{"id":"https://openalex.org/W7167056575","doi":"https://doi.org/10.48550/arxiv.2607.00005","title":"Topological Void Analysis A Mathematical Framework for Systematic Technical Innovation Discovery in Knowledge Spaces","display_name":"Topological Void Analysis A Mathematical Framework for Systematic Technical Innovation Discovery in Knowledge Spaces","publication_year":2026,"publication_date":"2026-04-20","ids":{"openalex":"https://openalex.org/W7167056575","doi":"https://doi.org/10.48550/arxiv.2607.00005"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.00005","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00005","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.00005","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134483012","display_name":"Kris Pan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pan, Kris","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5134483012"],"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.7702999711036682,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.7702999711036682,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.06260000169277191,"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"}},{"id":"https://openalex.org/T11710","display_name":"Biomedical Text Mining and Ontologies","score":0.017999999225139618,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.652999997138977},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.5429999828338623},{"id":"https://openalex.org/keywords/hypersphere","display_name":"Hypersphere","score":0.4934000074863434},{"id":"https://openalex.org/keywords/adversarial-system","display_name":"Adversarial system","score":0.3869999945163727},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.3799999952316284},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.37869998812675476},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.35910001397132874},{"id":"https://openalex.org/keywords/closeness","display_name":"Closeness","score":0.3490000069141388}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.652999997138977},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5896000266075134},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.5429999828338623},{"id":"https://openalex.org/C2776562905","wikidata":"https://www.wikidata.org/wiki/Q306610","display_name":"Hypersphere","level":2,"score":0.4934000074863434},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.3869999945163727},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.3799999952316284},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.37869998812675476},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36730000376701355},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36640000343322754},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.35910001397132874},{"id":"https://openalex.org/C2779545769","wikidata":"https://www.wikidata.org/wiki/Q5135364","display_name":"Closeness","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C2779772531","wikidata":"https://www.wikidata.org/wiki/Q19689164","display_name":"Void (composites)","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32330000400543213},{"id":"https://openalex.org/C29585364","wikidata":"https://www.wikidata.org/wiki/Q1079166","display_name":"Domain theory","level":2,"score":0.30979999899864197},{"id":"https://openalex.org/C70943382","wikidata":"https://www.wikidata.org/wiki/Q505356","display_name":"Antipodal point","level":2,"score":0.3073999881744385},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2863999903202057},{"id":"https://openalex.org/C194147245","wikidata":"https://www.wikidata.org/wiki/Q1076368","display_name":"Chord (peer-to-peer)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.26660001277923584},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.26440000534057617},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.2551000118255615}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.00005","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00005","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.00005","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00005","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Identifying":[0],"where":[1],"to":[2,53,141],"innovate":[3],"in":[4,23,80],"a":[5,20,24,54,68,81,110,126],"dense":[6],"technical":[7],"domain":[8,101],"-":[9,17,114],"such":[10],"as":[11,75],"operating":[12],"systems":[13],"or":[14,36],"hardware/software":[15],"co-design":[16],"is":[18,50,138],"fundamentally":[19],"search":[21],"problem":[22],"high-dimensional":[25],"knowledge":[26],"space.":[27,85],"Existing":[28],"approaches":[29],"rely":[30],"on":[31,134],"keyword":[32],"search,":[33],"citation":[34],"proximity,":[35],"human":[37],"intuition,":[38],"none":[39],"of":[40,45],"which":[41],"formalise":[42],"the":[43,131,135,175],"notion":[44],"an":[46],"unexplored":[47],"region":[48],"that":[49,71],"simultaneously":[51],"relevant":[52],"target":[55],"goal":[56],"and":[57,95,119,122,161],"absent":[58],"from":[59,165],"prior":[60],"art.":[61],"We":[62],"present":[63],"Topological":[64],"Void":[65],"Analysis":[66],"(TVA),":[67],"mathematical":[69],"framework":[70,176],"defines":[72],"topological":[73],"voids":[74],"triads":[76],"(A,":[77],"B,":[78],"C)":[79],"dense-sparse":[82],"hybrid":[83],"embedding":[84,136],"A":[86,94],"void":[87],"requires":[88],"three":[89],"conditions:":[90],"(i)":[91],"both":[92,116],"concepts":[93],"B":[96],"are":[97],"semantically":[98],"cohesive":[99],"with":[100],"anchor":[102],"C;":[103],"(ii)":[104],"their":[105],"pairwise":[106],"similarity":[107],"falls":[108],"within":[109],"calibrated":[111],"marginality":[112],"band":[113],"avoiding":[115],"obvious":[117,184],"combinations":[118],"unrelated":[120],"noise;":[121],"(iii)":[123],"they":[124],"share":[125],"sparse":[127],"lexical":[128],"bridge":[129],"while":[130],"geodesic":[132],"midpoint":[133],"hypersphere":[137],"unoccupied.":[139],"Applied":[140],"~140k":[142],"indexed":[143],"documents,":[144],"TVA":[145],"generates":[146],"2,128":[147],"invention":[148],"candidates":[149],"across":[150],"96":[151],"targets;":[152],"90%":[153],"survive":[154],"automated":[155],"quality":[156],"filtering,":[157],"yielding":[158],"191":[159],"REVISE":[160],"1":[162],"APPROVE":[163],"verdict":[164],"four-specialist":[166],"adversarial":[167],"review":[168],"(0.05%":[169],"end-to-end).":[170],"Two":[171],"case":[172],"studies":[173],"demonstrate":[174],"surfaces":[177],"non-obvious":[178],"connective":[179],"tissue":[180],"rather":[181],"than":[182],"merely":[183],"related":[185],"pairs.":[186]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-03T00:00:00"}