{"id":"https://openalex.org/W7213438907","doi":"https://doi.org/10.48550/arxiv.2609.16351","title":"Requirement-Induced Predictive Geometry for Finite-Resource Prediction in Dynamical Systems","display_name":"Requirement-Induced Predictive Geometry for Finite-Resource Prediction in Dynamical Systems","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213438907","doi":"https://doi.org/10.48550/arxiv.2609.16351"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.16351","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16351","pdf_url":"https://arxiv.org/pdf/2609.16351","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/2609.16351","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151913367","display_name":"Song-Ju Kim","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kim, Song-Ju","raw_affiliation_strings":["SOBIN Institute LLC , Kawanishi , Hyogo , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SOBIN Institute LLC , Kawanishi , Hyogo , Japan","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5151913367"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.6913999915122986,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.6913999915122986,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.0357000008225441,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.032099999487400055,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-prediction","display_name":"nonlinear prediction","score":0.7480000257492065},{"id":"https://openalex.org/keywords/finite-time-dynamics","display_name":"finite-time dynamics","score":0.6669999957084656},{"id":"https://openalex.org/keywords/tangent-map","display_name":"tangent map","score":0.6990000009536743},{"id":"https://openalex.org/keywords/error-propagation","display_name":"error propagation","score":0.6299999952316284},{"id":"https://openalex.org/keywords/spectral-law","display_name":"spectral law","score":0.6320000290870667},{"id":"https://openalex.org/keywords/standard-map","display_name":"standard map","score":0.9470000267028809},{"id":"https://openalex.org/keywords/double-pendulum","display_name":"double pendulum","score":0.9940000176429749},{"id":"https://openalex.org/keywords/hamiltonian-systems","display_name":"Hamiltonian systems","score":0.8429999947547913},{"id":"https://openalex.org/keywords/condition-number","display_name":"condition number","score":0.5299999713897705},{"id":"https://openalex.org/keywords/adaptive-sensing","display_name":"adaptive sensing","score":0.5720000267028809},{"id":"https://openalex.org/keywords/state-estimation","display_name":"state estimation","score":0.6610000133514404}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7321000099182129},{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.6288999915122986},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5410000085830688},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4609000086784363},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4242999851703644},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.40369999408721924},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.39980000257492065},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.3804999887943268},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.36579999327659607},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.36410000920295715},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3221000134944916},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.30640000104904175},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.29339998960494995},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.28369998931884766},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2793000042438507},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2766000032424927},{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2623000144958496},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.16351","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16351","pdf_url":"https://arxiv.org/pdf/2609.16351","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.2609.16351","doi":"https://doi.org/10.48550/arxiv.2609.16351","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.16351","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.16351","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16351","pdf_url":"https://arxiv.org/pdf/2609.16351","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/W7213438907.pdf","grobid_xml":"https://content.openalex.org/works/W7213438907.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W2000252897","https://openalex.org/W2014330362","https://openalex.org/W2039671349","https://openalex.org/W2122424119","https://openalex.org/W2134889984","https://openalex.org/W2143723307","https://openalex.org/W2160163816","https://openalex.org/W2162752666","https://openalex.org/W2164454345","https://openalex.org/W2485135680","https://openalex.org/W2591072568","https://openalex.org/W2963695017","https://openalex.org/W3043004836","https://openalex.org/W3203905183","https://openalex.org/W4229574485","https://openalex.org/W4231002530","https://openalex.org/W4243970992","https://openalex.org/W4254197176","https://openalex.org/W4300031234","https://openalex.org/W4392122892","https://openalex.org/W4403182763","https://openalex.org/W7133197302","https://openalex.org/W7162395783","https://openalex.org/W7202367915"],"related_works":["https://openalex.org/W2138966337","https://openalex.org/W7213513538","https://openalex.org/W7213501316","https://openalex.org/W587825268","https://openalex.org/W7117410357","https://openalex.org/W3145732661","https://openalex.org/W3143950810","https://openalex.org/W346101669","https://openalex.org/W7115172691","https://openalex.org/W7065158711"],"abstract_inverted_index":{"In":[0,136],"nonlinear":[1,198],"prediction,":[2],"two":[3],"state":[4,33,209],"representations":[5],"with":[6,24,175],"the":[7,41,50,59,62,65,72,77,80,88,93,109,120,125,158,162,176],"same":[8],"local":[9,67],"uncertainty":[10,107],"volume":[11],"can":[12],"have":[13],"radically":[14],"different":[15],"predictive":[16,47,95,126,134,155,171],"value.":[17],"We":[18,85],"consider":[19],"differentiable":[20],"finite-time":[21,143],"dynamics":[22,60,150],"together":[23,174],"a":[25,45,116,130,141,186,204],"quadratic":[26],"terminal":[27,32,110],"requirement":[28,38,111],"that":[29,82,87,99,183],"specifies":[30],"which":[31,215],"differences":[34],"matter.":[35],"Pulling":[36],"this":[37,139],"back":[39],"through":[40],"tangent":[42,52],"map":[43],"defines":[44],"requirement-induced":[46],"geometry":[48,55,217],"on":[49],"present":[51],"space.":[53],"This":[54],"is":[56,101,119,218],"fixed":[57,66],"by":[58,103],"and":[61,146,157,191,211],"requirement;":[63],"under":[64],"uncertainty-volume":[68],"constraint":[69],"used":[70],"here,":[71],"capacity":[73],"parameter":[74],"fixes":[75],"only":[76,173],"scale":[78],"of":[79,105,124,133,161],"representation":[81,118,216],"realizes":[83],"it.":[84],"show":[86],"unique":[89],"optimal":[90,163],"covariance":[91],"has":[92],"inverse":[94],"shape":[96],"and,":[97],"equivalently,":[98],"optimality":[100],"characterized":[102],"isotropization":[104],"propagated":[106],"in":[108,197,214],"geometry.":[112,164],"The":[113,201],"gain":[114,156,172,188],"over":[115],"baseline-isotropic":[117],"arithmetic-to-geometric":[121],"mean":[122],"ratio":[123],"spectrum,":[127],"making":[128],"it":[129],"coordinate-invariant":[131],"measure":[132],"anisotropy.":[135],"Euclidean":[137],"coordinates":[138],"yields":[140],"general":[142],"spectral":[144],"law,":[145],"for":[147,206],"two-dimensional":[148],"area-preserving":[149],"an":[151],"exact":[152],"identity":[153],"between":[154],"condition":[159],"number":[160],"Stronger":[165],"directional":[166],"stretching":[167],"therefore":[168],"increases":[169],"potential":[170],"anisotropy":[177,184],"required":[178],"to":[179,220],"realize":[180],"it;":[181],"bounding":[182],"imposes":[185],"finite":[187],"ceiling.":[189],"Standard-map":[190],"double-pendulum":[192],"calculations":[193],"demonstrate":[194],"these":[195],"relations":[196],"Hamiltonian":[199],"systems.":[200],"framework":[202],"provides":[203],"basis":[205],"adaptive":[207],"sensing,":[208],"estimation,":[210],"model-predictive":[212],"computation":[213],"matched":[219],"predicted":[221],"task":[222],"consequences.":[223]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-17T00:00:00"}