{"id":"https://openalex.org/W7225577686","doi":"https://doi.org/10.5281/zenodo.24053909","title":"Certified Finite Robust Reconstruction of Fibonacci-Modulo-9 Translation Classes: Exact Channel Minima in Two Prescribed 24-Channel Observation Families","display_name":"Certified Finite Robust Reconstruction of Fibonacci-Modulo-9 Translation Classes: Exact Channel Minima in Two Prescribed 24-Channel Observation Families","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225577686","doi":"https://doi.org/10.5281/zenodo.24053909"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24053909","doi":"https://doi.org/10.5281/zenodo.24053909","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24053909","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.24053909","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158272999","display_name":"Ivo Vajc","orcid":"https://orcid.org/0009-0005-5145-6491","observed_orcids":["https://orcid.org/0009-0005-5145-6491"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Vajc, Ivo","raw_affiliation_strings":["ORCID"],"raw_orcid":"https://orcid.org/0009-0005-5145-6491","affiliations":[{"raw_affiliation_string":"ORCID","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5158272999"],"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/T11130","display_name":"Coding theory and cryptography","score":0.7724999785423279,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11130","display_name":"Coding theory and cryptography","score":0.7724999785423279,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.07500000298023224,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.02539999969303608,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pisano-period","display_name":"Pisano period","score":0.9829999804496765},{"id":"https://openalex.org/keywords/robust-reconstruction","display_name":"robust reconstruction","score":0.656000018119812},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.8999999761581421},{"id":"https://openalex.org/keywords/minimum-hamming-distance","display_name":"minimum Hamming distance","score":0.6919999718666077},{"id":"https://openalex.org/keywords/channel-selection","display_name":"channel selection","score":0.6650000214576721},{"id":"https://openalex.org/keywords/error-correction","display_name":"error correction","score":0.46000000834465027},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.3479999899864197},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"computer-assisted proof","score":0.3240000009536743},{"id":"https://openalex.org/keywords/reproducibility","display_name":"reproducibility","score":0.37299999594688416}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7127000093460083},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.47279998660087585},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.451200008392334},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.4472000002861023},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40959998965263367},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.3817000091075897},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.37779998779296875},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.35249999165534973},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.33709999918937683},{"id":"https://openalex.org/C15001198","wikidata":"https://www.wikidata.org/wiki/Q3241394","display_name":"Toroid","level":3,"score":0.3361999988555908},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.33559998869895935},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.32179999351501465},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.30869999527931213},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.30550000071525574},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30169999599456787},{"id":"https://openalex.org/C7720571","wikidata":"https://www.wikidata.org/wiki/Q1136880","display_name":"Power of two","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.2858000099658966},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.2727999985218048},{"id":"https://openalex.org/C149364088","wikidata":"https://www.wikidata.org/wiki/Q185917","display_name":"Translation (biology)","level":4,"score":0.2628999948501587},{"id":"https://openalex.org/C68010082","wikidata":"https://www.wikidata.org/wiki/Q192445","display_name":"Delaunay triangulation","level":2,"score":0.25690001249313354}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24053909","doi":"https://doi.org/10.5281/zenodo.24053909","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24053909","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.24053910","doi":"https://doi.org/10.5281/zenodo.24053910","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24053910","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.24053909","doi":"https://doi.org/10.5281/zenodo.24053909","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24053909","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":["https://openalex.org/W7225245239","https://openalex.org/W7222634368","https://openalex.org/W2525323044","https://openalex.org/W2750201272","https://openalex.org/W2871595077","https://openalex.org/W2040364500","https://openalex.org/W2564662827","https://openalex.org/W2145592457","https://openalex.org/W2491479787","https://openalex.org/W45483875"],"abstract_inverted_index":{"Certified":[0],"Finite":[1],"Robust":[2],"Reconstruction":[3],"of":[4,23,26,75,112,147,152,158,178,229,248,290,299,305,381,387,443],"Fibonacci-Modulo-9":[5],"Translation":[6],"Classes:":[7],"Exact":[8],"Channel":[9],"Minima":[10],"in":[11,42,395],"Two":[12,54],"Prescribed":[13],"24-Channel":[14],"Observation":[15],"Families":[16],"We":[17],"investigate":[18],"exact":[19,109,175,207],"and":[20,45,65,94,124,135,156,182,202,235,303,331,367,408,429,455],"robust":[21,263],"reconstruction":[22],"translation-equivalence":[24],"classes":[25],"a":[27,328],"three-dimensional":[28],"periodic":[29],"Fibonacci-residue":[30],"product":[31],"field":[32,37],"modulo":[33,257],"nine.":[34],"The":[35,86,162,187,204,232,310,334,347,358,411,436],"underlying":[36,233],"has":[38],"spatial":[39,68],"period":[40],"24":[41,76],"each":[43],"coordinate,":[44],"its":[46],"translation":[47],"action":[48],"yields":[49],"3,456":[50],"distinct":[51],"equivalence":[52],"classes.":[53],"explicitly":[55,250,362,430],"prescribed":[56],"observation":[57,77,104,213,223,253,365],"families":[58],"are":[59,96,165,206],"studied:":[60],"toroidal":[61,230],"meridian":[62],"sampling":[63,70,197,326],"curves":[64],"independently":[66],"constructed":[67],"wave-loop":[69],"curves.":[71],"Each":[72],"family":[73],"consists":[74],"channels,":[78],"with":[79,286],"12":[80],"sampled":[81],"lattice":[82],"sites":[83],"per":[84],"channel.":[85],"resulting":[87],"observations":[88],"define":[89],"finite":[90,212,246,261,322,364],"codes":[91],"whose":[92],"distinguishability":[93],"robustness":[95],"characterized":[97],"by":[98,167],"minimum":[99,110,118],"Hamming":[100,119,265],"distance.":[101],"For":[102],"both":[103],"families,":[105],"we":[106],"establish":[107,218],"the":[108,209,241,244,249,287,291,300,306,313,355,417,421,425,432,441,444,447,456],"numbers":[111],"retained":[113],"channels":[114],"required":[115],"to":[116,143,458],"achieve":[117],"distances":[120],"1,":[121],"2,":[122],"3,":[123],"5:":[125],"m(1)":[126],"=":[127,130,133,137],"6,":[128],"m(2)":[129],"7,":[131],"m(3)":[132],"9,":[134],"m(5)":[136],"13.":[138],"These":[139],"thresholds":[140],"correspond":[141],"respectively":[142],"error-free":[144],"identification,":[145],"tolerance":[146],"one":[148,153],"known":[149],"erasure,":[150],"correction":[151,157],"arbitrary":[154,160,222],"substitution,":[155],"two":[159,210],"substitutions.":[161],"optimality":[163,220],"results":[164,205,360],"supported":[166],"explicit":[168,288],"channel":[169,180,274],"constructions,":[170],"exhaustive":[171],"pairwise":[172],"separation":[173],"analysis,":[174],"combinatorial":[176],"exclusion":[177],"smaller":[179],"subsets,":[181],"an":[183,320],"independent":[184,321,465],"verification":[185,323],"implementation.":[186],"accompanying":[188,307,348,422],"reproducibility":[189,332],"package":[190],"includes":[191,312],"Python":[192,318,349,400],"source":[193,350,449],"code,":[194],"fixed":[195,325],"integer":[196],"offsets,":[198],"computational":[199,271,308,402],"audit":[200],"materials,":[201,428],"documentation.":[203,333],"within":[208],"specified":[211],"families.":[214],"They":[215],"do":[216],"not":[217,369,463],"global":[219],"over":[221],"geometries,":[224],"physical":[225,376],"realizability,":[226],"or":[227,378,469],"superiority":[228],"sampling.":[231],"coding-theoretic":[234],"multicover":[236],"methods":[237],"have":[238,368],"established":[239],"precedents;":[240],"contribution":[242],"is":[243,284,336,352,384],"certified":[245],"analysis":[247],"defined":[251],"Fibonacci-modulo-nine":[252],"systems.":[254],"Keywords:":[255],"Fibonacci":[256],"9;":[258],"Pisano":[259],"period;":[260],"reconstruction;":[262],"identification;":[264],"distance;":[266],"test":[267],"cover;":[268],"set":[269],"multicover;":[270],"proof;":[272],"optimal":[273],"selection.":[275],"Author-approved":[276],"release":[277,311,427],"\u2014":[278],"8":[279],"November":[280],"2026.":[281],"This":[282],"preprint":[283],"released":[285,448],"approval":[289],"named":[292,412],"author,":[293,413],"Ivo":[294,414],"Vajc,":[295,415],"following":[296],"author":[297,437],"review":[298,406,468],"mathematical":[301,359,382,396,418,445],"manuscript":[302,335,409,433],"execution":[304],"programs.":[309],"final":[314,426],"manuscript,":[315],"LaTeX":[316],"source,":[317],"implementations,":[319],"procedure,":[324],"coordinates,":[327],"literature":[329,405],"audit,":[330],"licensed":[337,353],"under":[338,354],"Creative":[339],"Commons":[340],"Attribution":[341],"4.0":[342],"International":[343],"(CC":[344],"BY":[345],"4.0).":[346],"code":[351],"MIT":[356],"License.":[357],"concern":[361],"stipulated":[363],"models":[366],"undergone":[370],"external":[371],"peer":[372,467],"review.":[373],"No":[374],"empirical":[375],"validation":[377],"unrestricted":[379],"claim":[380],"novelty":[383],"asserted.":[385],"Declaration":[386],"AI":[388,460],"Assistance":[389],"OpenAI":[390],"ChatGPT":[391],"was":[392],"used":[393],"substantially":[394],"exploration,":[397],"algorithm":[398],"development,":[399],"programming,":[401],"certificate":[403],"design,":[404],"assistance,":[407],"drafting.":[410],"reviewed":[416],"content,":[419],"tested":[420],"programs,":[423],"examined":[424],"approved":[431],"for":[434,440],"publication.":[435],"retains":[438],"responsibility":[439],"accuracy":[442],"statements,":[446],"files,":[450],"bibliographic":[451],"references,":[452],"originality":[453],"claims,":[454],"decision":[457],"publish.":[459],"assistance":[461],"does":[462],"constitute":[464],"human":[466],"experimental":[470],"validation.":[471]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}