Solver Agent: an Agentic AI Framework for Theoretical Physics Computations Applied to F-theory Uplifts of O3-planes and S-folds
Abstract
We introduce Solver Agent, an AI framework based on large language models for calculations and proofs in mathematics and theoretical physics. The solution process is tracked through a persistent ledger that records assumptions, derivations, and computations. A central agent delegates tasks to specialized sub-agents, while independent agents verify both intermediate steps and the final result. This setup improves the traceability, reproducibility, and verification of computer-assisted calculations. Applying Solver Agent, we study global F-theory uplifts of Type IIB orientifolds and their S-fold generalizations. We establish sufficient conditions for Weierstrass models over projective threefolds with terminal ℤk quotient singularities (k∈{2,3,4,6}) to give ℚ-factorial projective elliptically fibered Calabi-Yau fourfolds with isolated Gorenstein terminal quotient singularities. These geometries realize O3-planes and S-folds, where local D3-brane probes of the latter yield four-dimensional 𝒩=3 superconformal field theories. Using stringy invariants, we derive fixed-point contributions to Hodge data and Euler characteristics, and show that these Euler corrections determine the localized D3-brane charges required for tadpole cancellation. We illustrate these results using toric hypersurface constructions, where a single three-dimensional polytope determines both the Type IIB Calabi-Yau threefold and the F-theory base; here, the orientifold double cover naturally forms a bisection of an alternative genus-one-fibered uplift with discrete ℤ2 gauge symmetry. Finally, we provide methods for toric computations and four-form flux analysis in four-dimensional 𝒩=1 compactifications with non-abelian gauge sectors.
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BibTeX
@misc{morgensztern2026solver,
title = {{Solver Agent: an Agentic AI Framework for Theoretical Physics Computations Applied to F-theory Uplifts of O3-planes and S-folds}},
author = {Eliott Morgensztern and Cesar Fierro Cota and Alessandro Mininno},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35958},
eprint = {2609.35958},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05784515v1},
}
RIS
TY - UNPB
TI - Solver Agent: an Agentic AI Framework for Theoretical Physics Computations Applied to F-theory Uplifts of O3-planes and S-folds
AU - Eliott Morgensztern
AU - Cesar Fierro Cota
AU - Alessandro Mininno
PY - 2026
DA - 2026/09/28
PB - HAL
DO - 10.48550/arxiv.2609.35958
UR - https://hal.science/hal-05784515v1
AB - We introduce Solver Agent, an AI framework based on large language models for calculations and proofs in mathematics and theoretical physics. The solution process is tracked through a persistent ledger that records assumptions, derivations, and computations. A central agent delegates tasks to specialized sub-agents, while independent agents verify both intermediate steps and the final result. This setup improves the traceability, reproducibility, and verification of computer-assisted calculations. Applying Solver Agent, we study global F-theory uplifts of Type IIB orientifolds and their S-fold generalizations. We establish sufficient conditions for Weierstrass models over projective threefolds with terminal ℤ_k quotient singularities (k∈{2,3,4,6}) to give ℚ-factorial projective elliptically fibered Calabi-Yau fourfolds with isolated Gorenstein terminal quotient singularities. These geometries realize O3-planes and S-folds, where local D3-brane probes of the latter yield four-dimensional 𝒩=3 superconformal field theories. Using stringy invariants, we derive fixed-point contributions to Hodge data and Euler characteristics, and show that these Euler corrections determine the localized D3-brane charges required for tadpole cancellation. We illustrate these results using toric hypersurface constructions, where a single three-dimensional polytope determines both the Type IIB Calabi-Yau threefold and the F-theory base; here, the orientifold double cover naturally forms a bisection of an alternative genus-one-fibered uplift with discrete ℤ_2 gauge symmetry. Finally, we provide methods for toric computations and four-form flux analysis in four-dimensional 𝒩=1 compactifications with non-abelian gauge sectors.
ER -