Tootfinder

Synthesis Benchmarks for Automated Reasoning
M\'arton Hajdu, Petra Hozzov\'a, Laura Kov\'acs, Andrei Voronkov, Eva Maria Wagner, Richard Steven \v{Z}ilin\v{c}\'ik
https://arxiv.org/abs/2507.19827

Synthesis Benchmarks for Automated Reasoning
Program synthesis is the task of constructing a program conforming to a given specification. We focus on deductive synthesis, and in particular on synthesis problems with specifications given as $\forall\exists$-formulas, expressing the existence of an output corresponding to any input. So far there has been no canonical benchmark set for deductive synthesis using the $\forall\exists$-format and supporting the so-called uncomputable symbol restriction. This work presents such a data set, compos…

The pure spinor superparticle and 10D super-Yang-Mills amplitudes
Max Guillen, Marcelo dos Santos, Eggon Viana
https://arxiv.org/abs/2508.19601 https://arx…

The pure spinor superparticle and 10D super-Yang-Mills amplitudes
We present a prescription for computing tree-level scattering amplitudes in 10D super-Yang-Mills (SYM) theory using the pure spinor worldline formalism. The pure spinor formalism has proven to be a powerful framework for studying supersymmetric field theories, providing manifestly covariant and BRST-invariant formulations of amplitudes. By incorporating the worldline approach, we construct a first-quantized representation of SYM amplitudes in 10D, where interactions are encoded through the inse…

A Formalization of the Yul Language and Some Verified Yul Code Transformations
Alessandro Coglio (Kestrel Institute), Eric McCarthy (Kestrel Institute)
https://arxiv.org/abs/2507.19012

A Formalization of the Yul Language and Some Verified Yul Code Transformations
Yul is an intermediate language used in the compilation of the Solidity programming language for Ethereum smart contracts. The compiler applies customizable sequences of transformations to Yul code. To help ensure the correctness of these transformations and their sequencing, we used the ACL2 theorem prover to develop a formalization of the syntax and semantics of Yul, proofs relating static and dynamic semantics, a formalization of some Yul code transformations, and correctness proofs for thes…

Björn Müller, researcher at #MPSGoettingen and #IMPRS at #UniGoettingen graduate, has been awarded the Otto Hahn Medal for outstanding achievements in his dissertation. The

An approximate zero-one law via the Dialectica interpretation
Thomas Powell, Alex Wan
https://arxiv.org/abs/2508.20849 https://arxiv.org/pdf/2508.20849

An approximate zero-one law via the Dialectica interpretation
Zero-one laws state that probabilistic events of a certain type must occur with probability either $0$ or $1$, and nothing in between. We formulate a syntactic zero-one law, which enjoys good logical properties while being broadly applicable in probability theory. Then, inspired by Gödel's Dialectica interpretation, we finitise it: The result is an approximate zero-one law which states that events with a particular finite structure occur with probability close to $0$ or $1$ up to an arbitrary …

Operational Experience of the NML Cryogenic Plant at the FAST Test Facility
Timothy Wallace (Fermilab), Joaquim Creus-Prats (Fermilab), Joseph Hurd (Fermilab), Michael J White (Fermilab), Jerry Makara (Fermilab), Liujin Pei (Fermilab), Benjamin Hansen (Fermilab), Jay Theilacker (Fermilab), Rick Bossert (Fermilab), Alexander Martinez (Fermilab), James K Santucci (Fermilab), Sasha Romanov (Fermilab)

Operational Experience of the NML Cryogenic Plant at the FAST Test Facility
The NML cryogenic plant cools two individually cryostated superconducting radio frequency (SRF) capture cavities and one prototype ILC cryomodule with eight SRF cavities. This complex accelerates electrons at 150 MeV for the Integrable Optics Test Accelerator (IOTA) ring, located at the Fermilab Accelerator Science and Technology (FAST) facility. The cryogenic plant is composed of two nitrogen precooled Tevatron satellite refrigerators, two Mycom 2016C compressors, a cryogenic distribution syst…

Who Wins the Multi-Structural Game?
Ronald Fagin, Neil Immerman, Phokion Kolaitis, Jonathan Lenchner, Rik Sengupta
https://arxiv.org/abs/2507.18718 https://

Who Wins the Multi-Structural Game?
Combinatorial games played between two players, called Spoiler and Duplicator, have often been used to capture syntactic properties of formal logical languages. For instance, the widely used Ehrenfeucht-Fraïssé (EF) game captures the syntactic measure of quantifier rank of first-order formulas. For every such game, there is an associated natural decision problem: "given an instance of the game, does Spoiler win the game on that instance?" For EF games, this problem was shown to be PSPACE-comp…

Tree-level 11D supergravity amplitudes from the pure spinor worldline
Max Guillen, Marcelo dos Santos, Eggon Viana
https://arxiv.org/abs/2508.19748 https://

Tree-level 11D supergravity amplitudes from the pure spinor worldline
We develop a pure spinor worldline formalism for computing tree-level scattering amplitudes in 11D supergravity. Focusing first on the 4-point amplitude, we demonstrate that our prescription is consistent with BRST symmetry and gauge invariance, and that the resulting expression is invariant under permutation of the external particles. Remarkably, the amplitude admits a compact representation in pure spinor superspace and agrees precisely with the result obtained via perturbiner methods. We fur…

The 11D pure spinor ghost number zero vertex operator
Max Guillen, Marcelo dos Santos, Eggon Viana
https://arxiv.org/abs/2508.19744 https://arxiv.org/pdf/2…

The 11D pure spinor ghost number zero vertex operator
The 11D pure spinor worldline has been proved to successfully describe the physical states of 11D supergravity in a manifestly super-Poincaré covariant fashion. Within this framework, the computation of scattering amplitudes requires the existence of vertex operators carrying different ghost numbers. A recent no-go theorem demonstrated the impossibility of constructing a ghost number zero vertex operator consistent with 11D supergravity in the minimal pure spinor formalism. In this letter, we …

Lean Meets Theoretical Computer Science: Scalable Synthesis of Theorem Proving Challenges in Formal-Informal Pairs
Terry Jingchen Zhang, Wenyuan Jiang, Rongchuan Liu, Yisong Wang, Junran Yang, Ning Wang, Nicole Ni, Yinya Huang, Mrinmaya Sachan
https://arxiv.org/abs/2508.15878

Lean Meets Theoretical Computer Science: Scalable Synthesis of Theorem Proving Challenges in Formal-Informal Pairs
Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by limited datasets due to the high cost of manual curation and the scarcity of challenging problems with verified formal-informal correspondences. We propose leveraging theoretical computer science (TCS) as a scalable source of rigorous proof problems, where a…