Tootfinder

Pure Data Spaces
Saul Youssef
https://arxiv.org/abs/2508.14271 https://arxiv.org/pdf/2508.14271

Pure Data Spaces
In a previous work, "pure data" is proposed as an axiomatic foundation for mathematics and computing, based on "finite sequence" as the foundational concept rather than based on logic or type. Within this framework, objects with mathematical meaning are "data" and collections of mathematical objects must then be associative data, called a "space." A space is then the basic collection in this framework analogous to sets in Set Theory or objects in Category Theory. A theory of spaces is developed…

Security Analysis of Ponzi Schemes in Ethereum Smart Contracts
Chunyi Zhang, Qinghong Wei, Xiaoqi Li
https://arxiv.org/abs/2510.03819 https://arxiv.org/pdf…

Security Analysis of Ponzi Schemes in Ethereum Smart Contracts
The rapid advancement of blockchain technology has precipitated the widespread adoption of Ethereum and smart contracts across a variety of sectors. However, this has also given rise to numerous fraudulent activities, with many speculators embedding Ponzi schemes within smart contracts, resulting in significant financial losses for investors. Currently, there is a lack of effective methods for identifying and analyzing such new types of fraudulent activities. This paper categorizes these scams …

Generation of Grothendieck topologies, provability and operations on subtoposes
Olivia Caramello, Laurent Lafforgue
https://arxiv.org/abs/2508.21134 https://

Generation of Grothendieck topologies, provability and operations on subtoposes
After reviewing the multiple roles of toposes - as generalized topological spaces, as universal invariants, as categorical analogues of the set-theoretic universe, and as semantic environments for first-order theories - we recall the notion of subtopos and its dual expression: both in terms of Grothendieck topologies and in terms of first-order logic. We emphasize the significance of this duality, which enables the translation of provability problems in first-order logic into problems concernin…

The category of propositional deductive systems
Ciro Russo
https://arxiv.org/abs/2508.19426 https://arxiv.org/pdf/2508.19426…

The category of propositional deductive systems
We define the category $\mathcal{QM}$ of quantales and their modules and prove the existence of coproducts, and the one of pushout and amalgamated coproducts under certain conditions. Then we define the non-full subcategory $\mathcal{DS}_0$, of propositional deductive systems, show that it is equivalent to the one of ``real'' propositional logics whose morphisms are interpretations (modulo a language translation, when needed), and prove that the coproduct in $\mathcal{DS}_0$ is precisely the de…

Probabilistically stable revision and comparative probability: a representation theorem and applications
Krzysztof Mierzewski
https://arxiv.org/abs/2509.02495 https://

Probabilistically stable revision and comparative probability: a representation theorem and applications
The stability rule for belief, advocated by Leitgeb [Annals of Pure and Applied Logic 164, 2013], is a rule for rational acceptance that captures categorical belief in terms of $\textit{probabilistically stable propositions}$: propositions to which the agent assigns resiliently high credence. The stability rule generates a class of $\textit{probabilistically stable belief revision}$ operators, which capture the dynamics of belief that result from an agent updating their credences through Bayesi…