Humanities Helping Hands

Every logged attempt at P vs NP.

126 claimed proofs so far. For 28 the step where it broke is read in a named source; the rest are open work. Nothing failed is ever repeated.

Back to the open problems · Data mostly from Woeginger's list, which stops in 2016, plus later critiques on arXiv · Download: attempts.csv · attempts.json (CC BY 4.0 on our additions only)

I.How to read a row

SOURCED

Where it broke was read in the named source. A source, not a machine proof.

GUESS

A likely break step, with its reason, not yet read in a source.

NOT TRACED

Unaccepted, but where it broke is not logged yet. Pick one: that is open work.

II.The attempts, oldest first

SOURCED
Ted Swart, 1986: P = NP
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 it hit: extended-formulation lower bound. Source: dx.doi.org/10.1016/0022-0000(91)90024-Y. The claim: dx.doi.org/10.1016/0022-0000(91)90024-Y.
NOT TRACED
Anatoly Plotnikov, 1996: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.emis.de/journals/SWJPAM/vol1-96.html.
SOURCED
Tang Pushan, 1997: P = NP
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. Source: portal.acm.org/citation.cfm?id=501491. The claim: portal.acm.org/citation.cfm?id=501491&dl=.
NOT TRACED
Miron Telpiz, 2000: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.tarusa.ru/~mit/ENG/eng.html.
NOT TRACED
Seenil Gram, 2001: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: springerlink.metapress.com/openurl.asp?genre=issue&issn=0302-9743&volume=2229.
NOT TRACED
Charles Sauerbier, 2002: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/cs.CC/0205064.
NOT TRACED
Givi Bolotashvili, 2003: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/cs.CC/0303008.
NOT TRACED
Nicholas Argall, 2003: undecidable
Where it broke is not logged yet. A small job anyone can take: find the step and its source.
SOURCED
N.C.A. da Costa; F.A. Doria, 2003: unprovable
Andreas Blass (MR2009291) says the consistency proof (Corollary 4.6) contains an error; Ralf Schindler also reviewed it. Source: wwwmath.uni-muenster.de/math/inst/logik/org/staff/rds/review.ps. The claim: www.elsevier.com/locate/amc.
SOURCED
Hubert Chen; Craig Alan Feinstein, 2003: P ≠ NP
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. Source: arxiv.org/abs/cs/0305035. The claim: www.tecn.upf.es/~hchen/.
NOT TRACED
Ki-Bong Nam; S.H. Wang; Yang Gon Kim, 2004: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source.
NOT TRACED
Mikhail N. Kupchik, 2004: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: users.i.com.ua/~zkup/pvsnp_en.pdf.
NOT TRACED
Selmer Bringsjord; Joshua Taylor, 2004: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/cs/0406056.
NOT TRACED
Bhupinder Singh Anand, 2004: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1510.04225.
NOT TRACED
Marius Ionescu, 2004: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/cs/0409039.
GUESS
Moustapha Diaby, 2004: P = NP
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). Source: arxiv.org/abs/1111.0837. The claim: www.business.uconn.edu/users/mdiaby/tsplp/.
NOT TRACED
Mircea Alexandru Popescu Moscu, 2004: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/cs.CC/0411033.
NOT TRACED
Andrea Bianchini, 2005: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: es-andreabianchini.it/ssp_eng.pdf.
NOT TRACED
Raju Renjit Grover, 2005: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/cs/0502030v1.
NOT TRACED
Viktor V. Ivanov, 2005: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.math.usf.edu/~eclark/NPvsP.pdf.
NOT TRACED
Bhupinder Singh Anand, 2005: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: xxx.lanl.gov/pdf/math.GM/0506126.
NOT TRACED
Craig Alan Feinstein, 2005: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/cs.CC/0507008.
NOT TRACED
Lev Gordeev, 2005: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.wsi.uni-tuebingen.de/lehrstuehle/logik-und-sprachtheorie/personen/ehemalige-und-sonstige-mitarbeiter/pd-dr-lev-gordeev/publications.html.
NOT TRACED
Lokman Kolukisa, 2005: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: geocities.com/lkoluk2003/.
NOT TRACED
Francesco Capasso, 2005: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/cs.CC/0511071.
NOT TRACED
Ron Cohen, 2005: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.arxiv.org/abs/cs.CC/0511085.
NOT TRACED
Miron Teplitz, 2005: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.tarusa.ru/~mit/ENG/sigma01_e.php.
GUESS
Joachim Mertz, 2005: P = NP
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). Source: arxiv.org/abs/1111.0837. The claim: www.merlins-world.de/.
NOT TRACED
Bhupinder Singh Anand, 2006: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/math.GM/0603605.
SOURCED
Craig Alan Feinstein, 2006: P ≠ NP
Critique by Sabo, Schmitt, Silverman (June 2007) answers this proof; step not quoted here. Source: arxiv.org/abs/0706.2035. The claim: arxiv.org/abs/cs.CC/0607093.
NOT TRACED
Mohamed Mimouni, 2006: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.wbabin.net/science/mimouni.pdf.
SOURCED
Sergey Gubin, 2006: P = NP
Full refutation by Christopher, Huo, Jacobs (April 2008); Hofman also commented. Source: arxiv.org/abs/0804.2699. The claim: arxiv.org/abs/cs.DM/0610042.
NOT TRACED
Radoslaw Hofman, 2006: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0704.0514.
NOT TRACED
Rubens Ramos Viana, 2006: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/quant-ph/0612001.
NOT TRACED
Howard Kleiman, 2006: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/math.CO/0612114.
NOT TRACED
Khadija Riaz and Malik Sikander Hayat Khiyal, 2006: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.scialert.net/pdfs/itj/2006/851-859.pdf.
NOT TRACED
Anatoly D. Plotnikov, 2007: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0706.3565.
NOT TRACED
Guohun Zhu, 2007: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0704.0309v3.
NOT TRACED
Matthew Delacorte, 2007: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0708.4075.
SOURCED
Jaeger, 2008: other
Non-standard model of computation, unsupported assumptions, missing proofs. Source: arxiv.org/abs/0904.3927. The claim: arxiv.org/abs/0904.3927.
NOT TRACED
Cynthia Ann Harlan Krieger, 2008: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.freepatentsonline.com/y2008/0071849.html.
NOT TRACED
Jerrald Meek, 2008: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0804.1079.
NOT TRACED
Bhupinder Singh Anand, 2008: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: alixcomsi.com/18_A_trivial_solution_to_PvNP.pdf.
NOT TRACED
Rafee Ebrahim Kamouna, 2008: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0806.2947.
NOT TRACED
Jerrald Meek, 2008: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0808.3222.
NOT TRACED
Jorma Jormakka, 2008: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0809.4935.
NOT TRACED
Sten-Ake Tarnlund, 2008: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0810.5056.
NOT TRACED
Zohreh O. Akbari, 2008: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.waset.org/pwaset/v35/v35-74.pdf.
SOURCED
Javaid Aslam, 2008: P = NP
Ferraro, Hall, Wood "Refutation of Aslam's Proof that NP = P" points out a flaw; Aslam replied. Source: arxiv.org/abs/0812.1385. The claim: arxiv.org/abs/0812.1385.
NOT TRACED
Rafael Valls Hidalgo-Gato, 2009: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source.
SOURCED
Doron Zeilberger (1 April 2009, joke date), 2009: P = NP
Definitions are ambiguous; every way to make them exact breaks the main proof. Source: arxiv.org/abs/1711.07132. The claim: www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/pnp.pdf.
NOT TRACED
Xinwen Jiang, 2009: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: xinwenjiang.googlepages.com/.
NOT TRACED
Arto Annila, 2009: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0906.1084.
NOT TRACED
Andre Luiz Barbosa, 2009: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0907.3965.
NOT TRACED
Yann Dujardin, 2009: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0909.3466.
NOT TRACED
Luigi Salemi, 2009: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/0909.3868.
NOT TRACED
Ari Blinder, 2009: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: sites.google.com/site/ariblindercswork/.
NOT TRACED
Narendra S. Chaudhari, 2009: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: dcis.uohyd.ernet.in/~wankarcs/index_files/pdf/Vol-31-No-2-2009-pp407-444-scanned-copy.pdf.
NOT TRACED
Lizhi Du, 2010: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1004.3702.
NOT TRACED
Changlin Wan, 2010: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1005.3010.
NOT TRACED
Carlos Barron-Romero, 2010: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1006.2218.
NOT TRACED
Han Xiao Wen, 2010: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1006.2495.
NOT TRACED
Mikhail Katkov, 2010: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1007.4257v2.
GUESS
Vinay Deolalikar, 2010: P ≠ NP
Reason: widely reported issues in the FO(LFP)/solution-space step, discussed on Lipton's blog; not verified this run. Source: rjlipton.wordpress.com/. The claim: rjlipton.wordpress.com/.
SOURCED
Sergey Gubin, 2010: P = NP
Refutation by Romeo Rizzi (January 2011) per Woeginger; no link given on the page. Source: www.win.tue.nl/~gwoegi/P-versus-NP.htm.
NOT TRACED
Vladimir Romanov, 2010: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1011.3944.
NOT TRACED
Frank Vega Delgado, 2010: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1011.2730.
NOT TRACED
Carlos Barron-Romero, 2010: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1101.0160.
NOT TRACED
Bangyan Wen and Yi Lin, 2010: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.iigss.net/Scientific-Inquiry/Dec2010/table.htm.
NOT TRACED
Ruijia Liao, 2011: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1101.2018.
NOT TRACED
Amar Mukherjee, 2011: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1104.4490.
NOT TRACED
Angela Weiss, 2011: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.ime.usp.br/~weiss/.
NOT TRACED
Matt Groff, 2011: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1106.0683.
NOT TRACED
Sergey Kardash, 2011: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1108.0408.
NOT TRACED
Anatoly Plotnikov, 2011: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1109.5531.
NOT TRACED
Koji Kobayashi, 2011: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1110.0200.
NOT TRACED
Jason W. Steinmetz, 2011: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1110.1658.
NOT TRACED
Jose Ignacio Alvarez-Hamelin, 2011: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1110.5355.
NOT TRACED
Roman Yampolskiy, 2011: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1111.0305.
NOT TRACED
Craig Alan Feinstein, 2011: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/cs/0611082.
NOT TRACED
Jeffrey W. Holcomb, 2011: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.holcombtechnologies.com.
NOT TRACED
Algirdas Antano Maknickas, 2011: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1203.6020.
NOT TRACED
Douglas Youvan, 2012: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.amazon.com/Approaches-Equivalent-Computations-Zero-Mass-ebook/dp/B006SA3KIA/ref=zg_bs_158742011_29.
NOT TRACED
Gilberto Rodrigo Diduch, 2012: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: paper.ijcsns.org/07_book/201201/20120124.pdf.
NOT TRACED
Koji Kobayashi, 2012: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1202.1194.
NOT TRACED
Frank Vega Delgado, 2012: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: the-point-of-view-of-frank.blogspot.com/.
SOURCED
Minseong Kim, 2012: P ≠ NP
The logic is inconsistent; under two reasonable readings of the definitions, P != NP does not follow. Source: arxiv.org/abs/1404.5352. The claim: arxiv.org/abs/1203.0494.
GUESS
Michel Feldmann, 2012: P = NP
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). Source: arxiv.org/abs/1111.0837. The claim: arxiv.org/abs/1205.6658.
NOT TRACED
Junichiro Fukuyama, 2012: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: junfukuyama.wordpress.com/.
NOT TRACED
Satoshi Tazawa, 2012: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1207.2171.
NOT TRACED
Wen-Qi Duan, 2012: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1208.0542.
NOT TRACED
Sergey V. Yakhontov, 2012: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1208.0954.
NOT TRACED
Natalia L. Malinina, 2012: unprovable
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1211.3492.
NOT TRACED
Louis Coder, 2012: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: vixra.org/abs/1212.0109.
NOT TRACED
Dmitriy Nuriyev, 2013: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1301.3093.
GUESS
Algirdas Antano Maknickas, 2013: P = NP
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). Source: arxiv.org/abs/1111.0837. The claim: link.springer.com/chapter/10.1007/978-94-007-7684-5_22.
NOT TRACED
Rustem Chingizovich Valeyev, 2013: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: www.idosi.org/wasj/wasj24%288%292013.htm.
SOURCED
Frederic Gillet, 2013: P = NP
Author added to arXiv (Nov 2013): the proposed method does not work, paper to be withdrawn. Source: arxiv.org/abs/1310.1971. The claim: arxiv.org/abs/1310.1971.
SOURCED
Sopin, 2014: PH = PSPACE
The paper fails to establish PH = PSPACE (problems listed in critique). Source: arxiv.org/abs/2301.03487. The claim: arxiv.org/abs/2301.03487.
NOT TRACED
Hanlin Liu, 2014: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1401.6423.
SOURCED
Pawan Tamta; B.P. Pande; H.S. Dhami, 2014: P = NP
Refuted (with LaPlante) in "A Refutation of the Clique-Based P=NP Proofs of LaPlante and Tamta-Pande-Dhami". Source: arxiv.org/abs/1504.06890. The claim: arxiv.org/abs/1403.1178.
NOT TRACED
Peng Cui, 2014: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1401.6520.
NOT TRACED
Daegene Song, 2014: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1402.6970.
NOT TRACED
Joonmo Kim, 2014: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1403.4143.
NOT TRACED
Anatoly Panyukov, 2014: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1409.0375.
SOURCED
Michael LaPlante, 2015: P = NP
Refuted (with Tamta-Pande-Dhami) in "A Refutation of the Clique-Based P=NP Proofs of LaPlante and Tamta-Pande-Dhami". Source: arxiv.org/abs/1504.06890. The claim: arxiv.org/abs/1503.04794.
SOURCED
Alejandro Sanchez Guinea, 2015: P = NP
The 3-SAT algorithm is flawed and does not show 3-SAT is in P. Source: arxiv.org/abs/1711.04412. The claim: arxiv.org/abs/1504.00337.
NOT TRACED
Frank Vega, 2015: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: hal.archives-ouvertes.fr/hal-01161668.
NOT TRACED
Yubin Huang, 2015: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: peerj.com/preprints/1455/.
SOURCED
Daniel Uribe, 2016: P ≠ NP
The decision-tree lower bound does not cover all algorithms, and is flawed even where it applies. Source: arxiv.org/abs/2205.01189. The claim: arxiv.org/abs/1601.03619.
NOT TRACED
Mathias Hauptmann, 2016: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1602.04781.
NOT TRACED
Steven Meyer, 2016: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1603.06018.
NOT TRACED
Javier A. Arroyo-Figueroa, 2016: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1604.03758.
NOT TRACED
Eli Halylaurin, 2016: P = NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: vixra.org/abs/1605.0278.
NOT TRACED
Stefan Rass, 2016: P ≠ NP
Where it broke is not logged yet. A small job anyone can take: find the step and its source. The claim: arxiv.org/abs/1609.01575.
SOURCED
Manuel Blum, 2017: P ≠ NP
Author withdrew it; arXiv now calls the original paper "incorrect" (replaced by another paper). The exact failing step is not stated there. Source: arxiv.org/abs/1708.03486v3. The claim: arxiv.org/abs/1708.03486.
SOURCED
Sima, 2019: P ≠ NP
Fails where it claims to close the monotone vs non-monotone gap; a simple example shows the failure. Source: arxiv.org/abs/2005.03256. The claim: arxiv.org/abs/2005.03256.
SOURCED
Cho, 2021: P ≠ NP
A crucial step is not justified. Source: arxiv.org/abs/2104.01736. The claim: arxiv.org/abs/2104.01736.
SOURCED
Kumar, 2021: P = NP
The core step takes exponentially many steps on infinitely many inputs. Source: arxiv.org/abs/2112.06062. The claim: arxiv.org/abs/2112.06062.
SOURCED
Czerwinski, 2021: PSPACE != EXP
Counterexample to one of the theorems. Source: arxiv.org/abs/2304.14575. The claim: arxiv.org/abs/2304.14575.
SOURCED
Tianrong Lin, 2021: NSPACE[n] != DSPACE[n]
Proof incomplete and wrong; strategy cannot be repaired. Source: arxiv.org/abs/2110.12421. The claim: arxiv.org/abs/2110.12421.
SOURCED
Yangjun Chen, 2023: P = NP
Multiple counterexamples; structures not properly defined; time analysis over-generalized. Source: arxiv.org/abs/2404.00006. The claim: arxiv.org/abs/2404.00006.
SOURCED
Lizhi Du, 2024: P = NP
Says an infinite family of satisfiable 3-CNF formulas is unsatisfiable. Source: arxiv.org/abs/2404.04395. The claim: arxiv.org/abs/2404.04395.
SOURCED
Deng, 2024: P = NP
Confuses subgraphs with induced subgraphs. Source: arxiv.org/abs/2507.09018. The claim: arxiv.org/abs/2507.09018.
SOURCED
Quigley, 2024: P = NP
Counterexamples to several lemmas; an infinite class of unsatisfiable formulas is called satisfiable. Source: arxiv.org/abs/2510.22985. The claim: arxiv.org/abs/2510.22985.
SOURCED
Tianrong Lin, 2025: NP != coNP
The nondeterministic machine D does not work; the critics prove L_d is not in NP. Source: arxiv.org/abs/2505.05658. The claim: arxiv.org/abs/2505.05658.