831":[73],"octic's":[76],"3.6804,":[78],"while":[79],"decic":[81],"still":[83],"short":[84],"stated":[87],"scan":[88],"end":[89],"4.00":[92],"(0.5935).":[93],"Below":[94],"every":[97],"maximum":[98],"falls":[99],"monotonically":[100],"nothing":[102],"conditions":[103],"in":[104,106],"[0.10,":[107],"0.50).":[108],"now":[111],"reads":[112],"as":[113],"a":[114],"staircase":[115],"four":[117],"located":[118],"thresholds.":[119],"Odd":[120],"n":[121],"excluded":[122],"printed":[126],"ground.":[127],"Quantum":[128],"gravity":[129],"NOT":[130,134],"SOLVED;":[131],"vacuum":[132],"catastrophe":[133],"SOLVED.":[135]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-11-05T00:00:00"}