{"id":"https://openalex.org/W7221825841","doi":"https://doi.org/10.48550/arxiv.2610.16994","title":"The point is a trap: Mathematics of Elastic States in Complex Multiscale Systems","display_name":"The point is a trap: Mathematics of Elastic States in Complex Multiscale Systems","publication_year":2026,"publication_date":"2026-10-12","ids":{"openalex":"https://openalex.org/W7221825841","doi":"https://doi.org/10.48550/arxiv.2610.16994"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.16994","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16994","pdf_url":"https://arxiv.org/pdf/2610.16994","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.16994","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158751852","display_name":"Juan G. Diaz Ochoa","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ochoa, Juan G. Diaz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5158751852"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T14299","display_name":"Complex Systems and Dynamics","score":0.9800000190734863,"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/T14299","display_name":"Complex Systems and Dynamics","score":0.9800000190734863,"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/T10778","display_name":"Philosophy of Biology and Scientific Explanation","score":0.0032999999821186066,"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/T12469","display_name":"Chaos, Complexity, and Education","score":0.003000000026077032,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/elastic-state","display_name":"elastic state","score":0.722000002861023},{"id":"https://openalex.org/keywords/mathematical-abstraction","display_name":"mathematical abstraction","score":0.6819999814033508},{"id":"https://openalex.org/keywords/phase-space","display_name":"phase space","score":0.7459999918937683},{"id":"https://openalex.org/keywords/system-environment-coupling","display_name":"system-environment coupling","score":0.671999990940094},{"id":"https://openalex.org/keywords/affordances","display_name":"affordances","score":0.8500000238418579},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.7910000085830688},{"id":"https://openalex.org/keywords/axiomatic-representation","display_name":"axiomatic representation","score":0.6269999742507935},{"id":"https://openalex.org/keywords/biological-systems-modelling","display_name":"biological systems modelling","score":0.5389999747276306}],"concepts":[{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.6057999730110168},{"id":"https://openalex.org/C130327152","wikidata":"https://www.wikidata.org/wiki/Q748349","display_name":"Mathematical structure","level":2,"score":0.5375999808311462},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5101000070571899},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4749999940395355},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.46549999713897705},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.45350000262260437},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.4526999890804291},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.41100001335144043},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.39259999990463257},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.3815000057220459},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37380000948905945},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.37220001220703125},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.36469998955726624},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3605000078678131},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3596000075340271},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.35199999809265137},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.3425000011920929},{"id":"https://openalex.org/C9136319","wikidata":"https://www.wikidata.org/wiki/Q362640","display_name":"Covariant transformation","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.3149000108242035},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.3057999908924103},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C106624574","wikidata":"https://www.wikidata.org/wiki/Q5270387","display_name":"Diagrammatic reasoning","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.2578999996185303}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.16994","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16994","pdf_url":"https://arxiv.org/pdf/2610.16994","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.16994","doi":"https://doi.org/10.48550/arxiv.2610.16994","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.16994","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.16994","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.16994","pdf_url":"https://arxiv.org/pdf/2610.16994","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221825841.pdf","grobid_xml":"https://content.openalex.org/works/W7221825841.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W640118464","https://openalex.org/W1512167612","https://openalex.org/W2041042514","https://openalex.org/W2172687151","https://openalex.org/W2611912265","https://openalex.org/W2771291733","https://openalex.org/W2796560727","https://openalex.org/W2921169191","https://openalex.org/W3003381847","https://openalex.org/W3017505888","https://openalex.org/W3036859210","https://openalex.org/W3201719277","https://openalex.org/W3202715456","https://openalex.org/W3214728447","https://openalex.org/W4206339529","https://openalex.org/W4298159693","https://openalex.org/W4302317499","https://openalex.org/W4365515065","https://openalex.org/W4368372646","https://openalex.org/W4385377443","https://openalex.org/W4385657815","https://openalex.org/W4408349808","https://openalex.org/W4408349835","https://openalex.org/W4408349869","https://openalex.org/W4408848246","https://openalex.org/W4415742440","https://openalex.org/W4416162083","https://openalex.org/W7128437607"],"related_works":["https://openalex.org/W4408349835","https://openalex.org/W613402446","https://openalex.org/W2099742433","https://openalex.org/W153828495","https://openalex.org/W2972103296","https://openalex.org/W2200490064","https://openalex.org/W601140403","https://openalex.org/W2535486848","https://openalex.org/W82245214","https://openalex.org/W4301046916"],"abstract_inverted_index":{"Observables":[0],"in":[1,8,13,26,31,126,149,164,180,249],"complex":[2,150,181,223],"biological":[3],"systems":[4,151,182],"are":[5,196],"often":[6],"reduced":[7],"their":[9,99,153,158,162,203],"inherent":[10],"complexity,":[11],"resulting":[12],"abstract,":[14],"a":[15,134,138,232,243],"priori":[16],"mathematical":[17,46,84,113,220,247],"representations":[18],"based":[19],"on":[20],"simple":[21],"concepts":[22,114,177],"such":[23,67,115,183],"as":[24,116,184,242],"points":[25],"spaces":[27,125],"or":[28,33],"interconnected":[29],"nodes":[30],"lattices":[32],"networks.":[34],"This":[35],"reduction":[36],"is":[37],"relevant":[38],"not":[39,156],"only":[40,157],"for":[41,53,63,246],"the":[42,64,81,92,101,105,121,167,210,219],"formulation":[43],"of":[44,66,80,123,141,189,212,222,234],"multiscale":[45],"models":[47],"and":[48,56,88,98,104,152,170,172,225],"field":[49],"theories":[50],"but":[51,160],"also":[52,161],"experimental":[54],"planning":[55],"data":[57],"collection":[58],"to":[59,77,166,175,202,239],"gain":[60],"systematic":[61],"evidence":[62],"nature":[65],"systems,":[68,224],"thus":[69,119,173],"extracting":[70],"robust":[71],"causal":[72],"relationships":[73],"that":[74,107,195],"would":[75],"lead":[76],"better":[78],"control":[79],"system.":[82],"However,":[83],"abstraction":[85],"remains":[86],"challenging":[87],"problematic,":[89],"especially":[90],"given":[91],"tightly":[93],"intertwined":[94],"elements":[95],"between":[96,147],"objects":[97],"environment,":[100,154,204],"system's":[102],"affordance,":[103],"fact":[106],"all":[108],"these":[109],"aspects":[110],"limit":[111],"fundamental":[112],"set":[117,213],"theory,":[118,214],"hindering":[120],"definition":[122],"phase":[124],"extreme":[127],"cases.":[128],"In":[129,187],"this":[130,190,250],"work,":[131],"I":[132,192],"introduce":[133],"potential":[135],"axiomatic":[136],"representing":[137,145],"nonreducible":[139],"representation":[140,221],"high":[142,216],"order":[143],"structures":[144],"entanglement":[146],"observables":[148],"considering":[155],"coupling":[159],"affordance":[163],"relation":[165],"overall":[168],"system":[169],"context,":[171],"intend":[174],"formalize":[176],"already":[178],"used":[179],"Kantian":[185],"wholes.":[186],"light":[188],"axiomatic,":[191],"identify":[193],"states":[194,236],"rather":[197],"less":[198],"elastic":[199,235],"with":[200,231,237],"respect":[201,238],"discuss":[205],"how":[206],"low":[207],"elasticity":[208,217],"enables":[209],"application":[211],"while":[215],"limits":[218],"present":[226],"an":[227],"exemplary":[228],"Ising":[229],"model":[230],"network":[233],"different":[240],"contexts":[241],"limiting":[244],"case":[245],"modelling":[248],"context.":[251]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-15T00:00:00"}
