Results

203 statements

1. ●Proved
   A cited upper bound Λ ≤ 0.2

   BoundRiemann hypothesisPlatt & Trudgian 2020

2. ●Proved
   A constant determinant with three inputs sharing an output

   CounterexampleJacobian conjectureGao 2026Formalized

3. ●Proved
   A critical point within distance one

   Main statementSendov’s conjectureMazur 2026 · per Tao 2026Formalized

4. ●Proved
   A cubic witness in four real variables

   Supporting resultGaussian moments conjectureLong 2026

5. ●Proved
   A distinct symmetric 112-vertex counterexample

   CounterexamplePetersen coloring conjecturePutman 2026

6. ●Proved
   A double cover has total length twice the edge count

   Supporting resultCycle double cover conjectureOpenAI 2026

7. ●Proved
   A family attaining the parameter-dependent bound

   Related resultČerný synchronization conjectureZhu 2026

8. ●Proved
   A fixed power gain for infinitely many sizes

   CounterexampleErdős unit-distance problemOpenAI 2026Formalized

9. ●Proved
   A formal non-disk failing the Pompeiu property

   CounterexampleSchiffer and Pompeiu conjecturesJaume de Dios Pont & Cao-LaboraFormalized

10. ●Proved
    A fourth-moment lower bound: 1/8

    Related resultFeige’s probability conjectureHe, Zhang & Zhang 2010 · per Fu et al. 2026

11. ●Proved
    A gap bound of 186 from explicit input assumptions

    Conditional resultHow small can prime gaps be?OpenAI & PrimeGaps186 contributors 2026Formalized

12. ●Proved
    A logarithmic bound

    Related resultKannan–Lovász–Simonovits conjectureKlartag 2023 · per Bizeul et al. 2026

13. ●Proved
    A moment and Berry–Esseen lower bound: 0.1798

    Related resultFeige’s probability conjectureGuo, He, Ling & Liu 2020 · per Fu et al. 2026

14. ●Proved
    A poly-logarithmic bound

    Related resultKannan–Lovász–Simonovits conjectureKlartag & Lehec 2022 · per Bizeul et al. 2026

15. ●Proved
    A prime at or above every bound

    Equivalent formulationWhy are there infinitely many primes?mathlib contributorsFormalized

16. ●Proved
    A prime strictly above every bound

    Main statementWhy are there infinitely many primes?OpenMath staff

17. ●Proved
    A proved 0.3465 triangle threshold

    BoundCaccetta–Häggkvist cycle boundHladký et al. 2017

18. ●Proved
    A quartic witness in three real variables

    CounterexampleGaussian moments conjectureLong 2026

19. ◌Proposed
    A singular forced flow starting from rest

    Supporting resultNavier–Stokes existence and smoothnessOpenAI 2026

20. ●Proved
    A square-root bound

    Related resultKannan–Lovász–Simonovits conjectureLee & Vempala 2024 · per Bizeul et al. 2026

21. ●Proved
    A sub-polynomial bound

    Related resultKannan–Lovász–Simonovits conjectureChen 2021 · per Bizeul et al. 2026

22. ●Proved
    A truly subcubic deterministic APSP algorithm

    Related resultP versus NPAlman & Williams 2026

23. ●Proved
    A truly subquadratic deterministic 3SUM algorithm

    Related resultP versus NPAlman & Williams 2026

24. ◌Proposed
    A uniform Poincaré bound for isotropic log-concave measures

    Main statementKannan–Lovász–Simonovits conjectureSong & Zhang 2026

25. ●Proved
    Abelian fourfolds · Markman (2025)

    Special caseHodge conjectureMarkman 2025

26. ○Open
    Aharoni’s rainbow cycle conjecture

    VariantCaccetta–Häggkvist cycle boundHompe & Huynh 2025

27. ●Proved
    Airy factorization of the density and curvature

    Supporting resultStrong log-concavity of the Chernoff densityZhang & Zhou 2026

28. ●Proved
    Algebrizing techniques cannot settle P versus NP

    Proof barrierP versus NPAaronson & Wigderson 2008

29. ●Proved
    All codimensions in dimension ≤ 3

    Special caseHodge conjectureClay Mathematics Institute

30. ●Proved
    All powers of Weil fourfolds with discriminant 1

    Special caseHodge conjectureFloccari & Fu 2025

31. ●Proved
    An additive bound for rainbow cycles

    Related resultCaccetta–Häggkvist cycle boundHompe & Huynh 2025

32. ●Proved
    An analytic tenfold counterexample

    CounterexampleSchiffer and Pompeiu conjecturesColbrook & Stepaniants 2026Formalized

33. ●Proved
    An average bound for simplicity and line membership

    Supporting resultRiemann hypothesisLamzouri 2026

34. ●Proved
    An explicit zero-free region near Re(s) = 1

    BoundRiemann hypothesisBellotti et al. 2026

35. ●Proved
    At least 83.625% distinct zeros, asymptotically

    Supporting resultRiemann hypothesisAlpöge & Furman 2026

36. ●Proved
    At least 88.762% simple OR on-line zeros, asymptotically

    Supporting resultRiemann hypothesisLamzouri 2026

37. ●Proved
    Blowup from C^{1,α} data in ℝ³

    Related resultThree-dimensional Euler regularityElgindi 2021 · per OpenAI 2026

38. ●Proved
    Blowup with external forcing

    Related resultThree-dimensional Euler regularityCórdoba & Martínez-Zoroa 2023 · per OpenAI 2026

39. ●Proved
    Bombieri–Vinogradov implies recurring gaps at most 246

    Conditional resultHow small can prime gaps be?Math & PrimeGapsLib contributors 2026Formalized

40. ○Open
    BSD rank equality holds for every E/Q

    Main statementBirch and Swinnerton-Dyer conjectureper Wiles (official description)

41. ●Proved
    BSD would complete the odd squarefree congruent-number criterion

    Conditional implicationBirch and Swinnerton-Dyer conjectureper Wiles (official description)

42. ●Proved
    Černý’s examples meet the bound

    Related resultČerný synchronization conjectureČerný 1964 · per Zhu 2026

43. ●Proved
    Characterizing a natural-number prime

    Supporting resultWhy are there infinitely many primes?mathlib contributorsFormalized

44. ○Open
    classical RH fails

    Possible answerRiemann hypothesisper Bombieri (official description)

45. ○Open
    classical RH holds

    Main statementRiemann hypothesisper Bombieri (official description)

46. ●Proved
    Computer-assisted full formula · 16,714 curves

    Special caseBirch and Swinnerton-Dyer conjectureMiller 2010

47. ●Proved
    Conditional transfer through motivated varieties

    Conditional resultHodge conjectureArapura

48. ✕Disproved
    Constant Jacobian implies a polynomial inverse

    Main statementJacobian conjectureULAM research manuscript 2026

49. ◌Proposed
    Counterexamples in every dimension from three up

    CounterexampleJacobian conjectureGao 2026

50. ●Proved
    Decision NP-completeness for three complete ballots

    Main statementKemeny rank aggregation for three votersPeters 2026

51. ●Proved
    Depth-two threshold circuits require superquadratic size

    Restricted modelP versus NPChen et al. 2026

52. ●Proved
    Dimensions where every smooth sphere is standard

    VariantPoincaré conjectureMilnor 2014

53. ●Proved
    Dirichlet GRH implies classical RH

    Conditional implicationRiemann hypothesisAlpöge & Furman 2026

54. ●Proved
    Divisor classes · Lefschetz (1,1)

    Special caseHodge conjectureper Deligne (official description)

55. ●Proved
    Energy bounds for Leray–Hopf solutions

    Supporting resultNavier–Stokes existence and smoothnessKang & Protas 2022

56. ●Proved
    Erdős’s grid lower bound

    Related resultErdős unit-distance problemErdős · per Alon et al. 2026

57. ●Proved
    ETH would separate P and NP

    Conditional implicationP versus NPImpagliazzo & Paturi 2001

58. ✕Disproved
    Eventual mixed-moment vanishing in every dimension

    Main statementGaussian moments conjectureLong 2026

59. ✕Disproved
    Every bridgeless cubic graph admits a Petersen coloring

    Main statementPetersen coloring conjecturePutman 2026

60. ◌Proposed
    Every bridgeless graph has a cycle double cover

    Main statementCycle double cover conjectureOpenAI 2026Formalized

61. ●Proved
    Exotic spheres in every other dimension up to 63

    VariantPoincaré conjectureMilnor 2014

62. ○Open
    Exponential Time Hypothesis

    VariantP versus NPImpagliazzo & Paturi 2001

63. ●Proved
    Feige’s first universal lower bound: 1/13

    Related resultFeige’s probability conjectureFeige 2004 · per Fu et al. 2026

64. ●Proved
    Fewer possible zeros to the right of a fixed line

    BoundRiemann hypothesisGuth & Maynard 2024

65. ●Proved
    Finite extinction in the simply connected case

    Supporting resultPoincaré conjecturePerelman 2003

66. ●Proved
    Finite-time smooth breakdown requires divergent integrated vorticity

    Conditional implicationThree-dimensional Euler regularityBeale et al. 1984

67. ◌Proposed
    Forced breakdown on the three-torus

    VariantNavier–Stokes existence and smoothnessOpenAI 2026Formalized

68. ◌Proposed
    Forced whole-space nonexistence

    CounterexampleNavier–Stokes existence and smoothnessOpenAI 2026Formalized

69. ●Proved
    Fractional cost 58 versus unsplittable cost 60

    CounterexampleCost-preserving unsplittable flowRamos et al. 2026Formalized

70. ●Proved
    From boundary data to vanishing domain averages

    Conditional implicationSchiffer and Pompeiu conjecturesJaume de Dios Pont & Cao-Labora

71. ●Proved
    Full BSD in a specified infinite twist family

    Special caseBirch and Swinnerton-Dyer conjectureBurungale et al. 2024

72. ◌Proposed
    Gaps at most 212, infinitely often

    BoundHow small can prime gaps be?Charton et al. 2026

73. ●Proved
    Gaps at most 240, infinitely often

    BoundHow small can prime gaps be?Stadlmann 2026 · per Charton et al. 2026

74. ●Proved
    Gaps at most 246, infinitely often

    BoundHow small can prime gaps be?Polymath 2014

75. ●Proved
    Gaps at most 600, infinitely often

    BoundHow small can prime gaps be?Maynard 2015

76. ●Proved
    Gaps at most 70,000,000, infinitely often

    BoundHow small can prime gaps be?Zhang 2014

77. ○Open
    Gaps of two infinitely often

    Main statementHow small can prime gaps be?Polymath 2014

78. ●Proved
    General NP circuit lower bounds would separate P and NP

    Conditional implicationP versus NPWigderson 2019

79. ○Open
    Generalized RH for Dirichlet L-functions

    VariantRiemann hypothesisAlpöge & Furman 2026

80. ●Proved
    Global regularity for small initial data

    Special caseNavier–Stokes existence and smoothnessper Fefferman (official description)

81. ●Proved
    Global regularity in two dimensions

    VariantNavier–Stokes existence and smoothnessper Fefferman (official description)

82. ●Proved
    Global weak solutions (Leray)

    Supporting resultNavier–Stokes existence and smoothnessper Fefferman (official description)

83. ●Proved
    Hardness for every fixed voter count at least three

    Related resultKemeny rank aggregation for three votersPeters 2026

84. ●Proved
    Hodge would algebraize inverse Lefschetz maps

    Conditional implicationHodge conjectureper Deligne (official description)

85. ●Proved
    Hodge would make cohomological projectors algebraic

    Conditional implicationHodge conjectureper Deligne (official description)

86. ●Proved
    If P ≠ NP, intermediate problems exist

    Conditional implicationP versus NPWigderson 2019

87. ●Proved
    If P = NP, NP witnesses can be found efficiently

    Conditional implicationP versus NPCook

88. ●Proved
    If P ≠ NP, NP-complete problems have no polynomial algorithm

    Conditional implicationP versus NPCook

89. ●Proved
    If P = NP, the polynomial hierarchy collapses to P

    Conditional implicationP versus NPWigderson 2019

90. ●Proved
    Infinitely many Petersen-coloring counterexamples

    Related resultPetersen coloring conjecturePutman 2026

91. ●Proved
    Infinitely many smooth symmetry orders

    CounterexampleSchiffer and Pompeiu conjecturesCao-Labora & Jaume de Dios Pont 2026

92. ●Proved
    Integral Hodge variant · counterexamples

    VariantHodge conjectureper Deligne (official description)

93. ●Proved
    Low-rank formula at supersingular p ≥ 5

    Special caseBirch and Swinnerton-Dyer conjectureBurungale et al. 2024

94. ●Proved
    More than 67.25% simple zeros on the line, asymptotically

    BoundRiemann hypothesisAlpöge & Furman 2026

95. ●Proved
    Near-maximum general circuit lower bound in an oracle class

    Restricted modelP versus NPRen & Williams 2026

96. ●Proved
    NEXP has no polynomial-size ACC circuits

    Restricted modelP versus NPWilliams 2011

97. ◌Proposed
    No global smooth bounded-energy solution for selected data

    Supporting resultThree-dimensional Euler regularityOpenAI 2026Formalized

98. ●Proved
    No polynomial inverse for the three-variable witness

    Supporting resultJacobian conjecturealerad/alpoge-lean project 2026Formalized

99. ✕Disproved
    Normal five-edge-colorings for bridgeless cubic graphs

    Equivalent formulationPetersen coloring conjecturePutman 2026

100. ○Open
     NP ≠ coNP

     VariantP versus NPCook

101. ○Open
     NP lacks polynomial-size general circuits

     VariantP versus NPWigderson 2019

102. ●Proved
     NP versus coNP would separate P and NP

     Conditional implicationP versus NPWigderson 2019

103. ●Proved
     One-way functions would separate P and NP

     Conditional implicationP versus NPWigderson 2019

104. ●Proved
     Optimization NP-hardness for three voters

     Possible answerKemeny rank aggregation for three votersPeters 2026

105. ○Open
     P = NP

     Main statementP versus NPCook

106. ○Open
     P ≠ NP

     Possible answerP versus NPCook

107. ●Proved
     Partial bounds for a fixed Dirichlet character

     VariantRiemann hypothesisAlpöge & Furman 2026

108. ●Proved
     Petersen and normal-five colorings are equivalent

     Supporting resultPetersen coloring conjecturePutman 2026

109. ✕Disproved
     Planar disk rigidity for overdetermined Helmholtz data

     Main statementSchiffer and Pompeiu conjecturesColbrook & Stepaniants 2026

110. ●Proved
     Pointwise and tail curvature bounds

     BoundStrong log-concavity of the Chernoff densityZhang & Zhou 2026

111. ●Proved
     Polynomial NP circuits would collapse the hierarchy

     Conditional implicationP versus NPWigderson 2019

112. ●Proved
     Preserving cost with twice the allowance in planar graphs

     VariantCost-preserving unsplittable flowTraub et al. 2023

113. ◌Proposed
     Proposed cubic complex determinantal lower bound

     VariantP versus NPOpenAI internal model 2026

114. ◌Proposed
     Proposed depth-three bound beyond the square-root exponent

     Restricted modelP versus NPOpenAI internal model 2026

115. ◌Proposed
     Proposed full BSD at Selmer corank zero or one

     Special caseBirch and Swinnerton-Dyer conjectureOpenAI 2026

116. ◌Proposed
     Proposed half-densities in every quadratic-twist family

     VariantBirch and Swinnerton-Dyer conjectureOpenAI 2026

117. ◌Proposed
     Proposed Hodge result for all CM abelian varieties

     Special caseHodge conjectureOpenAI 2026

118. ◌Proposed
     Proposed rationality of specialized Hodge pairings

     VariantHodge conjectureOpenAI 2026

119. ◌Proposed
     Proposed result: a fixed zero-free half-plane Re(s) > 7/8

     BoundRiemann hypothesisOpenAI

120. ◌Proposed
     Proposed result: Λ ≤ 0.1787854

     BoundRiemann hypothesisGomila

121. ◌Proposed
     Proposed Unique Games gap reductions

     VariantP versus NPOpenAI internal model 2026

122. ●Proved
     Proved analogue: curves over finite fields

     VariantRiemann hypothesisper Bombieri (official description)

123. ●Proved
     Randomized SETH would separate P and NP

     Conditional implicationP versus NPCygan et al. 2014

124. ●Proved
     Rank BSD would decide finite versus infinite rational points analytically

     Conditional implicationBirch and Swinnerton-Dyer conjectureper Wiles (official description)

125. ●Proved
     Rank equality at analytic rank 0 or 1

     Special caseBirch and Swinnerton-Dyer conjectureSkinner 2020

126. ●Proved
     Rank-one converse assuming finite Sha

     Conditional resultBirch and Swinnerton-Dyer conjectureSkinner 2020

127. ●Proved
     Rank-one formula · selected p-parts

     Special caseBirch and Swinnerton-Dyer conjectureJetchev et al. 2015

128. ○Open
     rational Hodge holds in all codimensions

     Main statementHodge conjectureper Deligne (official description)

129. ●Proved
     Rational points form a finitely generated group

     Supporting resultBirch and Swinnerton-Dyer conjectureper Wiles (official description)

130. ●Proved
     Regularity criteria (Ladyzhenskaya–Prodi–Serrin)

     Conditional resultNavier–Stokes existence and smoothnessKang & Protas 2022

131. ●Proved
     Relative extending words on the unique cycle

     Supporting resultČerný synchronization conjectureZhu 2026

132. ●Proved
     Relativizing techniques cannot settle P versus NP

     Proof barrierP versus NPBaker et al. 1975

133. ●Proved
     RH is equivalent to the prime-counting error target

     Supporting resultRiemann hypothesisper Bombieri (official description)

134. ●Proved
     RH is equivalent to Λ = 0

     Supporting resultRiemann hypothesisRodgers & Tao 2018

135. ●Proved
     RH verified to height 3,000,175,332,800

     Special caseRiemann hypothesisPlatt & Trudgian 2020

136. ●Proved
     SAT captures P versus NP

     Equivalent formulationP versus NPCook

137. ○Open
     SAT in polynomial time

     Equivalent formulationP versus NPCook

138. ●Proved
     Sendov for all sufficiently large degree

     Special caseSendov’s conjectureTao 2022

139. ●Proved
     Sendov for degree at most eight

     Special caseSendov’s conjectureBrown & Xiang 1999 · per Tao 2022

140. ○Open
     Separate conjecture: all nontrivial zeros are simple

     VariantRiemann hypothesisLamzouri 2026

141. ○Open
     Sha is finite for every E/Q

     VariantBirch and Swinnerton-Dyer conjectureper Wiles (official description)

142. ●Proved
     Smooth solutions on a short time interval

     Special caseNavier–Stokes existence and smoothnessper Fefferman (official description)

143. ◌Proposed
     Smooth unforced data with finite-time breakdown

     Main statementThree-dimensional Euler regularityOpenAI 2026Formalized

144. ●Proved
     Smooth-data blowup with a boundary

     Related resultThree-dimensional Euler regularityChen & Hou 2022 · per OpenAI 2026

145. ●Proved
     Smoothing a topological three-manifold

     Supporting resultPoincaré conjectureQin et al. 2026

146. ○Open
     Standard one-way functions exist

     VariantP versus NPWigderson 2019

147. ●Proved
     Strict distance and the equality exception

     VariantSendov’s conjectureMazur 2026 · per Tao 2026Formalized

148. ●Proved
     Strong BSD implies its rank and finiteness assertions

     Conditional implicationBirch and Swinnerton-Dyer conjectureper Wiles (official description)

149. ●Proved
     Strong BSD would determine Sha’s order from the other invariants

     Conditional implicationBirch and Swinnerton-Dyer conjectureper Wiles (official description)

150. ○Open
     Strong Exponential Time Hypothesis — randomized version

     VariantP versus NPCygan et al. 2014

151. ●Proved
     Tate is proved for abelian fourfolds over finite fields

     VariantHodge conjectureBroe 2026

152. ●Proved
     The bound for positive-level one-cluster automata

     Special caseČerný synchronization conjectureZhu 2026

153. ○Open
     the classical Newman constant is zero

     Equivalent formulationRiemann hypothesisRodgers & Tao 2018

154. ●Proved
     The classical upper bound

     Related resultErdős unit-distance problemSpencer, Szemerédi & Trotter 1984 · per Alon et al. 2026

155. ●Proved
     The critical L³ endpoint (Escauriaza–Seregin–Šverák)

     Conditional resultNavier–Stokes existence and smoothnessTao 2021

156. ●Proved
     The dimension-free unit-slack inequality

     Main statementFeige’s probability conjectureFu et al. 2026

157. ●Proved
     The earlier ordinary log-concavity theorem

     Supporting resultStrong log-concavity of the Chernoff densityBalabdaoui & Wellner 2014

158. ✕Disproved
     The exact-cost rounding conjecture

     Main statementCost-preserving unsplittable flowRamos et al. 2026Formalized

159. ◌Proposed
     The first revision’s iterated-logarithm estimate

     Supporting resultKannan–Lovász–Simonovits conjectureSong & Zhang 2026

160. ○Open
     the full BSD formula holds for every E/Q

     VariantBirch and Swinnerton-Dyer conjectureper Wiles (official description)

161. ○Open
     The full directed cycle bound

     Main statementCaccetta–Häggkvist cycle boundHompe & Huynh 2025

162. ○Open
     The general quadratic reset-word conjecture

     Main statementČerný synchronization conjectureZhu 2026

163. ●Proved
     The global implication to polynomial inversion

     Conditional implicationGaussian moments conjectureDerksen et al. 2015

164. ●Proved
     The July bounds in two deviation ranges

     VariantFeige’s probability conjectureFu et al. 2026

165. ◌Proposed
     The later proposal for every positive deviation

     VariantFeige’s probability conjectureLing 2026

166. ●Proved
     The main 112-vertex counterexample

     CounterexamplePetersen coloring conjecturePutman 2026

167. ●Proved
     The natural-proofs barrier is conditional

     Proof barrierP versus NPRazborov & Rudich 1994

168. ✕Disproved
     The near-linear unit-distance conjecture

     Main statementErdős unit-distance problemAlon et al. 2026

169. ●Proved
     The Newman constant satisfies Λ ≥ 0

     BoundRiemann hypothesisRodgers & Tao 2018

170. ●Proved
     The normalized C² formal statement

     Supporting resultSchiffer and Pompeiu conjecturesJaume de Dios Pont & Cao-LaboraFormalized

171. ●Proved
     The older level-zero circular case

     Supporting resultČerný synchronization conjectureZhu 2026

172. ○Open
     The one-third directed triangle question

     VariantCaccetta–Häggkvist cycle boundHladký et al. 2017

173. ●Proved
     The one-variable case

     Special caseGaussian moments conjectureDerksen et al. 2015

174. ●Proved
     The optimal bound for a fixed number of variables

     BoundFeige’s probability conjectureFu et al. 2026Formalized

175. ●Proved
     The original congestion guarantee

     Supporting resultCost-preserving unsplittable flowTraub et al. 2023

176. ✕Disproved
     The planar Pompeiu property question

     VariantSchiffer and Pompeiu conjecturesColbrook & Stepaniants 2026

177. ●Proved
     The Poincaré theorem in dimensions five and higher (Smale)

     VariantPoincaré conjectureper Milnor (official description)

178. ○Open
     The remaining two-variable question

     VariantGaussian moments conjectureLong 2026

179. ●Proved
     The same witness works in every higher dimension

     Conditional implicationGaussian moments conjectureLong 2026

180. ●Proved
     The set of primes is unbounded

     Equivalent formulationWhy are there infinitely many primes?OpenMath staff

181. ●Proved
     The sharp bound for out-degree two through five

     Special caseCaccetta–Häggkvist cycle boundCaccetta–Häggkvist, Hamidoune, Hoàng–Reed · per Blair D. Sullivan

182. ●Proved
     The sharp bound for vertex-transitive graphs

     Special caseCaccetta–Häggkvist cycle boundHamidoune 1981 · per Blair D. Sullivan

183. ●Proved
     The sharp bound when n ≥ 2r² − 3r + 1

     Special caseCaccetta–Häggkvist cycle boundShen 2000 · per Blair D. Sullivan

184. ○Open
     The sharper origin-minimum curvature conjecture

     VariantStrong log-concavity of the Chernoff densityBalabdaoui & Wellner 2014

185. ●Proved
     The singular set is small (Caffarelli–Kohn–Nirenberg)

     BoundNavier–Stokes existence and smoothnessper Fefferman (official description)

186. ○Open
     The smooth four-dimensional Poincaré question

     VariantPoincaré conjectureManolescu 2026

187. ●Proved
     The smooth three-dimensional theorem

     Equivalent formulationPoincaré conjectureMorgan & Tian 2007Formalized

188. ○Open
     the square-root prime-counting error holds

     Equivalent formulationRiemann hypothesisper Bombieri (official description)

189. ●Proved
     The topological four-dimensional theorem

     VariantPoincaré conjectureManolescu 2026

190. ●Proved
     The topological three-dimensional Poincaré theorem

     Main statementPoincaré conjectureClay Mathematics InstituteFormalized

191. ○Open
     The two-variable Jacobian question

     VariantJacobian conjectureGao 2026

192. ●Proved
     The two-voter case is polynomial-time solvable

     Supporting resultKemeny rank aggregation for three votersPeters 2026

193. ●Proved
     The universal constant is a limit across dimensions

     Conditional implicationFeige’s probability conjectureFu et al. 2026

194. ●Proved
     The unrestricted compact Kähler extension is false

     VariantHodge conjectureper Deligne (official description)

195. ●Proved
     There are infinitely many primes

     Equivalent formulationWhy are there infinitely many primes?OpenMath staff

196. ●Proved
     Transporting the proposed bound beyond isotropic measures

     Conditional implicationKannan–Lovász–Simonovits conjectureBizeul et al. 2026

197. ●Proved
     Unbounded compactly supported velocity prevents smooth continuation

     Conditional implicationNavier–Stokes existence and smoothnessOpenAI 2026

198. ○Open
     Unforced global regularity in the whole space

     Main statementNavier–Stokes existence and smoothnessper Fefferman (official description)

199. ○Open
     Unforced global regularity on the three-torus

     VariantNavier–Stokes existence and smoothnessper Fefferman (official description)

200. ●Proved
     Uniform positive curvature of the Chernoff density

     Main statementStrong log-concavity of the Chernoff densityZhang & Zhou 2026

201. ○Open
     VP versus VNP

     VariantP versus NPWigderson 2019

202. ●Proved
     Why the radius one is sharp

     Supporting resultSendov’s conjectureTao 2026

203. ●Proved
     Why the rainbow conjecture would imply the directed bound

     Conditional implicationCaccetta–Häggkvist cycle boundHompe & Huynh 2025