{"id":"https://openalex.org/W7225735754","doi":"https://doi.org/10.5281/zenodo.24106004","title":"Persistent Particle Identity from Finite Spectral Response: Self-Certification, Robust Reconstruction, and a Pythagorean Regulator Budget","display_name":"Persistent Particle Identity from Finite Spectral Response: Self-Certification, Robust Reconstruction, and a Pythagorean Regulator Budget","publication_year":2026,"publication_date":"2026-11-10","ids":{"openalex":"https://openalex.org/W7225735754","doi":"https://doi.org/10.5281/zenodo.24106004"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24106004","doi":"https://doi.org/10.5281/zenodo.24106004","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24106004","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.24106004","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135392284","display_name":"Pawe\u0142 Nowak","orcid":"https://orcid.org/0009-0000-5562-1128","observed_orcids":["https://orcid.org/0009-0000-5562-1128"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nowak, Pawe\u0142","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-5562-1128","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029622427","display_name":"Maciej Stachowiak","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stachowiak, Maciej","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0003-1747-3656","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.5249000191688538,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.5249000191688538,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.2734000086784363,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.0568000003695488,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7534999847412109},{"id":"https://openalex.org/C133226019","wikidata":"https://www.wikidata.org/wiki/Q209812","display_name":"Linear span","level":2,"score":0.42089998722076416},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.40450000762939453},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3962000012397766},{"id":"https://openalex.org/C30072841","wikidata":"https://www.wikidata.org/wiki/Q1767080","display_name":"Diagonalizable matrix","level":4,"score":0.3961000144481659},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.38420000672340393},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.3659999966621399},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34209999442100525},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.3393000066280365},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3203999996185303},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3075000047683716},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2727000117301941},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.272599995136261},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.26750001311302185},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.26159998774528503},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.25769999623298645},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24106004","doi":"https://doi.org/10.5281/zenodo.24106004","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24106004","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.24106005","doi":"https://doi.org/10.5281/zenodo.24106005","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24106005","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.24106004","doi":"https://doi.org/10.5281/zenodo.24106004","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24106004","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":{"The":[0,61,91,128,155,189,282],"full":[1,92,265,379],"spectral":[2],"response":[3],"describes":[4],"a":[5,24,47,58,68,73,77,88,96,100,108,132,139,159,170,194,198,252,269,276,318,362,394],"particle":[6],"through":[7,166],"sources,":[8],"dynamics,":[9],"and":[10,42,76,122,150,161,197,206,236,244,255,275,291,317,334,358],"phase-sensitive":[11,246],"feature":[12],"correlations.":[13],"We":[14,208,306],"prove":[15],"that":[16],"on":[17,87,99],"an":[18,341,347],"atom":[19],"of":[20,26,84,107,114,135,174,181,223,272,279,293,302,320,330,335,377,384,397],"dimension":[21],"d,":[22],"for":[23,213,373],"bank":[25,102],"rank":[27,62,211],"r_src,":[28],"the":[29,43,52,65,85,105,115,118,120,123,126,136,143,147,151,175,178,182,186,221,242,245,264,273,280,309,314,328,332,337,354,370,374,378,385,388,398],"finite":[30],"word":[31],"Gram":[32,79,167,266,296],"matrix":[33,267],"up":[34,56],"to":[35,57,353],"depth":[36],"d":[37],"\u2212":[38],"r_src":[39],"+":[40],"1":[41],"resolvent":[44,70,93],"block":[45,200],"at":[46,95],"single":[48,59,74,97],"nonreal":[49],"point":[50,98],"determine":[51],"entire":[53,152],"visible":[54],"package":[55],"unitary.":[60],"plateau":[63],"determines":[64],"required":[66],"depth,":[67],"bounded":[69],"defect":[71,130],"recognizes":[72],"energy,":[75],"positive":[78,148,199,234],"margin":[80],"gives":[81,131,158],"linear":[82],"robustness":[83],"reconstruction":[86,222],"constant-rank":[89],"stratum.":[90],"moment":[94],"spanning":[101],"also":[103,192],"recovers":[104],"generator":[106],"split":[109,195],"multiplet.":[110],"A":[111,366],"Pythagorean":[112,277],"decomposition":[113],"leakage":[116,157],"carries":[117,193],"carrier,":[119],"source,":[121],"features":[124],"along":[125],"regulator.":[127],"centered":[129],"quadratic":[133],"cost":[134,141],"energy":[137],"change;":[138],"summable":[140],"preserves":[142],"invertible":[144],"source":[145,243],"profile,":[146],"margin,":[149,316],"complex":[153],"signature.":[154],"actual":[156,176],"necessary":[160],"sufficient":[162],"non-collapse":[163,179],"criterion,":[164],"readable":[165],"determinants.":[168],"For":[169],"two-sided":[171],"power":[172],"law":[173,191],"leakage,":[177],"threshold":[180],"profile":[183],"is":[184,285,369],"exactly":[185,308],"exponent":[187],"1/2.":[188],"operator":[190],"island,":[196],"construction":[201],"produces":[202,391],"its":[203],"isolation,":[204],"centering,":[205],"budget.":[207],"derive":[209],"checkable":[210],"conditions":[212],"data":[214],"with":[215,268,323,382],"controlled":[216],"error,":[217],"as":[218,220],"well":[219],"exact":[224,342,371],"PVMs.":[225],"An":[226],"explicit":[227],"q\u00b3D":[228,389],"realization":[229],"arises":[230],"from":[231,393],"local":[232,295],"excitations,":[233],"exchange,":[235],"co-occupation":[237],"energy.":[238],"Local":[239],"pulses":[240],"prepare":[241],"features.":[247],"Eight":[248],"Walsh":[249],"modes":[250],"give":[251],"common":[253],"anchor":[254],"seven":[256,259,284],"Fano":[257],"directions;":[258],"anchored":[260],"three-block":[261,289],"windows":[262],"reconstruct":[263],"sharp":[270],"contraction":[271],"error":[274],"balance":[278],"inconsistency.":[281],"number":[283],"minimal":[286],"in":[287],"this":[288],"architecture,":[290],"positivity":[292,301],"all":[294],"matrices":[297],"does":[298],"not":[299],"replace":[300],"their":[303],"global":[304],"gluing.":[305],"compute":[307],"ranks":[310],"1,":[311],"8,":[312,313],"unit":[315],"family":[319,350],"nonzero":[321],"regulators":[322],"tail":[324,333,368],"O(4\u207b\u207f).":[325],"Counterexamples":[326],"show":[327],"necessity":[329],"controlling":[331],"preserving":[336],"cycle":[338],"phases.":[339],"Moreover,":[340],"Schur":[343],"condition":[344,372],"decides":[345],"when":[346,359],"external":[348],"amplitude":[349],"actually":[351],"belongs":[352],"same":[355],"reconstructed":[356],"carrier":[357],"it":[360,392],"contributes":[361],"new":[363],"orthogonal":[364],"sector.":[365],"uniform":[367],"norm":[375],"limit":[376],"first-exit":[380],"record":[381],"preservation":[383],"persistent":[386],"leg;":[387],"model":[390],"constant":[395],"splitting":[396],"generator.":[399]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-11T00:00:00"}