arXiv Machine Learning
Jun 5
Interpretable Analytic Calabi-Yau Metrics via Symbolic Distillation
arXiv:2602. 07834v2 Announce Type: replace Abstract: The pointwise determinant ratio \[ R_\psi(z)\equiv \log\!
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.
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arXiv AI
Jul 20
A cubical formalisation of topos causal models: intervention, sheaf gluing, and the intuitionistic do-calculus
arXiv:2607. 15629v1 Announce Type: cross Abstract: Topos causal models recast causal inference inside a topos: a causal world is a presheaf, an intervention is a characteristic map into the subobject classifier, and reasoning is carried out in the intuitionistic internal language.
arXiv AI
Jul 8
Tangent classes of matroids and wonderful compactifications
arXiv:2607. 05835v1 Announce Type: cross Abstract: For every loopless matroid $M$ and every Feichtner--Yuzvinsky building set $\mathcal{G}$ containing the top flat, we construct an integral tangent class $T_{M,\mathcal{G}}^{\mathbb{Z}}\in K_{\mathbb{Z}}(M,\mathcal{G})$; in the realizable case it specializes to the class of the tangent bundle of the corresponding wonderful compactification, it recovers the Hilbert series of the Chow ring through Hirzebruch--Riemann--Roch, and it satisfies the expected Chern-alpha lower bounds.
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 Machine Learning
Aug 4
Polyatomic Complexes: A topologically-informed learning representation for atomistic systems
arXiv:2409. 15600v3 Announce Type: replace Abstract: A representation of a molecule or material should be invariant to the symmetries of physics, unique, continuous, efficient and general.
arXiv AI
6d ago
G\"odel's and Scott's Variants of the Ontological Argument in Lean 4 and TPTP THF
arXiv:2609.26806v2 Announce Type: replace-cross Abstract: This paper presents a complete, structure-preserving port to Lean 4 of the Isabelle/HOL dataset accompanying Benzm\"uller and Scott's study o...
arXiv Computer Vision
Sep 4
Spectral Hierarchy of the Cosmic Web
The paper presents a spectral hierarchy for classifying the cosmic web by applying scale-weighting kernels to the density field before using eigenvalue-based methods. This framework unifies existing web definitions—potential/tidal, curvature-based, and higher-derivative levels—into a single, interpretable hierarchy that captures structure from large to small scales. The authors quantify the hierarchy’s information content by correlating a web contrast field with halo distributions, showing that it retains significant tracer-relevant information across scales, especially at nonlinear levels.
arXiv AI
Jun 17
From Paper to Program: Knowledge Externalization for AI-Assisted Quantum Many-Body Code Generation
arXiv:2604. 04089v3 Announce Type: replace-cross Abstract: Large language models can write scientific code, but direct paper-to-program translation remains fragile when correctness depends on tacit conventions in the literature.
arXiv Machine Learning
Jun 26
Generating Special Triangulations with Transformers
arXiv:2606. 26660v1 Announce Type: cross Abstract: Triangulations, i.
arXiv Machine Learning
Jun 11
Minimal surfaces, Knots, and Neural Networks
arXiv:2605. 26234v2 Announce Type: replace-cross Abstract: A recent conjecture by Joel Fine posits a relationship between the coefficients of the HOMFLY polynomial of a knot $K$ in the 3-sphere $S^3$, and the signed count of minimal surfaces in hyperbolic 4-space $\mathrm{H}^4$ meeting the sphere at infinity at $K$, with prescribed genus and self-intersection number.
arXiv Machine Learning
1d ago
Beyond Diagonal State Space Models: Exact Non-Abelian Group Tracking, Solvability Barriers, and Geometric Physical Manifolds
The paper introduces a new class of selective state space models (SSMs) that move beyond traditional diagonal constraints by leveraging exact non‑Abelian group tracking and solvable affine transformation groups. It reports significant performance gains, including a 0.04‑degree dead‑reckoning error, high accuracy on Dyck‑2 and deep AST scope tracking tasks, and demonstrates that strict isometry is essential for lossless long‑range associative memory.