Tootfinder

Out of Control -- Why Alignment Needs Formal Control Theory (and an Alignment Control Stack)
Elija Perrier
https://arxiv.org/abs/2506.17846 https://…

Out of Control -- Why Alignment Needs Formal Control Theory (and an Alignment Control Stack)
This position paper argues that formal optimal control theory should be central to AI alignment research, offering a distinct perspective from prevailing AI safety and security approaches. While recent work in AI safety and mechanistic interpretability has advanced formal methods for alignment, they often fall short of the generalisation required of control frameworks for other technologies. There is also a lack of research into how to render different alignment/control protocols interoperable.…

49ers: Jennings hasn't formally asked for trade https://www.espn.com/nfl/story/_/id/45797538/49ers-say-jauan-jennings-formally-asked-trade

Approximate SMT Counting Beyond Discrete Domains
Arijit Shaw, Kuldeep S. Meel
https://arxiv.org/abs/2507.18612 https://arxiv.org/pdf/2507.18612

Approximate SMT Counting Beyond Discrete Domains
Satisfiability Modulo Theory (SMT) solvers have advanced automated reasoning, solving complex formulas across discrete and continuous domains. Recent progress in propositional model counting motivates extending SMT capabilities toward model counting, especially for hybrid SMT formulas. Existing approaches, like bit-blasting, are limited to discrete variables, highlighting the challenge of counting solutions projected onto the discrete domain in hybrid formulas. We introduce pact, an SMT model…

Variational formula for the logarithmic potential of free additive convolutions
Francesco Concetti, David Belius, Giuseppe Genovese
https://arxiv.org/abs/2506.19064

Variational formula for the logarithmic potential of free additive convolutions
We establish a general variational formula for the logarithmic potential of the free additive convolution of two compactly supported probability measure on $\R$. The formula is given in terms of the $R$-transform of the first measure, and the logarithmic potential of second measure. The result applies in particular to the additive convolution with the semicircle or Marchenko-Pastur laws, for which the formula simplifies. The logarithmic potential of additive convolutions appears for instance in…

Falsch sei freilich, dass nur der Boden unter dem Mondsee einer Privatperson gehöre, der See jedoch nicht. Alles gehöre ihr, nur gäbe es eine Dienstbarkeit (Servitut) zugunsten der Allgemeinheit an der Nutzung des Sees, so der Jurist Alfred Noll im Standard-Forum unter Verweis auf

A quadratic Abramovich-Bertram formula
Erwan Brugall\'e, Kirsten Wickelgren
https://arxiv.org/abs/2506.17854 https://arxiv.org/pd…

A quadratic Abramovich-Bertram formula
Quadratic Gromov--Witten invariants allow one to obtain an arithmetically meaningful count of curves satisfying constraints over a field $k$ without assuming that $k$ is the field of complex or real numbers. This paper studies the behavior of quadratic genus $0$ Gromov--Witten invariants during an algebraic analogue of surgery on del Pezzo surfaces. For this, we define and study (twisted) binomial coefficients in the Grothendieck--Witt group, building on work of Serre. We obtain a formula expre…

Sources: Mark Zuckerberg discussed a possible acquisition with Runway AI; the deal talks never reached a formal offer level (Bloomberg)
https://www.bloomberg.com/news/articles/2025-06-23/meta-held-deal-talks-with-st…

Conservative data-driven finite element formulation
Adriana Kulikov\'a (Glasgow Computational Engineering Centre), Andrei G. Shvarts (Glasgow Computational Engineering Centre), {\L}ukasz Kaczmarczyk (Glasgow Computational Engineering Centre), Chris J. Pearce (Glasgow Computational Engineering Centre)
https://arxiv.org/abs/25…

Conservative data-driven finite element formulation
This paper presents a new data-driven finite element framework derived with mixed finite element formulation. The standard approach to diffusion problems requires the solution of the mathematical equations that describe both the conservation law and the constitutive relations, where the latter is traditionally obtained after fitting experimental data to simplified material models. To exploit all available information and avoid bias in the material model, we follow a data-driven approach. While …

Optimization Studies of Radiation Shielding for the PIP-II Project at Fermilab
Alajos Makovec (Fermilab), Dali Georgobiani (Fermilab), Igor Rakhno (Fermilab), Igor Tropin (Fermilab)
https://arxiv.org/abs/2506.19763

Optimization Studies of Radiation Shielding for the PIP-II Project at Fermilab
The PIP-II project at Fermilab, which includes an 800-MeV superconducting LINAC, demands rigorous radiation shielding optimization to meet safety requirements. We updated the MARS geometry model to reflect new magnet and collimator designs and introduced high-resolution detector planes to better capture radiation field distributions. To overcome the significant computational demands, we implemented a well-known branching technique that drastically reduced simulation runtimes while maintaining s…

A Formalization of the Ionescu-Tulcea Theorem in Mathlib
Etienne Marion (ENS de Lyon)
https://arxiv.org/abs/2506.18616 https://arxiv.…

A Formalization of the Ionescu-Tulcea Theorem in Mathlib
We describe the formalization of the Ionescu-Tulcea theorem, showing the existence of a probability measure on the space of trajectories of a Markov chain, in the proof assistant Lean using the integrated library Mathlib. We first present a mathematical proof before exposing the difficulties which arise when trying to formalize it, and how they were overcome. We then build on this work to formalize the construction of the product of an arbitrary family of probability measures.