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We extend the exact fixed-point tensor construction of Cheng et al. to fermionic minimal models, providing an analytic construction of fixed-point tensors for fermionic rational conformal field theories. The fermionic fixed-point tensor is defined as a correlation function of boundary-changing operators on a triangle, with careful treatment of fermionic parity and spin structure. Boundary tensors are also constructed and combined with triangle tensors to form strips, enabling the extraction of scaling dimensions for boundary-changing operators. The construction incorporates modified weights for shrinkable boundary conditions, systematic depiction of spin structures, recovering both the Neveu-Schwarz and Ramond sectors. As a benchmark, our tensor with a minimal truncation of descendant levels yields convergence to the exact bulk scaling dimensions of many low energy states for the free Majorana fermion ($c=1/2$), demonstrating the efficiency of approximate fixed point tensors from boundary changing operators. We also make use of a more general description of fermionic CFTs based on fermionisation of rational bosonic CFTs, and make a generic prescription for discretisation making use of their connections to modular tensor categories. We show that the discretised spin structures on a spin surface naturally recover the signs needed to recover the R/NS sectors. We propose that the collection of OPE coefficients of the discretised 2d CFT can be naturally interpreted as a state-sum of spin-TQFTs, analogous to the bosonic case. This work provides analytically computed starting points for tensor network simulations of fermionic critical phenomena.

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In a former paper we proposed a model for the quantization of gravity by working in a bundle $E$ where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not in the base space. Therefore, we now discard the Wheeler-DeWitt equation and express the Hamilton constraint differently, either with the help of the Hamilton equations or by employing a geometric evolution equation. There are two possible modifications possible which both are equivalent to the Hamilton constraint and which lead to two new models. In the first model we obtain a hyperbolic operator that acts in the fibers as well as in the base space and we can construct a symplectic vector space and a Weyl system. In the second model the resulting equation is a wave equation in $\so \times (0,\infty)$ valid in points $(x,t,\xi)$ in $E$ and we look for solutions for each fixed $\xi$. This set of equations contains as a special case the equation of a quantized cosmological Friedman universe without matter but with a cosmological constant, when we look for solutions which only depend on $t$. Moreover, in case $\so$ is compact we prove a spectral resolution of the equation.

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This research provides insights for the separation of cryptocurrencies from other assets. Using dimensionality reduction techniques, we show that most of the variation among cryptocurrencies, stocks, exchange rates, commodities, bonds, and real estate indexes can be explained by the tail, memory and moment factors of their log-returns. By applying various classification methods, cryptocurrencies are categorized as a separate asset class, mainly due to the tail factor. The main result is the complete separation of cryptocurrencies from the other asset types, using the Maximum Variance Components Split method. Additionally, we show that cryptocurrencies tend to exhibit similar characteristics over time and become more distinguished from other asset classes (synchronic evolution).

We show that the pre-order defined on the category of contact manifolds by arbitrary symplectic cobordisms is considerably less rigid than its counterparts for exact or Stein cobordisms: in particular, we exhibit large new classes of contact 3-manifolds which are symplectically cobordant to something overtwisted, or to the tight 3-sphere, or which admit symplectic caps containing symplectically embedded spheres with vanishing self-intersection. These constructions imply new and simplified proofs of several recent results involving fillability, planarity, and non-separating contact type embeddings. The cobordisms are built from symplectic handles of the form Σ × D and Σ × [−1, 1] × S1, which have symplectic cores and can be attached to contact 3-manifolds along sufficiently large neighborhoods of transverse links and preLagrangian tori. We also sketch a construction of J-holomorphic foliations in these cobordisms and formulate a conjecture regarding maps induced on Embedded Contact Homology with twisted coefficients.