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. 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: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:2607. 24251v1 Announce Type: cross Abstract: We investigate the extent to which the reduced minimal Weierstrass coefficients of an elliptic curve over $\mathbb{Q}$ may be computed from it's Frobenius traces.
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.
arXiv:2608. 01670v1 Announce Type: new Abstract: This paper answers the one-dimensional local root anti-concentration questions posed by Balcan, Pegden, and Sharma in the context of online optimization of piecewise-Lipschitz functions.
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:2608. 10172v1 Announce Type: new Abstract: Mechanistic interpretability explains models by identifying circuits inside them, but has no way to tell whether a circuit is a property of the model or an artifact of the method that found it.
This paper answers the one-dimensional local root anti-concentration questions posed by Balcan, Pegden, and Sharma in the context of online optimization of piecewise-Lipschitz functions. For a homogeneous feature curve and coefficients whose density relative to the uniform law on a symmetric convex body $K$ is bounded by $A$, we show that the worst-case interval-hitting constant equals $A$ times a section-averaged projective incidence speed.
arXiv:2606. 05957v1 Announce Type: new Abstract: Singular learning theory and information geometry have studied the same parameter spaces in mostly separate vocabularies: the former computes Bayesian invariants in resolved coordinates, the latter works in original coordinates under a non-degeneracy assumption that overparameterised models routinely violate.
EncoTESS is a compact Time Series Foundation Model trained on TESS 2‑minute light curves that encodes stellar variability into a fixed‑size latent space, handling noise, irregular sampling, and data gaps. It improves age estimation for young K and M stars (≤100 Myr) and older M stars (≤1 Gyr) by outperforming traditional rotation period and variability amplitude indicators. The model’s lightweight architecture (~1 % of typical TSFMs) allows deployment on standard laptops and can be extended to other TESS cadences and missions like Kepler and PLATO.