{"id":"https://openalex.org/W7225830509","doi":"https://doi.org/10.5281/zenodo.24134407","title":"Generative Structural Theory v1.110 \u2014 Complete Chains for Eleven Fixed Inputs with Certified Local Obstructions","display_name":"Generative Structural Theory v1.110 \u2014 Complete Chains for Eleven Fixed Inputs with Certified Local Obstructions","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225830509","doi":"https://doi.org/10.5281/zenodo.24134407"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24134407","doi":"https://doi.org/10.5281/zenodo.24134407","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24134407","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.24134407","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135252223","display_name":"Koji Okino","orcid":"https://orcid.org/0009-0003-9273-9813","observed_orcids":["https://orcid.org/0009-0003-9273-9813"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Okino, Koji","raw_affiliation_strings":["SD Lab LLC"],"raw_orcid":"https://orcid.org/0009-0003-9273-9813","affiliations":[{"raw_affiliation_string":"SD Lab LLC","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5135252223"],"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/T10374","display_name":"Advanced Graph Theory Research","score":0.6571999788284302,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.6571999788284302,"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":0.13670000433921814,"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":0.02250000089406967,"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":[],"concepts":[{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.684499979019165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5467000007629395},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5295000076293945},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.4462999999523163},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.44440001249313354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4293000102043152},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4212999939918518},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3959999978542328},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.3862000107765198},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.37119999527931213},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33329999446868896},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.322299987077713},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C65180967","wikidata":"https://www.wikidata.org/wiki/Q130901","display_name":"Binary relation","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.30070000886917114},{"id":"https://openalex.org/C2333172","wikidata":"https://www.wikidata.org/wiki/Q1425985","display_name":"Preorder","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C46304622","wikidata":"https://www.wikidata.org/wiki/Q374814","display_name":"Certification","level":2,"score":0.28130000829696655},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.2632000148296356},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2621000111103058},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24134407","doi":"https://doi.org/10.5281/zenodo.24134407","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24134407","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.24134408","doi":"https://doi.org/10.5281/zenodo.24134408","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24134408","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.24134407","doi":"https://doi.org/10.5281/zenodo.24134407","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24134407","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":[],"abstract_inverted_index":{"This":[0],"version":[1,92],"provides":[2],"explicit":[3,120],"complete":[4,24,81,233],"chains":[5,20,25,82,121,191,330,384],"for":[6,29,83,283],"nine":[7,212,328],"further":[8,208],"fixed":[9,34,112,244],"eighteen-node":[10],"inputs":[11,35,47],"with":[12,17,58,68,103,177,262,279,294,349],"certified":[13,50],"local":[14,51],"obstructions.":[15],"Together":[16],"the":[18,32,65,94,99,104,136,141,172,219,239,252,275,280,324,339],"two":[19,155,164,289,393],"established":[21,41],"in":[22,202,211],"v1.109,":[23],"are":[26,125,192,216,385],"now":[27],"available":[28],"eleven":[30,190,204],"of":[31,44,64,122,130,269,286,299,392],"twelve":[33,46],"M1\u2013M12.":[36],"Versions":[37],"v1.107":[38],"and":[39,85,109,118,151,180,197,206,260,307,331,338,358,368],"v1.108":[40],"that":[42,170,305,382,388],"each":[43],"these":[45,383],"has":[48,235],"a":[49,167,249,270,317,346,389],"obstruction":[52],"at":[53,74,153,287,300,304],"leaf":[54],"3,":[55],"side":[56],"1,":[57],"D":[59,263],"empty:":[60],"an":[61,295],"undecided":[62],"stop":[63],"forcing":[66],"procedure":[67],"no":[69,222,232],"feasible":[70],"set,":[71],"first":[72,245],"detected":[73],"depth":[75],"six.":[76],"Version":[77],"v1.109":[78],"nevertheless":[79],"exhibited":[80],"M1":[84],"M12":[86],"through":[87],"alternative":[88],"choices.":[89],"The":[90,189,321,342,361,372],"present":[91],"applies":[93],"same":[95],"limited":[96],"construction":[97],"to":[98,140,319],"remaining":[100],"ten":[101,325],"inputs,":[102,326],"first-step":[105,178,354],"order,":[106],"witness":[107,276],"rules":[108],"resource":[110],"limits":[111],"before":[113],"execution.":[114],"For":[115,230],"M2,":[116],"M3":[117],"M5\u2013M11,":[119],"13\u201315":[123],"relations":[124,134],"given.":[126],"Each":[127,160],"chain":[128,162,234,250,352],"consists":[129],"minimal":[131],"strongly":[132],"connected":[133],"from":[135],"original":[137,173],"relation":[138,144],"h":[139,148],"bidirected":[142],"tree":[143],"P_S,":[145,150],"remains":[146,376],"inside":[147],"\u222a":[149],"deletes":[152],"most":[154,288,301],"ordered":[156],"pairs":[157,303],"per":[158],"transition.":[159],"new":[161,329],"passes":[163],"checkers,":[165],"including":[166],"separate":[168],"implementation":[169],"reads":[171],"input":[174,350],"records,":[175],"together":[176],"comparisons":[179],"controls.":[181],"These":[182,215,310],"checks":[183],"do":[184,312],"not":[185,313],"constitute":[186],"third-party":[187],"verification.":[188],"compared":[193],"by":[194,238],"their":[195,332],"operations":[196,209],"states.":[198],"One":[199],"operation":[200],"occurs":[201],"all":[203,265,327],"chains,":[205],"six":[207],"occur":[210],"or":[213,225,387],"ten.":[214],"observations":[217],"about":[218],"displayed":[220],"chains;":[221],"general":[223,373],"necessary":[224],"sufficient":[226],"condition":[227],"is":[228,380,394],"inferred.":[229],"M4,":[231],"been":[236],"obtained":[237],"specified":[240,257],"trials.":[241],"All":[242],"five":[243],"steps":[246],"ended":[247],"without":[248],"within":[251],"permitted":[253],"operations.":[254],"At":[255],"one":[256],"reduced":[258],"state":[259,306],"choice,":[261],"empty,":[264],"560":[266],"three-pair":[267],"subsets":[268],"sixteen-pair":[271],"residual":[272],"set":[273,297],"failed":[274],"test.":[277],"Combined":[278],"preceding":[281],"check":[282,334],"added":[284,296],"sets":[285],"pairs,":[290],"this":[291],"excludes":[292],"witnesses":[293],"C":[298],"three":[302],"choice":[308],"only.":[309],"trials":[311],"establish":[314],"M4":[315,340],"as":[316],"counterexample":[318],"(Q1).":[320],"supplement":[322],"gives":[323],"transitions,":[333],"results,":[335],"comparison":[336],"tables":[337],"records.":[341],"accompanying":[343],"ZIP":[344],"includes":[345],"verification":[347],"appendix":[348],"data,":[351],"files,":[353],"witnesses,":[355],"checking":[356,362],"scripts":[357,363],"reproduction":[359],"commands.":[360],"require":[364],"only":[365],"Python":[366],"3":[367],"its":[369],"standard":[370],"library.":[371],"question":[374],"(Q1)":[375],"open.":[377],"No":[378],"claim":[379],"made":[381],"shortest":[386],"deletion":[390],"budget":[391],"necessary.":[395]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}