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Pentagramma Mirificum. II
Vadim Schechtman
https://arxiv.org/abs/2508.13586 https://arxiv.org/pdf/2508.13586

Pentagramma Mirificum. II
This article is a continuation of my previous paper on miraculous pentagrams published in Annales Scientifiques de Faculté des Sciences de Toulouse in 2013. We discuss the moduli space of miraculous pentagrams which is the Del Pezzo surface of degree 5, and present some examples related to Fibonacci numbers. We discuss also some relations between Fermat ascent and Poncelet theorem.

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Ich hab's ausprobiert:
Pentagram und Hexagram ineinander verschachteln und man kann einen altgriechischen Dämon beschwören, der in Pentametern und Hexametern Wahrheiten deklamiert.
Das einzige Problem dabei: du kannst das Gesagte nicht aufnehmen und mein Altgriechisch ist im Wesentlichen nicht existent: ich hab kein Wort verstanden.

Collapsing in polygonal dynamics
Stiegler Jean-Baptiste
https://arxiv.org/abs/2507.16432 https://arxiv.org/pdf/2507.16432

Collapsing in polygonal dynamics
Polygonal dynamics is a family of dynamical systems containing many studied systems, like the famous pentagram map. Similar collapsing phenomena seem to occur in most of these systems. We give a unifying, general definition of polygonal dynamics, and conjecture that a generic orbit collapses towards a predictable point. For the special case of ``closed polygons'', we show that the collapse point depends algebraicly on the vertices of the starting polygon, using tools called scaling symmetry and…

Memory cost of quantum contextuality with Pauli observables
Stefan Trandafir, Colm Kelleher, Ad\'an Cabello
https://arxiv.org/abs/2506.06869 https://…

Memory cost of quantum contextuality with Pauli observables
Classically simulating the quantum contextual correlations produced by sequences of ideal measurements of compatible observables requires the measured system to have an internal memory. Computing the minimum amount of memory needed is, in general, challenging. Here, building upon the work of Kleinmann et al. [New J. Phys. 13, 113011 (2011)], we prove that the memory cost for simulating the contextuality produced by the $10$ three-qubit observables of Mermin's pentagram is only $\log_2(5) \appro…

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