Tootfinder

This https://arxiv.org/abs/2506.01291 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The Hasse principle for homogeneous polynomials with random coefficients over thin sets II
Let $d$ and $n$ be natural numbers. Let $ν_{d,n}: \mathbb{R}^n\rightarrow \mathbb{R}^{N}$ denote the Veronese embedding with $N=N_{n,d}:=\binom{n+d-1}{d}$, defined by listing all the monomials of degree $d$ in $n$ variables using the lexicographical ordering. Let $\langle \boldsymbol{a}, ν_{d,n}(\boldsymbol{x})\rangle\in \mathbb{Z}[\boldsymbol{x}]$ be a homogeneous polynomial in $n$ variables of degree $d$ with integer coefficients $\boldsymbol{a}$, where $\langle\cdot,\cdot\rangle$ denotes t…

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I bought Rosemary's Baby (eBook). I've always wondered 🤷‍♂️ I've never seen the movie either. The funny thing is, it came as a connection after browsing through the Beastie Boys Wikipedia page, following the path:
Beasty Boys -> Ad-Rock -> Molly Ringwald -> Tempest (1982 film) -> John Cassavetes (1929 - 1989) -> Rosemary's Baby (1968 film) -> Ira Levin (1929 - 2007).
...and then finding out there's a pricier, DRM-ed EPUB2 (2011) vs a little b…

The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
Mitchell Woolley
https://arxiv.org/abs/2506.08094 https://arxi…

The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
6d (2,0) SCFTs of type $\mathfrak{g}$ have protected subsectors that were conjectured in arxiv:1404.1079 to be captured by $\mathcal{W}_\mathfrak{g}$ algebras. We write down the crossing equations for mixed four-point functions $\langle S_{k_1} S_{k_2}S_{k_3}S_{k_4}\rangle$ of 1/2-BPS operators $S_{k_i}$ in 6d (2,0) theories and detail how a certain twist reduces this system to a 2d meromorphic CFT multi-correlator bootstrap problem. We identify the relevant 6d (2,0) $\mathcal{W}$-algebras of t…

This https://arxiv.org/abs/2409.17464 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Computation of $\langle Φ^2\rangle$ and quantum fluxes at the polar interior of a spinning black hole
Renormalization of physical quantities for quantum field theories in curved spacetimes can be achieved via the consistent subtraction of counterterms within a regularization scheme such as a point-splitting method. Pragmatic mode-sum regularization (PMR) is a point-splitting method which is particularly suitable for rotating black hole spacetimes. We extend and tailor the t-splitting variant of PMR specifically for the interior of a Kerr black hole on the axis of rotation, focusing on a minimal…

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Ronnie Hazlehurst, Gavin Sutherland, Gavin Sutherland & Fast Tunes Orchestra:
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On the analytical approach to infinite-mode Boson-Gaussian states
Jorge R. Bola\~nos-Serv\'in, Roberto Quezada, Josu\'e I. Rios-Cangas
https://arxiv.org/abs/2506.04537

On the analytical approach to infinite-mode Boson-Gaussian states
We develop an analytical approach to quantum Gaussian states in infinite-mode representation of the Canonical Commutation Relations (CCR's), using Yosida approximations to define integrability of possibly unbounded observables with respect to a state $ρ$ ($ρ$-integrability). It turns out that all elements of the commutative $*$-algebra generated by a possibly unbounded $ρ$-integrable observable $A$, denoted by $\langle A\rangle$, are normal and $ρ\, $-integrable. Besides, $\langle A\rangle$…

Yau-YauAL: A computer tool for solving nonlinear filtering problems
Yu Wang, Shuyuan Xu, Xueda Wei, Xinrui Luo, Stephen Shing-Toung Yau, Shing-Tung Yau, Rongling Wu
https://arxiv.org/abs/2506.08976

Yau-YauAL: A computer tool for solving nonlinear filtering problems
The Yau-Yau nonlinear filter has increasingly emerged as a powerful tool to study stochastic complex systems. To leverage it to a wider spectrum of application scenarios, we pack the Yau-Yau filtering ALgorithms (YauYauAL) into a package of computer software. Yau-YauAL was written in R, designed to simplify the implementation of the Yau-Yau filter for solving nonlinear filtering problems. Combining R's accessibility with C++ (via Rcpp) for computational efficiency, YauYauAL provides an intuitiv…

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🎵 Prelude a l'après-midi d'un faune
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