{"id":"https://openalex.org/W7225345002","doi":"https://doi.org/10.5281/zenodo.23983513","title":"Finite Certificates and Undecidable Gibbs Uniqueness","display_name":"Finite Certificates and Undecidable Gibbs Uniqueness","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225345002","doi":"https://doi.org/10.5281/zenodo.23983513"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23983513","doi":"https://doi.org/10.5281/zenodo.23983513","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23983513","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.23983513","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158765677","display_name":"Harjas Sandhu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I165143802","display_name":"The University of Queensland","ror":"https://ror.org/00rqy9422","country_code":"AU","type":"education","lineage":["https://openalex.org/I165143802"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Sandhu, Harjas","raw_affiliation_strings":["The University of Queensland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Queensland","institution_ids":["https://openalex.org/I165143802"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5158765677"],"corresponding_institution_ids":["https://openalex.org/I165143802"],"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.6478999853134155,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.6478999853134155,"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.09529999643564224,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.061000000685453415,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/undecidability","display_name":"undecidability","score":0.828000009059906},{"id":"https://openalex.org/keywords/lattice-spin-models","display_name":"lattice spin models","score":0.5920000076293945},{"id":"https://openalex.org/keywords/gibbs-measures","display_name":"Gibbs measures","score":0.5509999990463257},{"id":"https://openalex.org/keywords/ising-model","display_name":"Ising model","score":0.7129999995231628},{"id":"https://openalex.org/keywords/phase-coexistence","display_name":"phase coexistence","score":0.5649999976158142},{"id":"https://openalex.org/keywords/computability","display_name":"computability","score":0.4699999988079071},{"id":"https://openalex.org/keywords/exponential-clustering","display_name":"exponential clustering","score":0.34599998593330383},{"id":"https://openalex.org/keywords/finite-range-interactions","display_name":"finite-range interactions","score":0.5669999718666077},{"id":"https://openalex.org/keywords/parallel-tempering","display_name":"parallel tempering","score":0.41999998688697815}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7634999752044678},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.5307999849319458},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.44999998807907104},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44119998812675476},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4399000108242035},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.421099990606308},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4133000075817108},{"id":"https://openalex.org/C158444337","wikidata":"https://www.wikidata.org/wiki/Q2510435","display_name":"Gibbs measure","level":2,"score":0.40139999985694885},{"id":"https://openalex.org/C2780872131","wikidata":"https://www.wikidata.org/wiki/Q5558987","display_name":"Gibbs state","level":3,"score":0.3747999966144562},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.35760000348091125},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.33230000734329224},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.32089999318122864},{"id":"https://openalex.org/C98925819","wikidata":"https://www.wikidata.org/wiki/Q7235385","display_name":"Potts model","level":3,"score":0.30660000443458557},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.2930000126361847},{"id":"https://openalex.org/C70943382","wikidata":"https://www.wikidata.org/wiki/Q505356","display_name":"Antipodal point","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.2635999917984009},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.257099986076355}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23983513","doi":"https://doi.org/10.5281/zenodo.23983513","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23983513","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.23983514","doi":"https://doi.org/10.5281/zenodo.23983514","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23983514","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.23983513","doi":"https://doi.org/10.5281/zenodo.23983513","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23983513","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/W2015088144","https://openalex.org/W1977872443","https://openalex.org/W7225177239","https://openalex.org/W2003625596","https://openalex.org/W1993344701","https://openalex.org/W1973881670","https://openalex.org/W2144870401","https://openalex.org/W1547812559","https://openalex.org/W2923592962","https://openalex.org/W2000115706"],"abstract_inverted_index":{"This":[0],"preprint":[1],"studies":[2],"whether":[3],"an":[4,23,168],"algorithm":[5],"can":[6],"decide":[7],"uniqueness":[8,41,263,284,347],"of":[9,34,101,190],"equilibrium":[10],"for":[11,297],"a":[12,17,35,90,94,142,152,270,286,293,340,346],"classical":[13],"lattice":[14,29],"model":[15],"at":[16,207,212,239],"fixed":[18,58],"positive":[19,144,153,294],"temperature.":[20],"It":[21],"presents":[22],"effective":[24,336],"construction":[25,186],"on":[26,80,269],"the":[27,32,67,81,109,117,160,204,234,251,259,262],"square":[28],"in":[30],"which":[31],"halting":[33,91,249],"Turing":[36],"machine":[37,82,229],"is":[38,51,113,225,254,266,305],"equivalent":[39],"to":[40,116,163],"among":[42],"all":[43,228],"physical":[44,105,165,303],"Gibbs":[45,96,111,166],"states.":[46,127],"Main":[47],"construction.":[48],"The":[49,75,182,215,302,309],"interaction":[50],"translation":[52],"invariant":[53],"and":[54,61,73,83,175,194,224,233,250],"finite":[55,76,176,209],"range,":[56],"with":[57,98,123,274],"support":[59],"shapes":[60],"local":[62,104],"energy":[63],"terms":[64],"taking":[65],"only":[66],"exact":[68],"integer":[69],"values":[70,232],"0,":[71],"1":[72],"20.":[74],"on-site":[77],"alphabet":[78,304],"depends":[79],"its":[84,188],"input.":[85],"At":[86],"inverse":[87,210],"temperature":[88,211],"one,":[89],"computation":[92,130],"gives":[93,339],"unique":[95],"state":[97],"exponential":[99,222],"clustering":[100],"every":[102,208],"bounded":[103],"observable.":[106],"Without":[107],"halting,":[108],"full":[110],"simplex":[112],"affinely":[114],"isomorphic":[115],"low-temperature,":[118],"zero-field":[119,246],"two-dimensional":[120],"Ising":[121,169],"simplex,":[122],"exactly":[124,140],"two":[125],"extremal":[126],"Mechanism.":[128],"Finite":[129],"histories":[131],"act":[132],"as":[133],"certificates.":[134],"Character":[135],"orthogonality":[136],"cancels":[137],"invalid":[138],"selections":[139],"inside":[141],"strictly":[143],"finite-energy":[145],"model.":[146],"A":[147,199,334],"surviving":[148],"accepting":[149],"certificate":[150,161],"produces":[151],"phase-selection":[154],"bias.":[155],"Conditional":[156],"auxiliary":[157],"mixing":[158,324],"connects":[159],"representation":[162],"arbitrary":[164,298],"states;":[167],"comparison,":[170],"four":[171],"independent":[172],"upper":[173],"coverings":[174],"replica":[177],"exchange":[178],"then":[179],"establish":[180],"uniqueness.":[181],"manuscript":[183],"distinguishes":[184],"this":[185],"from":[187],"applications":[189],"established":[191],"Ising,":[192],"comparison":[193],"disagreement":[195],"methods.":[196],"Further":[197],"results.":[198],"distinct":[200],"soft-certificate":[201],"table":[202],"has":[203,219],"same":[205],"dichotomy":[206],"least":[213],"2/5.":[214],"selected":[216],"plus":[217],"phase":[218],"uniform":[220],"boundary-specific":[221],"convergence":[223,310],"computable":[226,257,341],"across":[227,258],"inputs.":[230],"Pressure":[231],"complete":[235],"right":[236],"smooth":[237],"jet":[238],"zero":[240],"field":[241,272],"are":[242],"uniformly":[243,256],"computable,":[244],"while":[245],"differentiability":[247],"encodes":[248],"left":[252],"derivative":[253],"not":[255,307,319,331],"family.":[260],"On":[261],"branch,":[264],"pressure":[265],"infinitely":[267],"differentiable":[268],"witness-dependent":[271,287],"interval,":[273],"absolutely":[275],"summable":[276],"cumulant":[277],"formulas.":[278],"Small":[279],"finite-range":[280],"spin-only":[281],"perturbations":[282],"preserve":[283],"within":[285],"neighbourhood.":[288],"Exact":[289],"microscopic":[290],"symmetrization":[291],"excludes":[292],"family-wide":[295],"radius":[296],"real":[299],"perturbations.":[300],"Scope.":[301],"variable,":[306],"fixed.":[308],"results":[311],"retain":[312],"their":[313],"stated":[314],"boundary":[315],"conventions;":[316],"they":[317],"do":[318],"assert":[320,332],"arbitrary-boundary":[321],"strong":[322],"spatial":[323],"or":[325],"rapid":[326],"Glauber":[327],"dynamics.":[328],"Smoothness":[329],"does":[330],"analyticity.":[333],"separate":[335],"compactness":[337],"argument":[338],"valid":[342],"all-boundary":[343],"modulus":[344],"under":[345],"promise.":[348]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-11-06T00:00:00"}