{"id":"https://openalex.org/W7214639680","doi":"https://doi.org/10.48550/arxiv.2609.31352","title":"Bellman's Forest Problem and Computability","display_name":"Bellman's Forest Problem and Computability","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214639680","doi":"https://doi.org/10.48550/arxiv.2609.31352"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.31352","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31352","pdf_url":"https://arxiv.org/pdf/2609.31352","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/2609.31352","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152828475","display_name":"Jacob Canel","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Canel, Jacob","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5152828475"],"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/shortest-path","display_name":"shortest path","score":0.6489999890327454},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"computable analysis","score":0.8019999861717224},{"id":"https://openalex.org/keywords/computable-real-numbers","display_name":"computable real numbers","score":0.4690000116825104},{"id":"https://openalex.org/keywords/optimal-paths","display_name":"optimal paths","score":0.4819999933242798},{"id":"https://openalex.org/keywords/evacuation-routes","display_name":"evacuation routes","score":0.5040000081062317},{"id":"https://openalex.org/keywords/plane-figures","display_name":"plane figures","score":0.3889999985694885}],"concepts":[{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.7332000136375427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6643000245094299},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.4961000084877014},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.48010000586509705},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C33436860","wikidata":"https://www.wikidata.org/wiki/Q341835","display_name":"Ackermann function","level":3,"score":0.4375999867916107},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39660000801086426},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.35350000858306885},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.328900009393692},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3172000050544739},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.2815000116825104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.265500009059906},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.31352","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31352","pdf_url":"https://arxiv.org/pdf/2609.31352","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.2609.31352","doi":"https://doi.org/10.48550/arxiv.2609.31352","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.31352","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","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":"pmh:oai:arXiv.org:2609.31352","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31352","pdf_url":"https://arxiv.org/pdf/2609.31352","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214639680.pdf","grobid_xml":"https://content.openalex.org/works/W7214639680.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7204624998","https://openalex.org/W6885030622","https://openalex.org/W4405468471","https://openalex.org/W2272610815","https://openalex.org/W1978855243","https://openalex.org/W2076500588","https://openalex.org/W201421346","https://openalex.org/W1988666520","https://openalex.org/W2020410476","https://openalex.org/W3084779176"],"abstract_inverted_index":{"The":[0],"goal":[1],"of":[2,19,21,50,65,73],"this":[3],"paper":[4],"is":[5,67,76],"to":[6,13,32],"refine":[7],"methods":[8],"in":[9,16],"computable":[10,58,84],"analysis":[11],"and":[12,69,80],"employ":[14],"them":[15],"the":[17,62,71,94],"study":[18],"solutions":[20],"an":[22,54],"optimization":[23],"problem":[24,29,52],"posed":[25],"by":[26],"Bellman.":[27],"This":[28],"asks":[30],"how":[31],"find":[33],"optimal":[34,74],"(shortest)":[35],"paths":[36,75,85],"which":[37,61,86],"do":[38],"not":[39],"fit":[40],"into":[41],"given":[42],"plane":[43],"figures.":[44],"We":[45],"show":[46],"that":[47],"each":[48],"instance":[49],"Bellman's":[51],"has":[53],"arbitrarily":[55,89],"small":[56,90],"uniformly":[57,83],"perturbation":[59],"for":[60],"minimal":[63],"length":[64,91],"path":[66],"computable,":[68],"thus":[70],"class":[72],"a":[77],"$\u03a0_1^0$":[78],"class,":[79],"there":[81],"are":[82],"escape":[87],"with":[88],"greater":[92],"than":[93],"minimum":[95],"possible.":[96]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-29T00:00:00"}
