{"id":"https://openalex.org/W7225752326","doi":"https://doi.org/10.5281/zenodo.24102794","title":"Mixed Hessians, Polynomial Communication, and the Discovery of Tensor Trees","display_name":"Mixed Hessians, Polynomial Communication, and the Discovery of Tensor Trees","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225752326","doi":"https://doi.org/10.5281/zenodo.24102794"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24102794","doi":"https://doi.org/10.5281/zenodo.24102794","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24102794","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.24102794","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5144231085","display_name":"Haitam Kadri","orcid":"https://orcid.org/0009-0001-3791-1401","observed_orcids":["https://orcid.org/0009-0001-3791-1401"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kadri, Haitam","raw_affiliation_strings":["Independent Researcher"],"raw_orcid":"https://orcid.org/0009-0001-3791-1401","affiliations":[{"raw_affiliation_string":"Independent Researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5144231085"],"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/T12303","display_name":"Tensor decomposition and applications","score":0.8734999895095825,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.8734999895095825,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.04600000008940697,"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":0.03920000046491623,"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"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.630299985408783},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5648999810218811},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5637000203132629},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45739999413490295},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4562999904155731},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.435699999332428},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42489999532699585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37470000982284546},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.36340001225471497},{"id":"https://openalex.org/C43169469","wikidata":"https://www.wikidata.org/wiki/Q580922","display_name":"Preprint","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.3424000144004822},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.33340001106262207},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31529998779296875},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2922999858856201},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.2522999942302704}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24102794","doi":"https://doi.org/10.5281/zenodo.24102794","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24102794","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.24102795","doi":"https://doi.org/10.5281/zenodo.24102795","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24102795","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.24102794","doi":"https://doi.org/10.5281/zenodo.24102794","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24102794","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0,103],"preprint":[1],"studies":[2],"the":[3,78,118],"discovery":[4],"of":[5,11],"exact":[6,52,99],"tree":[7],"tensor":[8,38],"network":[9],"representations":[10],"bounded-degree":[12],"polynomial":[13,35],"phase":[14],"tensors":[15],"over":[16],"finite":[17],"fields,":[18],"without":[19],"a":[20,27,47,57,105],"pre-supplied":[21],"variable":[22],"tree.":[23],"The":[24,74,92,108],"manuscript":[25,76],"develops":[26],"stationary-completion":[28],"construction":[29],"relating":[30],"mixed-Hessian":[31],"rank":[32],"to":[33,55,66],"interactive":[34],"evaluation":[36],"and":[37,50,60,80,89,98,117,134],"unfolding":[39],"rank.":[40],"It":[41],"then":[42],"combines":[43],"these":[44],"comparisons":[45],"with":[46,120,129],"connectivity-function":[48],"approximation":[49],"an":[51],"fixed-tree":[53],"compiler":[54],"obtain":[56],"proposed":[58],"topology-discovery":[59],"compilation":[61],"procedure.":[62],"A":[63],"Fourier-transform":[64],"application":[65],"fully":[67],"observed":[68],"functional":[69],"relations":[70],"is":[71,104,123],"also":[72],"presented.":[73],"revised":[75],"expands":[77],"algorithmic":[79],"complexity":[81],"arguments,":[82],"including":[83],"specialization,":[84],"threshold":[85],"search,":[86],"equivalence":[87],"testing,":[88],"counterexample":[90],"extraction.":[91],"accompanying":[93],"package":[94],"contains":[95],"source":[96],"files":[97],"small-instance":[100],"validation":[101],"scripts.":[102],"research":[106],"preprint.":[107],"mathematical":[109,130],"arguments":[110],"have":[111],"not":[112,124],"been":[113],"independently":[114],"peer":[115],"reviewed,":[116],"comparison":[119],"prior":[121],"work":[122],"exhaustive.":[125],"AI":[126],"tools":[127],"assisted":[128],"exploration,":[131],"drafting,":[132],"programming,":[133],"revision.":[135]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-11T00:00:00"}