{"id":"https://openalex.org/W7225182155","doi":"https://doi.org/10.5281/zenodo.23932592","title":"Can positive geometry fix the Standard Model? Evidence from a Lean-verified agentic research programme (Paper II: the evidence)","display_name":"Can positive geometry fix the Standard Model? Evidence from a Lean-verified agentic research programme (Paper II: the evidence)","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7225182155","doi":"https://doi.org/10.5281/zenodo.23932592"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23932592","doi":"https://doi.org/10.5281/zenodo.23932592","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23932592","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.23932592","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5160536088","display_name":"Savan Chhaniyara","orcid":"https://orcid.org/0009-0007-1570-3939","observed_orcids":["https://orcid.org/0009-0007-1570-3939"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chhaniyara, Savan","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0007-1570-3939","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5160536088"],"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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.8817999958992004,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.8817999958992004,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.04470000043511391,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.017400000244379044,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"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/positive-geometry","display_name":"positive geometry","score":0.8240000009536743},{"id":"https://openalex.org/keywords/amplituhedron","display_name":"amplituhedron","score":0.972000002861023},{"id":"https://openalex.org/keywords/associahedron","display_name":"associahedron","score":0.996999979019165},{"id":"https://openalex.org/keywords/scattering-amplitudes","display_name":"scattering amplitudes","score":0.9430000185966492},{"id":"https://openalex.org/keywords/standard-model","display_name":"Standard Model","score":0.8119999766349792},{"id":"https://openalex.org/keywords/resonance-linewidth","display_name":"resonance width","score":0.8679999709129333},{"id":"https://openalex.org/keywords/color-factors","display_name":"color factors","score":0.6359999775886536},{"id":"https://openalex.org/keywords/top-yukawa-coupling","display_name":"top quark Yukawa coupling","score":0.7990000247955322},{"id":"https://openalex.org/keywords/electroweak-couplings","display_name":"electroweak couplings","score":0.8999999761581421},{"id":"https://openalex.org/keywords/renormalization-group","display_name":"renormalization group","score":0.8220000267028809},{"id":"https://openalex.org/keywords/ollivier-ricci-curvature","display_name":"Ollivier-Ricci curvature","score":0.9810000061988831},{"id":"https://openalex.org/keywords/simple-polytopes","display_name":"simple polytopes","score":0.8999999761581421},{"id":"https://openalex.org/keywords/lean-4-formal-verification","display_name":"Lean 4 formal verification","score":0.746999979019165},{"id":"https://openalex.org/keywords/quantum-numbers","display_name":"quantum numbers","score":0.5429999828338623}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5947999954223633},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5101000070571899},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.4959999918937683},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.4781999886035919},{"id":"https://openalex.org/C151195881","wikidata":"https://www.wikidata.org/wiki/Q1153833","display_name":"Yukawa potential","level":2,"score":0.4609000086784363},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4593999981880188},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.42719998955726624},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.4219000041484833},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.41690000891685486},{"id":"https://openalex.org/C84976871","wikidata":"https://www.wikidata.org/wiki/Q2015673","display_name":"Openness to experience","level":2,"score":0.39649999141693115},{"id":"https://openalex.org/C101454708","wikidata":"https://www.wikidata.org/wiki/Q17106019","display_name":"Standard Model (mathematical formulation)","level":3,"score":0.38089999556541443},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3686999976634979},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.36320000886917114},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3562000095844269},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.335999995470047},{"id":"https://openalex.org/C17863212","wikidata":"https://www.wikidata.org/wiki/Q466416","display_name":"Electroweak interaction","level":2,"score":0.33489999175071716},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.31520000100135803},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.3147999942302704},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.31439998745918274},{"id":"https://openalex.org/C2777855551","wikidata":"https://www.wikidata.org/wiki/Q12310021","display_name":"Subject (documents)","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30720001459121704},{"id":"https://openalex.org/C153013531","wikidata":"https://www.wikidata.org/wiki/Q1322810","display_name":"Scattering amplitude","level":3,"score":0.30250000953674316},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2858999967575073},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2854999899864197},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.27059999108314514},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2671000063419342},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2574000060558319},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23932592","doi":"https://doi.org/10.5281/zenodo.23932592","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23932592","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.23932593","doi":"https://doi.org/10.5281/zenodo.23932593","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23932593","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.23932592","doi":"https://doi.org/10.5281/zenodo.23932592","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23932592","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/W2897677385","https://openalex.org/W7167597072","https://openalex.org/W4364387164","https://openalex.org/W7151532710","https://openalex.org/W7128235820","https://openalex.org/W7215688885","https://openalex.org/W3043427159","https://openalex.org/W7125417159","https://openalex.org/W6944564946","https://openalex.org/W7161593716"],"abstract_inverted_index":{"Positive":[0],"geometries,":[1],"such":[2,24],"as":[3,79,204,283],"the":[4,7,32,90,93,96,131,146,156,187,199,221,225,241,277,285,305],"amplituhedron":[5],"and":[6,39,73,104,148,169,211,244,266,279,293],"associahedron,":[8],"encode":[9],"scattering":[10],"amplitudes":[11],"without":[12],"reference":[13],"to":[14,160,289],"spacetime":[15],"or":[16,77,86,260],"a":[17,22,28,43,55,67,80,82,84,87,108,161,167,205,234,250,301],"Lagrangian.":[18],"We":[19,201],"ask":[20],"whether":[21],"single":[23],"structure":[25],"can":[26],"fix":[27],"dimensionless":[29],"quantity":[30],"of":[31,95,112,190,220,224,236,253,270],"Standard":[33,242],"Model":[34,243],"with":[35,70,141,256],"no":[36,137,257],"fitted":[37],"parameters,":[38],"we":[40,181,229,280],"report":[41],"what":[42],"human-directed,":[44],"AI-agentic":[45],"research":[46],"programme":[47],"has":[48],"established":[49],"so":[50],"far.":[51],"Every":[52],"claim":[53],"carries":[54],"status":[56],"tag:":[57],"proved":[58,62,271],"in":[59,66,130],"Lean":[60,251],"4,":[61],"on":[63,217],"paper,":[64],"computed":[65],"preregistered":[68,110],"simulation":[69],"locked":[71],"checkers":[72],"planted":[74],"controls,":[75],"cited,":[76],"stated":[78],"conjecture,":[81],"speculation,":[83],"record":[85],"reviewer":[88],"judgement;":[89],"method":[91],"is":[92,174,304],"subject":[94],"companion":[97],"Paper":[98],"I.":[99],"The":[100],"evidence":[101],"spans":[102],"physics":[103],"mathematics.":[105],"In":[106,179],"physics,":[107],"blind":[109],"test":[111],"Lovelace-Shapiro":[113],"coupling":[114,159,172],"ratios":[115],"against":[116],"measured":[117],"resonance":[118],"widths":[119],"passed":[120],"within":[121],"its":[122],"bands.":[123],"A":[124],"one-loop":[125],"colour-factor":[126],"no-go":[127],"shows":[128],"that,":[129],"cubic":[132],"Tr":[133],"\u03c6\u00b3":[134],"colour":[135,138,150],"model,":[136],"group":[139],"SU(N)":[140],"N":[142],"\u2265":[143],"3":[144],"makes":[145],"triangle-type":[147],"crossed-box":[149],"factors":[151],"sign-coherent.":[152],"Renormalisation-group":[153],"consistency":[154,294],"narrows":[155],"top":[157],"Yukawa":[158],"window":[162],"but":[163],"does":[164,247],"not":[165,248,288],"select":[166],"value,":[168],"one":[170,219],"electroweak":[171],"constraint":[173],"reproduced,":[175],"conditionally,":[176],"from":[177],"amplitudes.":[178],"mathematics,":[180],"give":[182],"exact":[183],"closed":[184],"forms":[185],"for":[186],"Ollivier-Ricci":[188],"curvature":[189],"associahedron":[191],"flip":[192],"graphs,":[193],"whose":[194],"mean":[195],"changes":[196],"sign":[197],"at":[198],"decagon.":[200],"also":[202],"state":[203],"conjecture":[206],"an":[207,267],"equality":[208],"between":[209],"Ollivier":[210],"capped":[212],"Forman":[213],"curvature,":[214],"which":[215],"holds":[216],"every":[218],"140,107":[222],"edges":[223],"513":[226],"simple":[227],"polytopes":[228],"tested.":[230],"Together":[231],"these":[232],"form":[233],"map":[235],"where":[237,245],"positive":[238],"geometry":[239,286],"reaches":[240],"it":[246],"yet:":[249],"library":[252],"1,378":[254],"theorems":[255],"unproved":[258],"steps":[259],"extra":[261],"axioms,":[262],"77":[263],"mapped":[264],"routes,":[265,278],"exclusion":[268],"ledger":[269],"no-gos.":[272],"Two":[273],"patterns":[274],"run":[275],"across":[276],"offer":[281],"them":[282],"conjectures:":[284],"tends":[287],"see":[290],"quantum":[291,302],"numbers,":[292],"yields":[295],"windows":[296],"rather":[297],"than":[298],"points.":[299],"Deriving":[300],"number":[303],"open":[306],"target.":[307]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-04T00:00:00"}
