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Geometric Constraints in Link Isotopy
Jos\'e Ayala
https://arxiv.org/abs/2506.04442 https://arxiv.org/pdf/2506.04442

Geometric Constraints in Link Isotopy
We prove the existence of families of distinct isotopy classes of physical unknots through the key concept of parametrised thickness. These unknots have prescribed length, tube thickness, a uniform bound on curvature, and cannot be disentangled into a thickened round circle by an isotopy that preserves these constraints throughout. In particular, we establish the existence of \emph{gordian unknots}: embedded tubes that are topologically trivial but geometrically locked, confirming a long-standi…

Isotypic blocks of finite groups algebras that are not $p$-permutation equivalent
John Revere McHugh
https://arxiv.org/abs/2506.03446 https://

Isotypic blocks of finite groups algebras that are not $p$-permutation equivalent
We show that Kessar's isotypy between Galois conjugate blocks of finite group algebras does not always lift to a $p$-permutation equivalence. We also provide examples of Galois conjugate blocks which are isotypic but not $p$-permutation equivalent. These results help to clarify the distinction between a $p$-permutation equivalence and an isotypy, and may be useful in determining necessary and sufficient conditions for when an isotypy lifts to a $p$-permutation equivalence.

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Bridging the Silos of Digitalization and Sustainability by Twin Transition: A Multivocal Literature Review
Baran Shajari, Istvan David
https://arxiv.org/abs/2506.04267

Bridging the Silos of Digitalization and Sustainability by Twin Transition: A Multivocal Literature Review
Twin transition is the method of parallel digital and sustainability transitions in a mutually supporting way or, in common terms, "greening of and by IT and data." Twin transition reacts to the growing problem of unsustainable digitalization, particularly in the ecological sense. Ignoring this problem will eventually limit the digital adeptness of society and the problem-solving capacity of humankind. Information systems engineering must find ways to support twin transition journeys through it…

I really like this approach
https://infosec.exchange/@masek/114624183034377452

This https://arxiv.org/abs/2310.14846 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Thin Gordian Unlinks
A gordian unlink is a finite number of unknots that are not topologically linked, each with prescribed length and thickness, and that cannot be disentangled into the trivial link by an isotopy preserving length and thickness throughout. In this note, we provide the first examples of gordian unlinks. As a consequence, we identify the existence of isotopy classes of unknots that differ from those in classical knot theory. More generally, we present a one-parameter family of gordian unlinks with…

Neutron emission following nuclear muon capture on palladium isotopes
T. Y. Saito, M. Niikura, T. Matsuzaki, S. Abe, K. Ishida, S. Kawase, Y. Kawashima, T. Koiwai, K. Matsui, S. Momiyama, A. Nambu, H. Otsu, H. Sakurai, A. Sato, X. Sun, A. Taniguchi, D. Tomono, H. Wang, Y. Watanabe, K. Wimmer
https://arxiv.org/abs/2508.00377

Neutron emission following nuclear muon capture on palladium isotopes
The energy spectra of the neutrons emitted following nuclear muon capture on palladium isotopes ($A=104$, 105, 106, 108, and 110) were measured using isotopically enriched target. \item[Method] The experiment was performed at the MuSIC-M1 beamline at the Research Center for Nuclear Physics (RCNP), Osaka University. The neutrons and $γ$ rays were detected with twenty-one liquid scintillators and BaF$_2$ detectors. The time-of-flight method was used to determine the neutron energy. \item[Results…

Pointed Racks and Their Applications to Braid Theory
Angel Apollos, Jose Ceniceros
https://arxiv.org/abs/2508.03013 https://arxiv.org/pdf/2508.03013…

Pointed Racks and Their Applications to Braid Theory
We define a new algebraic structure called a \emph{pointed rack} and use it to construct ambient isotopy invariants of $ n $-braids. We first introduce an integer-valued invariant of braids using pointed racks. This is then strengthened by defining a matrix-valued invariant using racks. Moreover, our invariant determines the rack coloring invariant previously defined for the closure of the braid. Finally, we include examples of braids that are distinguished by these new invariants.

Profiles of Critical Flat Ribbon Knots
Jos\'e Ayala
https://arxiv.org/abs/2506.04403 https://arxiv.org/pdf/2506.04403

Profiles of Critical Flat Ribbon Knots
The main open problem in geometric knot theory is to provide a tabulation of knots based on an energy criterion, with the goal of presenting this tabulation in terms of global energy minimisers within isotopy classes, often referred to as ideal knots. Recently, the first examples of minimal length diagrams and their corresponding length values have been determined by Ayala, Kirszenblat, and Rubinstein. This article is motivated by the scarcity of examples despite several decades of intense rese…

Gordian split links in the Gehring ropelength problem
Friedrich Bauermeister
https://arxiv.org/abs/2506.04644 https://arxiv.org/pdf/2…

Gordian split links in the Gehring ropelength problem
A thick link is a link in Euclidean three-space such that each component of the link lies at distance at least 1 from every other component. Strengthening the notion of thickness, we define a thickly embedded link to be a thick link whose open radius-1/2 normal disk bundles of all components are embedded. The Gehring ropelength problem asks how large the sum of the lengths of the components of a thick (respectively thickly embedded) link must be, given the link homotopy (respectively isotopy) c…