{
 "title": "Logged claimed proofs of P vs NP, with where they broke",
 "license_note": "License: CC BY 4.0 covers only our additions (the one-line break-step summaries, labels and arrangement). The claims themselves belong to their authors. The list of claims comes mostly from Woeginger's page, which has no license line, so none of his text is copied.",
 "count": 126,
 "rows": [
  {
   "id": "W001",
   "author": "Ted Swart",
   "year": "1986",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Yannakakis (STOC 1988; JCSS 1991) proved any symmetric LP for TSP/Hamiltonian cycle (as in Swart) needs exponential size, so the polynomial-size LP step fails.",
   "barrier": "extended-formulation lower bound",
   "break_source_url": "http://dx.doi.org/10.1016/0022-0000(91)90024-Y",
   "claim_url": "http://dx.doi.org/10.1016/0022-0000(91)90024-Y",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W002",
   "author": "Anatoly Plotnikov",
   "year": "1996",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.emis.de/journals/SWJPAM/vol1-96.html",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W003",
   "author": "Tang Pushan",
   "year": "1997",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Zhu Daming, Luan Junfeng, M.A. Shaohan refute the clique algorithm in \"Hardness and methods to solve CLIQUE\" (JCST 16, 2001). Woeginger does not state the exact step.",
   "barrier": "",
   "break_source_url": "http://portal.acm.org/citation.cfm?id=501491",
   "claim_url": "http://portal.acm.org/citation.cfm?id=501491&dl=",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W004",
   "author": "Miron Telpiz",
   "year": "2000",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.tarusa.ru/~mit/ENG/eng.html",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W005",
   "author": "Seenil Gram",
   "year": "2001",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0302-9743&volume=2229",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W006",
   "author": "Charles Sauerbier",
   "year": "2002",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/cs.CC/0205064",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W007",
   "author": "Givi Bolotashvili",
   "year": "2003",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/cs.CC/0303008",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W008",
   "author": "Nicholas Argall",
   "year": "2003",
   "claim": "undecidable",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W009",
   "author": "N.C.A. da Costa; F.A. Doria",
   "year": "2003",
   "claim": "unprovable",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Andreas Blass (MR2009291) says the consistency proof (Corollary 4.6) contains an error; Ralf Schindler also reviewed it.",
   "barrier": "",
   "break_source_url": "http://wwwmath.uni-muenster.de/math/inst/logik/org/staff/rds/review.ps",
   "claim_url": "http://www.elsevier.com/locate/amc",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W010",
   "author": "Hubert Chen; Craig Alan Feinstein",
   "year": "2003",
   "claim": "P ≠ NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Chen's piece is a joke argument; Feinstein's earlier \"P is not equal to NP\" paper was withdrawn after a counterexample was found (per Woeginger). Exact step not stated.",
   "barrier": "",
   "break_source_url": "http://arxiv.org/abs/cs/0305035",
   "claim_url": "http://www.tecn.upf.es/~hchen/",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W011",
   "author": "Ki-Bong Nam; S.H. Wang; Yang Gon Kim",
   "year": "2004",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W012",
   "author": "Mikhail N. Kupchik",
   "year": "2004",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://users.i.com.ua/~zkup/pvsnp_en.pdf",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W013",
   "author": "Selmer Bringsjord; Joshua Taylor",
   "year": "2004",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/cs/0406056",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W014",
   "author": "Bhupinder Singh Anand",
   "year": "2004",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1510.04225",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W015",
   "author": "Marius Ionescu",
   "year": "2004",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/cs/0409039",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W016",
   "author": "Moustapha Diaby",
   "year": "2004",
   "claim": "P = NP",
   "label": "GUESS",
   "traced": "no",
   "where_it_broke": "Reason: polynomial-size LP for TSP/SAT; Fiorini et al. 2012 proved TSP polytope needs exponential-size extended formulations, so the LP step likely fails (not checked against this paper).",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/1111.0837",
   "claim_url": "http://www.business.uconn.edu/users/mdiaby/tsplp/",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W017",
   "author": "Mircea Alexandru Popescu Moscu",
   "year": "2004",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/cs.CC/0411033",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W018",
   "author": "Andrea Bianchini",
   "year": "2005",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://es-andreabianchini.it/ssp_eng.pdf",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W019",
   "author": "Raju Renjit Grover",
   "year": "2005",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/cs/0502030v1",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W020",
   "author": "Viktor V. Ivanov",
   "year": "2005",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.math.usf.edu/~eclark/NPvsP.pdf",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W021",
   "author": "Bhupinder Singh Anand",
   "year": "2005",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://xxx.lanl.gov/pdf/math.GM/0506126",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W022",
   "author": "Craig Alan Feinstein",
   "year": "2005",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/cs.CC/0507008",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W023",
   "author": "Lev Gordeev",
   "year": "2005",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.wsi.uni-tuebingen.de/lehrstuehle/logik-und-sprachtheorie/personen/ehemalige-und-sonstige-mitarbeiter/pd-dr-lev-gordeev/publications.html",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W024",
   "author": "Lokman Kolukisa",
   "year": "2005",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://geocities.com/lkoluk2003/",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W025",
   "author": "Francesco Capasso",
   "year": "2005",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/cs.CC/0511071",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W026",
   "author": "Ron Cohen",
   "year": "2005",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.arxiv.org/abs/cs.CC/0511085",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W027",
   "author": "Miron Teplitz",
   "year": "2005",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.tarusa.ru/~mit/ENG/sigma01_e.php",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W028",
   "author": "Joachim Mertz",
   "year": "2005",
   "claim": "P = NP",
   "label": "GUESS",
   "traced": "no",
   "where_it_broke": "Reason: polynomial-size LP for TSP/SAT; Fiorini et al. 2012 proved TSP polytope needs exponential-size extended formulations, so the LP step likely fails (not checked against this paper).",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/1111.0837",
   "claim_url": "http://www.merlins-world.de/",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W029",
   "author": "Bhupinder Singh Anand",
   "year": "2006",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/math.GM/0603605",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W030",
   "author": "Craig Alan Feinstein",
   "year": "2006",
   "claim": "P ≠ NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Critique by Sabo, Schmitt, Silverman (June 2007) answers this proof; step not quoted here.",
   "barrier": "",
   "break_source_url": "http://arxiv.org/abs/0706.2035",
   "claim_url": "http://arxiv.org/abs/cs.CC/0607093",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W031",
   "author": "Mohamed Mimouni",
   "year": "2006",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.wbabin.net/science/mimouni.pdf",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W032",
   "author": "Sergey Gubin",
   "year": "2006",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Full refutation by Christopher, Huo, Jacobs (April 2008); Hofman also commented.",
   "barrier": "",
   "break_source_url": "http://arxiv.org/abs/0804.2699",
   "claim_url": "http://arxiv.org/abs/cs.DM/0610042",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W033",
   "author": "Radoslaw Hofman",
   "year": "2006",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0704.0514",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W034",
   "author": "Rubens Ramos Viana",
   "year": "2006",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/quant-ph/0612001",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W035",
   "author": "Howard Kleiman",
   "year": "2006",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/math.CO/0612114",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W036",
   "author": "Khadija Riaz and Malik Sikander Hayat Khiyal",
   "year": "2006",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.scialert.net/pdfs/itj/2006/851-859.pdf",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W037",
   "author": "Anatoly D. Plotnikov",
   "year": "2007",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0706.3565",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W038",
   "author": "Guohun Zhu",
   "year": "2007",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0704.0309v3",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W039",
   "author": "Matthew Delacorte",
   "year": "2007",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0708.4075",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "A-012",
   "author": "Jaeger",
   "year": "2008",
   "claim": "other",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Non-standard model of computation, unsupported assumptions, missing proofs.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/0904.3927",
   "claim_url": "https://arxiv.org/abs/0904.3927",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/0904.3927"
  },
  {
   "id": "W040",
   "author": "Cynthia Ann Harlan Krieger",
   "year": "2008",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.freepatentsonline.com/y2008/0071849.html",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W041",
   "author": "Jerrald Meek",
   "year": "2008",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0804.1079",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W042",
   "author": "Bhupinder Singh Anand",
   "year": "2008",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://alixcomsi.com/18_A_trivial_solution_to_PvNP.pdf",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W043",
   "author": "Rafee Ebrahim Kamouna",
   "year": "2008",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0806.2947",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W044",
   "author": "Jerrald Meek",
   "year": "2008",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0808.3222",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W045",
   "author": "Jorma Jormakka",
   "year": "2008",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0809.4935",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W046",
   "author": "Sten-Ake Tarnlund",
   "year": "2008",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0810.5056",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W047",
   "author": "Zohreh O. Akbari",
   "year": "2008",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.waset.org/pwaset/v35/v35-74.pdf",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W048",
   "author": "Javaid Aslam",
   "year": "2008",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Ferraro, Hall, Wood \"Refutation of Aslam's Proof that NP = P\" points out a flaw; Aslam replied.",
   "barrier": "",
   "break_source_url": "http://arxiv.org/abs/0812.1385",
   "claim_url": "http://arxiv.org/abs/0812.1385",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W049",
   "author": "Rafael Valls Hidalgo-Gato",
   "year": "2009",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W050",
   "author": "Doron Zeilberger (1 April 2009, joke date)",
   "year": "2009",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Definitions are ambiguous; every way to make them exact breaks the main proof.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/1711.07132",
   "claim_url": "http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/pnp.pdf",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W051",
   "author": "Xinwen Jiang",
   "year": "2009",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://xinwenjiang.googlepages.com/",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W052",
   "author": "Arto Annila",
   "year": "2009",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0906.1084",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W053",
   "author": "Andre Luiz Barbosa",
   "year": "2009",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0907.3965",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W054",
   "author": "Yann Dujardin",
   "year": "2009",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0909.3466",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W055",
   "author": "Luigi Salemi",
   "year": "2009",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/0909.3868",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W056",
   "author": "Ari Blinder",
   "year": "2009",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://sites.google.com/site/ariblindercswork/",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W057",
   "author": "Narendra S. Chaudhari",
   "year": "2009",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://dcis.uohyd.ernet.in/~wankarcs/index_files/pdf/Vol-31-No-2-2009-pp407-444-scanned-copy.pdf",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W058",
   "author": "Lizhi Du",
   "year": "2010",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1004.3702",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W059",
   "author": "Changlin Wan",
   "year": "2010",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1005.3010",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W060",
   "author": "Carlos Barron-Romero",
   "year": "2010",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1006.2218",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W061",
   "author": "Han Xiao Wen",
   "year": "2010",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1006.2495",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W062",
   "author": "Mikhail Katkov",
   "year": "2010",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1007.4257v2",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W063",
   "author": "Vinay Deolalikar",
   "year": "2010",
   "claim": "P ≠ NP",
   "label": "GUESS",
   "traced": "no",
   "where_it_broke": "Reason: widely reported issues in the FO(LFP)/solution-space step, discussed on Lipton's blog; not verified this run.",
   "barrier": "",
   "break_source_url": "http://rjlipton.wordpress.com/",
   "claim_url": "http://rjlipton.wordpress.com/",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W064",
   "author": "Sergey Gubin",
   "year": "2010",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Refutation by Romeo Rizzi (January 2011) per Woeginger; no link given on the page.",
   "barrier": "",
   "break_source_url": "https://www.win.tue.nl/~gwoegi/P-versus-NP.htm",
   "claim_url": "",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W065",
   "author": "Vladimir Romanov",
   "year": "2010",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1011.3944",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W066",
   "author": "Frank Vega Delgado",
   "year": "2010",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1011.2730",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W067",
   "author": "Carlos Barron-Romero",
   "year": "2010",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1101.0160",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W068",
   "author": "Bangyan Wen and Yi Lin",
   "year": "2010",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.iigss.net/Scientific-Inquiry/Dec2010/table.htm",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W069",
   "author": "Ruijia Liao",
   "year": "2011",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1101.2018",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W070",
   "author": "Amar Mukherjee",
   "year": "2011",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1104.4490",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W071",
   "author": "Angela Weiss",
   "year": "2011",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.ime.usp.br/~weiss/",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W072",
   "author": "Matt Groff",
   "year": "2011",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1106.0683",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W073",
   "author": "Sergey Kardash",
   "year": "2011",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1108.0408",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W074",
   "author": "Anatoly Plotnikov",
   "year": "2011",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1109.5531",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W075",
   "author": "Koji Kobayashi",
   "year": "2011",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1110.0200",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W076",
   "author": "Jason W. Steinmetz",
   "year": "2011",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1110.1658",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W077",
   "author": "Jose Ignacio Alvarez-Hamelin",
   "year": "2011",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1110.5355",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W078",
   "author": "Roman Yampolskiy",
   "year": "2011",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1111.0305",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W079",
   "author": "Craig Alan Feinstein",
   "year": "2011",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/cs/0611082",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W080",
   "author": "Jeffrey W. Holcomb",
   "year": "2011",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.holcombtechnologies.com",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W086",
   "author": "Algirdas Antano Maknickas",
   "year": "2011",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1203.6020",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W081",
   "author": "Douglas Youvan",
   "year": "2012",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
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  },
  {
   "id": "W082",
   "author": "Gilberto Rodrigo Diduch",
   "year": "2012",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
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  },
  {
   "id": "W083",
   "author": "Koji Kobayashi",
   "year": "2012",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1202.1194",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W084",
   "author": "Frank Vega Delgado",
   "year": "2012",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://the-point-of-view-of-frank.blogspot.com/",
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   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W085",
   "author": "Minseong Kim",
   "year": "2012",
   "claim": "P ≠ NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "The logic is inconsistent; under two reasonable readings of the definitions, P != NP does not follow.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/1404.5352",
   "claim_url": "http://arxiv.org/abs/1203.0494",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W087",
   "author": "Michel Feldmann",
   "year": "2012",
   "claim": "P = NP",
   "label": "GUESS",
   "traced": "no",
   "where_it_broke": "Reason: polynomial-size LP for TSP/SAT; Fiorini et al. 2012 proved TSP polytope needs exponential-size extended formulations, so the LP step likely fails (not checked against this paper).",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/1111.0837",
   "claim_url": "http://arxiv.org/abs/1205.6658",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W088",
   "author": "Junichiro Fukuyama",
   "year": "2012",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
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   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W089",
   "author": "Satoshi Tazawa",
   "year": "2012",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1207.2171",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W090",
   "author": "Wen-Qi Duan",
   "year": "2012",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1208.0542",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W091",
   "author": "Sergey V. Yakhontov",
   "year": "2012",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1208.0954",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W092",
   "author": "Natalia L. Malinina",
   "year": "2012",
   "claim": "unprovable",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1211.3492",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W093",
   "author": "Louis Coder",
   "year": "2012",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://vixra.org/abs/1212.0109",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W094",
   "author": "Dmitriy Nuriyev",
   "year": "2013",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1301.3093",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W095",
   "author": "Algirdas Antano Maknickas",
   "year": "2013",
   "claim": "P = NP",
   "label": "GUESS",
   "traced": "no",
   "where_it_broke": "Reason: polynomial-size LP for TSP/SAT; Fiorini et al. 2012 proved TSP polytope needs exponential-size extended formulations, so the LP step likely fails (not checked against this paper).",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/1111.0837",
   "claim_url": "http://link.springer.com/chapter/10.1007/978-94-007-7684-5_22",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W096",
   "author": "Rustem Chingizovich Valeyev",
   "year": "2013",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://www.idosi.org/wasj/wasj24%288%292013.htm",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W097",
   "author": "Frederic Gillet",
   "year": "2013",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Author added to arXiv (Nov 2013): the proposed method does not work, paper to be withdrawn.",
   "barrier": "",
   "break_source_url": "http://arxiv.org/abs/1310.1971",
   "claim_url": "http://arxiv.org/abs/1310.1971",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "A-009",
   "author": "Sopin",
   "year": "2014",
   "claim": "PH = PSPACE",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "The paper fails to establish PH = PSPACE (problems listed in critique).",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2301.03487",
   "claim_url": "https://arxiv.org/abs/2301.03487",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/2301.03487"
  },
  {
   "id": "W098",
   "author": "Hanlin Liu",
   "year": "2014",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1401.6423",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W099",
   "author": "Pawan Tamta; B.P. Pande; H.S. Dhami",
   "year": "2014",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Refuted (with LaPlante) in \"A Refutation of the Clique-Based P=NP Proofs of LaPlante and Tamta-Pande-Dhami\".",
   "barrier": "",
   "break_source_url": "http://arxiv.org/abs/1504.06890",
   "claim_url": "http://arxiv.org/abs/1403.1178",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W100",
   "author": "Peng Cui",
   "year": "2014",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1401.6520",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W101",
   "author": "Daegene Song",
   "year": "2014",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1402.6970",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W102",
   "author": "Joonmo Kim",
   "year": "2014",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1403.4143",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W103",
   "author": "Anatoly Panyukov",
   "year": "2014",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1409.0375",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W104",
   "author": "Michael LaPlante",
   "year": "2015",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Refuted (with Tamta-Pande-Dhami) in \"A Refutation of the Clique-Based P=NP Proofs of LaPlante and Tamta-Pande-Dhami\".",
   "barrier": "",
   "break_source_url": "http://arxiv.org/abs/1504.06890",
   "claim_url": "http://arxiv.org/abs/1503.04794",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W105",
   "author": "Alejandro Sanchez Guinea",
   "year": "2015",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "The 3-SAT algorithm is flawed and does not show 3-SAT is in P.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/1711.04412",
   "claim_url": "http://arxiv.org/abs/1504.00337",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W106",
   "author": "Frank Vega",
   "year": "2015",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "https://hal.archives-ouvertes.fr/hal-01161668",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W107",
   "author": "Yubin Huang",
   "year": "2015",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "https://peerj.com/preprints/1455/",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W108",
   "author": "Daniel Uribe",
   "year": "2016",
   "claim": "P ≠ NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "The decision-tree lower bound does not cover all algorithms, and is flawed even where it applies.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2205.01189",
   "claim_url": "http://arxiv.org/abs/1601.03619",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W109",
   "author": "Mathias Hauptmann",
   "year": "2016",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1602.04781",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W110",
   "author": "Steven Meyer",
   "year": "2016",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1603.06018",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W111",
   "author": "Javier A. Arroyo-Figueroa",
   "year": "2016",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1604.03758",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W112",
   "author": "Eli Halylaurin",
   "year": "2016",
   "claim": "P = NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://vixra.org/abs/1605.0278",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "W113",
   "author": "Stefan Rass",
   "year": "2016",
   "claim": "P ≠ NP",
   "label": "NOT TRACED",
   "traced": "no",
   "where_it_broke": "",
   "barrier": "",
   "break_source_url": "",
   "claim_url": "http://arxiv.org/abs/1609.01575",
   "listed_in": "woeginger",
   "source": "Gerhard Woeginger's P-versus-NP page (https://wscor.win.tue.nl/woeginger/P-versus-NP.htm)"
  },
  {
   "id": "X001",
   "author": "Manuel Blum",
   "year": "2017",
   "claim": "P ≠ NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Author withdrew it; arXiv now calls the original paper \"incorrect\" (replaced by another paper). The exact failing step is not stated there.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/1708.03486v3",
   "claim_url": "https://arxiv.org/abs/1708.03486",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/1708.03486v3"
  },
  {
   "id": "A-001",
   "author": "Sima",
   "year": "2019",
   "claim": "P ≠ NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Fails where it claims to close the monotone vs non-monotone gap; a simple example shows the failure.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2005.03256",
   "claim_url": "https://arxiv.org/abs/2005.03256",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/2005.03256"
  },
  {
   "id": "A-002",
   "author": "Cho",
   "year": "2021",
   "claim": "P ≠ NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "A crucial step is not justified.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2104.01736",
   "claim_url": "https://arxiv.org/abs/2104.01736",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/2104.01736"
  },
  {
   "id": "A-003",
   "author": "Kumar",
   "year": "2021",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "The core step takes exponentially many steps on infinitely many inputs.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2112.06062",
   "claim_url": "https://arxiv.org/abs/2112.06062",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/2112.06062"
  },
  {
   "id": "A-010",
   "author": "Czerwinski",
   "year": "2021",
   "claim": "PSPACE != EXP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Counterexample to one of the theorems.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2304.14575",
   "claim_url": "https://arxiv.org/abs/2304.14575",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/2304.14575"
  },
  {
   "id": "A-011",
   "author": "Tianrong Lin",
   "year": "2021",
   "claim": "NSPACE[n] != DSPACE[n]",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Proof incomplete and wrong; strategy cannot be repaired.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2110.12421",
   "claim_url": "https://arxiv.org/abs/2110.12421",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/2110.12421"
  },
  {
   "id": "A-004",
   "author": "Yangjun Chen",
   "year": "2023",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Multiple counterexamples; structures not properly defined; time analysis over-generalized.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2404.00006",
   "claim_url": "https://arxiv.org/abs/2404.00006",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/2404.00006"
  },
  {
   "id": "A-005",
   "author": "Lizhi Du",
   "year": "2024",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Says an infinite family of satisfiable 3-CNF formulas is unsatisfiable.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2404.04395",
   "claim_url": "https://arxiv.org/abs/2404.04395",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/2404.04395"
  },
  {
   "id": "A-006",
   "author": "Deng",
   "year": "2024",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Confuses subgraphs with induced subgraphs.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2507.09018",
   "claim_url": "https://arxiv.org/abs/2507.09018",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/2507.09018"
  },
  {
   "id": "A-007",
   "author": "Quigley",
   "year": "2024",
   "claim": "P = NP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "Counterexamples to several lemmas; an infinite class of unsatisfiable formulas is called satisfiable.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2510.22985",
   "claim_url": "https://arxiv.org/abs/2510.22985",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/2510.22985"
  },
  {
   "id": "A-008",
   "author": "Tianrong Lin",
   "year": "2025",
   "claim": "NP != coNP",
   "label": "SOURCED",
   "traced": "yes",
   "where_it_broke": "The nondeterministic machine D does not work; the critics prove L_d is not in NP.",
   "barrier": "",
   "break_source_url": "https://arxiv.org/abs/2505.05658",
   "claim_url": "https://arxiv.org/abs/2505.05658",
   "listed_in": "arxiv-critique",
   "source": "https://arxiv.org/abs/2505.05658"
  }
 ]
}