{"id":"https://openalex.org/W7220996252","doi":"https://doi.org/10.48550/arxiv.2610.09698","title":"Spurious zero-dispersion continua in full $(2,q)$-positivity: A linear hierarchy-depth lower bound from an exactly solvable counting operator","display_name":"Spurious zero-dispersion continua in full $(2,q)$-positivity: A linear hierarchy-depth lower bound from an exactly solvable counting operator","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220996252","doi":"https://doi.org/10.48550/arxiv.2610.09698"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09698","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09698","pdf_url":"https://arxiv.org/pdf/2610.09698","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/2610.09698","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157906257","display_name":"Maho Nakata","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210110652","display_name":"RIKEN","ror":"https://ror.org/01sjwvz98","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652"]},{"id":"https://openalex.org/I4405286309","display_name":"RIKEN Pioneering Research Institute","ror":"https://ror.org/01s6zhz21","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4405286309"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Nakata, Maho","raw_affiliation_strings":["Computational Condensed Matter Physics Laboratory , RIKEN Pioneering Research Institute , 2-1 Hirosawa , Wako , Saitama 351-0198 , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computational Condensed Matter Physics Laboratory , RIKEN Pioneering Research Institute , 2-1 Hirosawa , Wako , Saitama 351-0198 , Japan","institution_ids":["https://openalex.org/I4210110652","https://openalex.org/I4405286309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5157906257"],"corresponding_institution_ids":["https://openalex.org/I4210110652","https://openalex.org/I4405286309"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T11804","display_name":"Quantum many-body systems","score":0.6068999767303467,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11804","display_name":"Quantum many-body systems","score":0.6068999767303467,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.2824999988079071,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.02630000002682209,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/two-particle-reduced-density-matrix","display_name":"two-particle reduced density matrix","score":0.7829999923706055},{"id":"https://openalex.org/keywords/dispersion-test","display_name":"dispersion test","score":0.6430000066757202},{"id":"https://openalex.org/keywords/variational-methods","display_name":"variational methods","score":0.3440000116825104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8184000253677368},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5602999925613403},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5091999769210815},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4641999900341034},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.429500013589859},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.427700012922287},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.41530001163482666},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.4052000045776367},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.39089998602867126},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.38909998536109924},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.3384999930858612},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.33340001106262207},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3124000132083893},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.2687000036239624},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09698","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09698","pdf_url":"https://arxiv.org/pdf/2610.09698","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.2610.09698","doi":"https://doi.org/10.48550/arxiv.2610.09698","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09698","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09698","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09698","pdf_url":"https://arxiv.org/pdf/2610.09698","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/W7220996252.pdf","grobid_xml":"https://content.openalex.org/works/W7220996252.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2028107163","https://openalex.org/W7044402232","https://openalex.org/W2277697925","https://openalex.org/W7139018347","https://openalex.org/W82562055","https://openalex.org/W7207888350","https://openalex.org/W1989092880","https://openalex.org/W7223365350","https://openalex.org/W7222564988","https://openalex.org/W2023576036"],"abstract_inverted_index":{"Variational":[0],"two-particle":[1,227],"reduced-density-matrix":[2,228],"methods":[3],"impose":[4],"hierarchies":[5],"of":[6,15,55,62,69,75,79,92,132],"semidefinite":[7,81,142,220],"constraints.":[8,82],"We":[9,214],"ask":[10],"whether":[11],"a":[12,17,32,133,137,177,211],"fixed":[13,212],"level":[14,74,98],"such":[16],"hierarchy":[18,78,97],"can":[19],"recover":[20],"even":[21],"an":[22,37,45,89],"elementary":[23],"many-fermion":[24],"spectrum,":[25],"using":[26],"the":[27,40,56,66,76,84,96,102,108,123,129,161,165,172,192,198,218,237,242],"dispersion":[28,42,167],"test,":[29],"in":[30,52,122,232],"which":[31],"value":[33,205],"is":[34,189],"accepted":[35,70],"as":[36],"eigenvalue":[38],"when":[39],"minimized":[41],"vanishes.":[43],"For":[44,157],"exactly":[46],"solvable":[47],"operator":[48],"that":[49,119,181,196,217,236],"counts":[50],"fermions":[51],"one":[53],"half":[54],"spin":[57],"orbitals,":[58],"whose":[59],"spectrum":[60,200],"consists":[61],"integers,":[63,85],"we":[64,106],"determine":[65],"complete":[67,224],"set":[68,87],"values":[71,94],"at":[72,210],"every":[73,203],"full":[77,219],"particle-hole":[80],"Besides":[83],"this":[86,158],"contains":[88],"entire":[90],"interval":[91],"noninteger":[93,138],"unless":[95],"grows":[99],"linearly":[100],"with":[101],"particle":[103,139],"number,":[104],"and":[105,176,222],"give":[107],"exact":[109],"threshold.":[110],"The":[111,187],"proof":[112],"constructs":[113],"explicit":[114],"pseudo":[115],"reduced":[116],"density":[117],"matrices":[118],"are":[120,207,230],"diagonal":[121],"occupation":[124,130,145],"basis,":[125],"obtained":[126],"by":[127,148],"continuing":[128],"probabilities":[131],"fixed-particle-number":[134],"state":[135],"to":[136,153,191,241],"number.":[140],"Classical":[141],"constraints":[143,221],"on":[144],"correlations,":[146],"supplemented":[147],"nonnegative":[149],"occupation-pattern":[150],"probabilities,":[151],"suffice":[152],"establish":[154],"fermionic":[155],"positivity.":[156],"counting":[159],"model":[160],"two":[162],"relaxations":[163],"have":[164],"same":[166,173],"zero":[168],"set,":[169],"not":[170,208],"necessarily":[171],"feasible":[174],"states,":[175],"converse":[178],"argument":[179],"shows":[180],"no":[182],"other":[183],"false":[184,204],"eigenvalues":[185],"occur.":[186],"limitation":[188],"specific":[190],"hierarchy:":[193],"two-body":[194],"inequalities":[195],"encode":[197],"integer":[199],"would":[201],"remove":[202],"but":[206],"generated":[209],"level.":[213],"also":[215],"verify":[216],"their":[223],"projection":[225],"onto":[226],"space":[229],"equivalent":[231],"finite":[233],"dimensions,":[234],"so":[235],"result":[238],"applies":[239],"equally":[240],"polar":[243],"formulation.":[244]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-10-09T00:00:00"}