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Topological invariant for holographic Weyl-Nodal line coexisting semimetal
Xiantong Chen, Xuanting Ji, Ya-Wen Sun
https://arxiv.org/abs/2509.15574 https://…

Topological invariant for holographic Weyl-Nodal line coexisting semimetal
The presence of a topological phase in a topological many-body system can be distinguished through the analysis of topological invariants. In the present study, the topological invariants for the strongly coupled holographic semimetals have been systematically computed, especially focusing on the holographic Weyl-Nodal line coexisting semimetal. The topological invariants that we calculate include the Weyl charge, the topological charges for a nodal ring $ζ_0$, $ζ_1$, $ζ_2$ and an additional…

From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
Kiran Babasaheb Estake, T. R. Vishnu, Dibyendu Roy
https://arxiv.org/abs/2508.14560

From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
We propose a Hermitian quadratic bosonic model (QBH) whose dynamical matrix exhibits distinct topological and dynamical phenomena depending on whether the hopping and pairing amplitudes are real or purely imaginary. In the real-parameter regime, the dynamical matrix is unitarily equivalent to four decoupled copies of the sublattice-symmetric non-Hermitian Su-Schrieffer-Heeger (nSSH2) model, thereby inheriting its topological phases and energy spectrum-including the Möbius phase, a gapless topo…

GW/DT invariants and 5D BPS indices for strips from topological recursion
Sibasish Banerjee, Alexander Hock, Olivier Marchal
https://arxiv.org/abs/2508.15459 https://

GW/DT invariants and 5D BPS indices for strips from topological recursion
Topological string theory partition function gives rise to Gromov-Witten invariants, Donaldson-Thomas invariants and 5D BPS indices. Via the remodeling conjecture connecting Topological Recursion and topological string theory for toric Calabi-Yau 3-folds, a more direct connection is studied for the subclass of strip geometries. In doing so, new developments in the theory of topological recursion are applied as its extension to Logarithmic Topological Recursion (Log-TR) and the universal $x$--$y…

Typed Topological Structures Of Datasets
Wanjun Hu
https://arxiv.org/abs/2508.14008 https://arxiv.org/pdf/2508.14008

Typed Topological Structures Of Datasets
A datatset $X$ on $R^2$ is a finite topological space. Current research of a dataset focuses on statistical methods and the algebraic topological method \cite{carlsson}. In \cite{hu}, the concept of typed topological space was introduced and showed to have the potential for studying finite topological spaces, such as a dataset. It is a new method from the general topology perspective. A typed topological space is a topological space whose open sets are assigned types. Topological concepts and m…

Metrizability, connectedness, completeness and boundedness of generalized $u$-topology and $m$-topology in $C(X)$
Soumajit Dey, Sudip Kumar Acharyya, Dhananjoy Mandal
https://arxiv.org/abs/2508.14651

Metrizability, connectedness, completeness and boundedness of generalized $u$-topology and $m$-topology in $C(X)$
If $I$ is an ideal in the ring $C(X)$ of all real valued continuous functions defined over a Tychonoff space $X$, then $X$ is called $I$-$pseudocompact$ if the set $X\setminus \bigcap Z[I]$ is a bounded subset of $X$. Corresponding to $I$, the $m^I$-topology and $u^I$-topology on $C(X)$, generalizing the well-known $m$-topology and $u$-topology in $C(X)$ respectively are already there in the literature. It is proved amongst others that the $m^I$-topology is first countable if and only if the $u…

Bakkt shares jump 40% after naming Mike Alfred, the crypto veteran who co-founded Digital Assets Data, to its board (RT Watson/The Block)
https://www.theblock.co/post/371733/bakkt-stock-jumps-over-40-after-naming-crypto-vet-mike-alf…

AI Methods for Permutation Circuit Synthesis Across Generic Topologies
Victor Villar, Juan Cruz-Benito, Ismael Faro, David Kremer
https://arxiv.org/abs/2509.16020 https://

AI Methods for Permutation Circuit Synthesis Across Generic Topologies
This paper investigates artificial intelligence (AI) methodologies for the synthesis and transpilation of permutation circuits across generic topologies. Our approach uses Reinforcement Learning (RL) techniques to achieve near-optimal synthesis of permutation circuits up to 25 qubits. Rather than developing specialized models for individual topologies, we train a foundational model on a generic rectangular lattice, and employ masking mechanisms to dynamically select subsets of topologies during…

Poseidon, an AI-focused decentralized data layer built on the Story protocol, raised a $15M seed led by a16z (Daniel Kuhn/The Block)
https://www.theblock.co/post/363702/a16z-leads-15-million-seed-roun…

Thermodynamic topology of Einstein-Maxwell-Dilaton Theories
H. Babaei-Aghbolagh, Habib Esmaili, Song He, Hosein Mohammadzadeh
https://arxiv.org/abs/2508.14453 https://

Thermodynamic topology of Einstein-Maxwell-Dilaton Theories
We present a systematic investigation of the thermodynamic topology for a broad class of asymptotically charged Anti-de Sitter (AdS) black holes in Einstein-Maxwell-Dilaton (EMD) theories, examining how scalar coupling parameters and spacetime dimensions influence black hole thermodynamics. Employing a topological approach that utilizes the torsion number of vector fields constructed from the generalized free energy, we characterize black hole states as topological defects within the thermodyna…