arXiv:2609. 03801v1 Announce Type: new Abstract: We study the ordered Bernoulli-word kernel f(p,n,k)=p^k(1-p)^(n-k) and the geometry generated by its inverse-integer level sets.
We study the ordered Bernoulli-word kernel f(p,n,k)=p^k(1-p)^(n-k) and the geometry generated by its inverse-integer level sets. The binary level 2^(-n) selects p=1/2 as the unique real split-independent anchor.
arXiv:2609. 17899v1 Announce Type: new Abstract: We extend the discrete complex complement quotient (DCCQ) framework from binary Bernoulli counts to multinomial count compositions.
arXiv:2504. 19451v4 Announce Type: replace-cross Abstract: This paper presents two concrete applications of Artificial Intelligence to algorithmic and analytic number theory.
arXiv:2604. 02995v3 Announce Type: replace-cross Abstract: We introduce the penalised Saito functional $\mathfrak S_{\lambda,\beta}(\mathcal{A};d_1,d_2)$ for a reduced arrangement $\mathcal{A}$ of $n$ lines and a prescribed pair $d_1+d_2=n-1$.
arXiv:2609.23249v1 Announce Type: new Abstract: The Fresnel wave surface governs the propagation of light in a transparent biaxial crystal. It is a special Kummer quartic, and we identify it exactly....
The Fresnel wave surface governs the propagation of light in a transparent biaxial crystal. It is a special Kummer quartic, and we identify it exactly. Over the complex numbers the wave surface of a c...
arXiv:2604. 01275v3 Announce Type: replace-cross Abstract: In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization.
arXiv:2607. 09906v1 Announce Type: cross Abstract: We present, to our knowledge, the first adaptation of Pauli Correlation Encoding (PCE) to quantum topological data analysis, reformulating Betti number estimation as a depth-efficient variational optimization over a compressed qubit register.
arXiv:2609. 17926v1 Announce Type: new Abstract: The standard geometric derivation of neural scaling exponents takes the intrinsic dimension of a data manifold as its input.
arXiv:2605. 29151v2 Announce Type: replace-cross Abstract: We prove real-rootedness for the Poincar\'e polynomial \[ P_n(t)=\sum_{i=0}^{n-3} \dim H^{2i}(\overline{\mathcal M}_{0,n};\mathbb{Q})t^i \] of the Deligne--Mumford moduli space $\overline{\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi--Chen--Marcolli.
arXiv:2606. 08985v1 Announce Type: new Abstract: While neural collapse (NC) predicts that a $K$-class-balanced classifier should organize terminal representations as a $(K-1)$-dimensional simplex equiangular tight frame (ETF), modular addition consistently enters a different regime: networks compress to a two-dimensional cyclic geometry in which both classifier weights and token embeddings lie on circles.
arXiv:2608. 14369v1 Announce Type: cross Abstract: We consider the notion of shattering introduced by Ben Arous and Jagannath for spherical pure $p$-spin glasses with overlap $q$.