Hugging Face Trending Papers
Exact Quotients of Fresnel-Kummer Surfaces and Certified Biaxial Refraction
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arXiv Computer Vision
Sep 22
Exact Quotients of Fresnel-Kummer Surfaces and Certified Biaxial Refraction
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....
arXiv Machine Learning
Sep 4
From Ordered Bernoulli Levels to Critical-Line Geometry: Integer Quantization, Bernoulli Residual Phase, and Prime-Power Spectra
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.
Hugging Face Trending Papers
Sep 3
From Ordered Bernoulli Levels to Critical-Line Geometry: Integer Quantization, Bernoulli Residual Phase, and Prime-Power Spectra
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 AI
Jun 12
Real-rootedness of the Poincar\'e polynomials of $\overline{\mathcal M}_{0,n}$: an AI-assisted proof
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 Machine Learning
Jul 30
Exact Symmetry as Algebra: A Machine-Verified Tensor Calculus that Enforces Physical Selection Rules
arXiv:2605. 20440v2 Announce Type: replace Abstract: Symmetry is central to the physical sciences, yet machine learning usually captures it only approximately, leaving a residual per-step equivariance error $\varepsilon$ that compounds with depth $M$ as $M\varepsilon$, whereas exact equivariance holds at unbounded depth; we demonstrate this divergence at fourteen orders of magnitude.
arXiv AI
4d ago
Solver Agent: an Agentic AI Framework for Theoretical Physics Computations Applied to F-theory Uplifts of O3-planes and S-folds
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.