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. 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.
By Y. Kenan Y{\i}lmaz
arXiv:2603. 20861v2 Announce Type: replace-cross Abstract: The homology of an ample groupoid is computed from the complex of compactly supported continuous functions on the nerve.
By Luciano Melodia
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.
By Gergely B\'erczi, Young-Hoon Kiem
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.
By Chon-Fai Kam, Miloud Bessafi, Fr\'ed\'eric Cadet
arXiv:2606. 10806v1 Announce Type: new Abstract: Moonshine is an autonomous agent whose central objective is to generate mathematical conjectures.
By Xiaoyang Chen, Xiang Jiang