Tootfinder

Investigating the Araki-Uhlmann relative entropy between two coherent states in relativistic Quantum Field Theory
Jo\~ao G. A. Carib\'e, Marcelo S. Guimaraes, Itzhak Roditi, Silvio P. Sorella
https://arxiv.org/abs/2508.17165

Investigating the Araki-Uhlmann relative entropy between two coherent states in relativistic Quantum Field Theory
A numerical setup for investigating the Araki-Uhlmann relative entropy between two coherent states is presented for a scalar massive Quantum Field Theory ($1+1$)-dimensional Minkowski spacetime. These states are constructed using smeared Weyl operators compactly supported in two diamond regions belonging to the right Rindler wedge. Using this setup, we verified the known properties of the relative entropy, namely: positivity, increase with the size of the spacetime regions considered, decrease …

Panorbital residues and elliptic summability
Carlos E. Arreche, Matthew W. Babbitt
https://arxiv.org/abs/2508.18247 https://arxiv.org/pdf/2508.18247…

Panorbital residues and elliptic summability
For $τ$ the translation automorphism defined by a non-torsion point in an elliptic curve, we consider the elliptic summability problem of deciding whether a given elliptic function $f$ is of the form $f=τ(g)-g$ for some elliptic function $g$. We introduce two new panorbital residues and show that they, together with the orbital residues introduced in 2018 by Dreyfus, Hardouin, Roques, and Singer, comprise a complete obstruction to the elliptic summability problem. The underlying elliptic curv…

Elliptic Curves, Riordan arrays and Lattice Paths
Paul Barry
https://arxiv.org/abs/2507.16765 https://arxiv.org/pdf/2507.16765…

Elliptic Curves, Riordan arrays and Lattice Paths
In this note, we show that to each elliptic curve of the form $$y^2-axy-y=x^3-bx^2-cx,$$ we can associate a family of lattice paths whose step set is determined by the parameters of the elliptic curve. The enumeration of these lattice paths is by means of an associated Riordan array. The curves and the paths have associated Somos $4$ sequences which are essentially the same. For the curves the link to Somos $4$ sequences is a classical result, via the elliptic divisibility sequence. For the pat…

Breaking a 5-Bit Elliptic Curve Key using a 133-Qubit Quantum Computer
Steve Tippeconnic
https://arxiv.org/abs/2507.10592 https://arx…

Breaking a 5-Bit Elliptic Curve Key using a 133-Qubit Quantum Computer
This experiment breaks a 5-bit elliptic curve cryptographic key using a Shor-style quantum attack. Executed on IBM's 133-qubit ibm_torino with Qiskit Runtime 2.0, a 15-qubit circuit, comprised of 10 logical qubits and 5 ancilla, interferes over an order-32 elliptic curve subgroup to extract the secret scalar k from the public key relation Q = kP, without ever encoding k directly into the oracle. From 16,384 shots, the quantum interference reveals a diagonal ridge in the 32 x 32 QFT outcome spac…

Symplectification of Circular Arcs and Arc Splines
Stefan G\"ossner
https://arxiv.org/abs/2508.07726 https://arxiv.org/pdf/2508.07726

Symplectification of Circular Arcs and Arc Splines
In this article, circular arcs are considered both individually and as elements of a piecewise circular curve. The endpoint parameterization proves to be quite advantageous here. The perspective of symplectic geometry provides new vectorial relationships for the circular arc. Curves are considered whose neighboring circular elements each have a common end point or, in addition, a common tangent. These arc splines prove to be a one-parameter curve family, whereby this parameter can be optimized …

Dissecting Bar-Induced Stellar Kinematics in Disk Galaxies: The Bisymmetric Model and Rotation Curve Modifications
Seungwon Baek, Woong-Tae Kim, Dajeong Jang, Taehyun Kim
https://arxiv.org/abs/2507.15204

Dissecting Bar-Induced Stellar Kinematics in Disk Galaxies: The Bisymmetric Model and Rotation Curve Modifications
We analyze bars formed in $N$-body simulations to investigate two key aspects of stellar kinematic structure of barred galaxies: the angular distributions of the radial and azimuthal components of stellar velocities, and the impact of bars on rotation curves. We find that stars on bar-supporting $x_1$-like orbits exhibit characteristic sawtooth-like radial velocity patterns and arch-like tangential velocity patterns as a function of azimuth. In contrast, stars on box and disk orbits show little…

Doubly robust pointwise confidence intervals for a monotonic continuous treatment effect curve
Charles R. Doss
https://arxiv.org/abs/2508.08415 https://arx…

Doubly robust pointwise confidence intervals for a monotonic continuous treatment effect curve
We study nonparametric inference for the causal dose-response (or treatment effect) curve when the treatment variable is continuous rather than binary or discrete. We do this by developing doubly robust confidence intervals for the continuous treatment effect curve (at a fixed point) under the assumption that it is monotonic, based on inverting a likelihood ratio-type test. Monotonicity of the treatment effect curve is often a very natural assumption, and this assumption removes the need to cho…

Hyperbolic spaces not quasi-isometric to curve complexes
Javier Aramayona, Hugo Parlier, Richard Webb
https://arxiv.org/abs/2507.08086 https://

Hyperbolic spaces not quasi-isometric to curve complexes
We identify a condition that prevents a hyperbolic space from being quasi-isometric to the curve complex of any non-sporadic surface. Our result applies to several hyperbolic complexes, including arc complexes, disk complexes, non-separating curve complexes, (hyperbolic) pants complexes, and to free splitting complexes of free groups.

Restricted tangent bundle of rational curves on projective hypersurfaces
Lucas Mioranci
https://arxiv.org/abs/2507.13927 https://arxi…

Restricted tangent bundle of rational curves on projective hypersurfaces
We determine all triples $(e,d,n)$ for which a general degree $d$ hypersurface $X\subset \mathbb{P}^n$ contains a degree $e$ rational curve $C$ with balanced restricted tangent bundle $T_X|_C$. In addition, we show how to compute explicit examples of hypersurfaces with balanced $T_X|_C$ when $C$ is a rational normal curve.

Curve semistable Higgs bundles and smooth projective varieties whose canonical bundle is ample
Armando Capasso
https://arxiv.org/abs/2508.12062 https://arx…

Curve semistable Higgs bundles and smooth projective varieties whose canonical bundle is ample
Considering the so-called Simpson system on smooth projective varieties, defined over an algebraically closed field of characteristic $0$, whose canonical bundle is ample, I prove the stability of this Higgs bundle. From this I obtain another proof of the Guggenheimer-Yau inequality. Where the equality holds, I prove that the discriminant class of the Simpson system vanishes. This follows from the study of the relations between ampleness and numerically nefness for Higgs bundles which "feel" th…