{"id":"https://openalex.org/W7225599468","doi":"https://doi.org/10.5281/zenodo.24053735","title":"Cost\u2013Support Frontiers of Internally Stable Continuations on Trees and Cacti: Realizability, Obstructions, and Representation Size","display_name":"Cost\u2013Support Frontiers of Internally Stable Continuations on Trees and Cacti: Realizability, Obstructions, and Representation Size","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225599468","doi":"https://doi.org/10.5281/zenodo.24053735"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24053735","doi":"https://doi.org/10.5281/zenodo.24053735","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24053735","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","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24053735","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133403265","display_name":"Kelly Rhys","orcid":"https://orcid.org/0009-0009-4744-1923","observed_orcids":["https://orcid.org/0009-0009-4744-1923"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kelly Rhys","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0009-4744-1923","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5133403265"],"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.5264000296592712,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.5264000296592712,"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/T11031","display_name":"Game Theory and Applications","score":0.4309000074863434,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.019600000232458115,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rooted-trees","display_name":"rooted trees","score":0.921999990940094},{"id":"https://openalex.org/keywords/cactaceae","display_name":"Cactaceae","score":0.847000002861023},{"id":"https://openalex.org/keywords/realizability","display_name":"realizability","score":0.8069999814033508},{"id":"https://openalex.org/keywords/nash-inequality","display_name":"Nash inequality","score":0.847000002861023}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5555999875068665},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.5357999801635742},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.503600001335144},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43540000915527344},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4196999967098236},{"id":"https://openalex.org/C160145156","wikidata":"https://www.wikidata.org/wiki/Q778586","display_name":"Executable","level":2,"score":0.41429999470710754},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38850000500679016},{"id":"https://openalex.org/C43169469","wikidata":"https://www.wikidata.org/wiki/Q580922","display_name":"Preprint","level":2,"score":0.3828999996185303},{"id":"https://openalex.org/C2780106946","wikidata":"https://www.wikidata.org/wiki/Q14560","display_name":"Cactus","level":2,"score":0.38029998540878296},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.37139999866485596},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3700999915599823},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.33090001344680786},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3212999999523163},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.3174000084400177},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C136519935","wikidata":"https://www.wikidata.org/wiki/Q2859802","display_name":"Ternary search tree","level":5,"score":0.29670000076293945},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28299999237060547},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C182964748","wikidata":"https://www.wikidata.org/wiki/Q208216","display_name":"Triangle inequality","level":2,"score":0.258899986743927},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25769999623298645},{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24053735","doi":"https://doi.org/10.5281/zenodo.24053735","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24053735","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.24053736","doi":"https://doi.org/10.5281/zenodo.24053736","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24053736","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.24053735","doi":"https://doi.org/10.5281/zenodo.24053735","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24053735","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/W7225583239","https://openalex.org/W2186661603","https://openalex.org/W2063190838","https://openalex.org/W2949977728","https://openalex.org/W4237877248","https://openalex.org/W6887745936","https://openalex.org/W181332617","https://openalex.org/W2094315959","https://openalex.org/W1756732160","https://openalex.org/W2289067258"],"abstract_inverted_index":{"This":[0],"research":[1],"preprint":[2],"investigates":[3],"the":[4,82,106],"realizability":[5],"and":[6,24,47,67,115,126],"representation":[7],"size":[8],"of":[9,54,98],"cost\u2013support":[10],"frontiers":[11],"arising":[12],"from":[13],"internally":[14],"stable":[15],"continuations":[16,80],"in":[17],"binary":[18,42],"polymatrix":[19,43],"games":[20],"on":[21],"rooted":[22],"trees":[23],"cacti.":[25],"The":[26,57,75],"results":[27,76],"establish":[28,90],"a":[29,48,51,95],"rooted-tree":[30],"correspondence":[31],"with":[32,81],"zero\u2013one":[33],"knapsack":[34],"value":[35],"functions,":[36],"an":[37],"explicit":[38],"frontier":[39],"that":[40],"no":[41],"cactus":[44,65,99],"can":[45],"realize,":[46],"family":[49],"requiring":[50],"quadratic":[52],"number":[53],"interior":[55],"players.":[56],"analysis":[58],"also":[59],"identifies":[60],"structural":[61],"constraints":[62],"imposed":[63],"by":[64],"interfaces":[66],"demonstrates":[68],"information":[69],"loss":[70],"under":[71],"scalar":[72],"tropical":[73],"evaluation.":[74],"concern":[77],"fixed-reference,":[78],"at-most-budget":[79],"root\u2019s":[83],"Nash":[84],"inequality":[85],"deferred.":[86],"They":[87],"do":[88],"not":[89,131],"dynamic-update":[91],"complexity":[92],"bounds":[93],"or":[94],"complete":[96],"characterization":[97],"frontiers.":[100],"A":[101],"separate":[102],"reproducibility":[103,116],"archive":[104],"provides":[105],"LaTeX":[107],"manuscript":[108],"source,":[109],"executable":[110],"verification":[111],"programs,":[112],"expected":[113],"outputs,":[114],"instructions.":[117],"Version":[118],"1.0":[119],"\u2014":[120],"Research":[121],"preprint.":[122],"External":[123],"peer":[124],"review":[125],"exhaustive":[127],"historical-priority":[128],"assessment":[129],"have":[130],"been":[132],"completed.":[133]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}