Testing the weak cosmic censorship conjecture in the massive gravitational theories by Jie Jiang

“…This result implies that the weak cosmic censorship conjecture is satisfied in the gravitational theories with massive graviton.…”
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On a conjecture concerning total domination subdivision number in graphs by S. Kosari, Z. Shao, R. Khoeilar, H. Karami, S. M. Sheikholeslami, G. Hao

“…In this paper, we show that for some classes of graphs G, which partially solve the conjecture presented by Favaron et al.…”
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Supersymmetric Cardy formula and the Weak Gravity Conjecture in AdS/CFT by Minseok Cho, Sunjin Choi, Ki-Hong Lee, Jaewon Song

“…Abstract The Weak Gravity Conjecture (WGC) in anti-de Sitter spacetime (AdS) asserts the existence of an operator in the boundary conformal field theory (CFT) whose scaling dimension-to-charge ratio satisfies a certain upper bound. …”
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Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians by Lakshmibai Venkatramani, Raghavan Komaranapuram, Sankaran Parameswaran

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Nonperturbative test of the Maldacena-Milekhin conjecture for the BMN matrix model by Stratos Pateloudis, Georg Bergner, Norbert Bodendorfer, Masanori Hanada, Enrico Rinaldi, Andreas Schäfer

“…Abstract We test a conjecture by Maldacena and Milekhin for the ungauged version of the Berenstein-Maldacena-Nastase (BMN) matrix model by lattice Monte Carlo simulation. …”
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Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues by Krushkal Samuel

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A conjecture of Mallows and Sloane with the universal denominator of Hilbert series by Zhang Yang, Nan Jizhu, Ma Yongsheng

“…However, the conjecture does not hold in general by a well-known counterexample of Stanley. …”
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The difference vectors for convex sets and a resolution of the geometry conjecture by Alwadani, Salihah, Bauschke, Heinz H., Revalski, Julian P., Wang, Xianfu

“…The geometry conjecture, which was posed nearly a quarter of a century ago, states that the fixed point set of the composition of projectors onto nonempty closed convex sets in Hilbert space is actually equal to the intersection of certain translations of the underlying sets.In this paper, we provide a complete resolution of the geometry conjecture. …”
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Tests of the Charge Convexity Conjecture in Caswell-Banks-Zaks theory by Ofer Aharony, Yacov-Nir Breitstein

“…More precisely, this was conjectured to be true when q is restricted to positive integer multiples of some integer q 0. …”
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Anisotropic constant-roll inflation with noncommutative model and swampland conjectures by J. Sadeghi, S. Noori Gashti

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IGUSA’S CONJECTURE FOR EXPONENTIAL SUMS: OPTIMAL ESTIMATES FOR NONRATIONAL SINGULARITIES by RAF CLUCKERS, MIRCEA MUSTAŢĂ, KIEN HUU NGUYEN

“…We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa’s conjecture on exponential sums, with the log canonical threshold in the exponent of the estimates. …”
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Scale and quality of Peccei-Quinn symmetry and weak gravity conjectures by Wen Yin

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Conjecture on the butterfly velocity across a quantum phase transition by Matteo Baggioli, Bikash Padhi, Philip W. Phillips, Chandan Setty

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Domination Game: Extremal Families for the 3/5-Conjecture for Forests by Henning Michael A., Löwenstein Christian

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Solution of the Chen-Chvátal conjecture for specific classes of metric spaces by Juan Alberto Rodríguez-Velázquez

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Postoperative C5 Palsy: Conjectured Causes and Effective Countermeasures by Shigeru Hirabayashi, Tomoaki Kitagawa, Iwao Yamamoto, Kazuaki Yamada, Hirotaka Kawano

“…These countermeasures have been proved effective, and may support the nerve root injury theory as the main conjectured theory on the causes of C5 palsy.…”
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Special Cases of the Parking Functions Conjecture and Upper-Triangular Matrices by Paul Levande

“…We examine the $q=1$ and $t=0$ special cases of the parking functions conjecture. The parking functions conjecture states that the Hilbert series for the space of diagonal harmonics is equal to the bivariate generating function of $area$ and $dinv$ over the set of parking functions. …”
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Solving Two Conjectures regarding Codes for Location in Circulant Graphs by Ville Junnila, Tero Laihonen, Gabrielle Paris

“…Moreover, they proved that the lower bound is strict when $n \equiv 0, 1, 4 \pmod{6}$ and conjectured that the lower bound can be increased by one for other $n$. …”
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A Min-Max theorem about the Road Coloring Conjecture by Rajneesh Hegde, Kamal Jain

“…The Road Coloring Conjecture is an old and classical conjecture e posed in Adler and Weiss (1970); Adler et al. (1977). …”
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The Trans-Planckian Censorship Conjecture in Different Frameworks of Viable Inflation by Bruno Sanna, Lorenzo Sebastiani

“…We review the recently proposed <i>Trans-Planckian Censorship Conjecture</i> (TCC) that stems from the trans-Planckian problem of cosmological perturbations. …”
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