The paper introduces Solver Agent, an AI framework that uses large language models to perform calculations and proofs in mathematics and theoretical physics, tracking the solution process via a persistent ledger. It applies this framework to study global F‑theory uplifts of Type IIB orientifolds and S‑folds, establishing conditions for Weierstrass models over projective threefolds with terminal ζ_k quotient singularities to yield Ε-factorial elliptically fibered Calabi‑Yau fourfolds. The authors derive fixed‑point contributions to Hodge data and Euler characteristics, demonstrate how these corrections determine localized D3‑brane charges for tadpole cancellation, and illustrate the results with toric hypersurface constructions and methods for four‑form flux analysis in Δ=1 compactifications.
By Eliott Morgensztern, Cesar Fierro Cota, Alessandro Mininno
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: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
The paper investigates the polynomial coefficients of lightning self‑attention, treating them as coordinates of an algebraic variety. In the single‑token case it identifies the coefficient variety as a rank‑constrained Chow‑type variety and derives algebraic equations; for multiple tokens it shows that linear relations reduce the geometry to coefficients involving interactions between distinct tokens, characterized by a common linear factor and a low‑rank condition. The authors provide explicit families of determinantal, Veronese‑type, and Sylvester resultant‑based invariants, and in the rank‑one case give pencil and flattening equations that define the variety set‑theoretically, with small‑dimension computations confirming the theoretical generators.
By Yulia Alexandr, Hao Duan, Guido Mont\'ufar
arXiv:2608. 19584v1 Announce Type: new Abstract: We study landscapes for complex-parameterized networks.
By Andrew Gracyk
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
arXiv:2602. 07834v2 Announce Type: replace Abstract: The pointwise determinant ratio \[ R_\psi(z)\equiv \log\!
By D Yang Eng
arXiv:2609. 06050v1 Announce Type: cross Abstract: For a compact set $K\subset\mathbb{C}$, let $\vartheta(K)$ be the infimum of the planar areas of the unit lemniscates of all monic polynomials with zeros in $K$, allowing arbitrary degree and repeated zeros.
By Ioannis Tzachristas
arXiv:2603. 25414v4 Announce Type: replace-cross Abstract: A prevailing assumption in machine learning is that model correctness must be enforced after the fact.
By Houston Haynes
arXiv:2607. 13749v1 Announce Type: new Abstract: Neural networks trained on modular arithmetic exhibit grokking, a delayed transition from memorisation to generalisation known to depend on model capacity: too little and the network memorises slowly or not at all, too much and it generalises almost immediately.
By Chon-Fai Kam, Xavier Cadet, Miloud Bessafi, Frederic Cadet
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: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