Tootfinder

Fixed-Point Theorems and the Ethics of Radical Transparency: A Logic-First Treatment
Faruk Alpay, Hamdi Alakkad
https://arxiv.org/abs/2509.06055 https://ar…

Fixed-Point Theorems and the Ethics of Radical Transparency: A Logic-First Treatment
This paper establishes a formal framework, grounded in mathematical logic and order theory, to analyze the inherent limitations of radical transparency. We demonstrate that self-referential disclosure policies inevitably encounter fixed-point phenomena and diagonalization barriers, imposing fundamental trade-offs between openness and stability. Key results include: (i) an impossibility theorem showing no sufficiently expressive system can define a total, consistent transparency predicate for …

Generative Logic: A New Computer Architecture for Deterministic Reasoning and Knowledge Generation
Nikolai Sergeev
https://arxiv.org/abs/2508.00017 https://

Generative Logic: A New Computer Architecture for Deterministic Reasoning and Knowledge Generation
We present Generative Logic (GL), a deterministic architecture that begins from user-supplied axiomatic definitions -- written in a minimalist Mathematical Programming Language (MPL) -- and systematically explores their deductive neighborhood. Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages; any time several expressions unify under an inference rule, a new fact is emitted with full provenance to its sources, yielding replayable, auditable pro…

Geoint-R1: Formalizing Multimodal Geometric Reasoning with Dynamic Auxiliary Constructions
Jingxuan Wei, Caijun Jia, Qi Chen, Honghao He, Linzhuang Sun, Conghui He, Lijun Wu, Bihui Yu, Cheng Tan
https://arxiv.org/abs/2508.03173

Geoint-R1: Formalizing Multimodal Geometric Reasoning with Dynamic Auxiliary Constructions
Mathematical geometric reasoning is essential for scientific discovery and educational development, requiring precise logic and rigorous formal verification. While recent advances in Multimodal Large Language Models (MLLMs) have improved reasoning tasks, existing models typically struggle with formal geometric reasoning, particularly when dynamically constructing and verifying auxiliary geometric elements. To address these challenges, we introduce Geoint-R1, a multimodal reasoning framework des…

Proceedings of the 22nd International Conference on Quantum Physics and Logic
Alejandro D\'iaz-Caro, Ognyan Oreshkov, Ana Bel\'en Sainz
https://arxiv.org/abs/2508.13619 …

Proceedings of the 22nd International Conference on Quantum Physics and Logic
This volume contains the proceedings of the 22nd International Conference on Quantum Physics and Logic (QPL 2025), which was held from 14th to 18th July 2025, in Varna, Bulgaria, organised by Université libre de Bruxelles. QPL is an annual conference that brings together academic and industry researchers working on the mathematical foundations of quantum computation, quantum physics, and related areas. The main focus is on the use of algebraic and categorical structures, formal languages, sema…

Universal Gluing and Contextual Choice: Categorical Logic and the Foundations of Analytic Approximation
Andreu Ballus Santacana
https://arxiv.org/abs/2506.22693

Universal Gluing and Contextual Choice: Categorical Logic and the Foundations of Analytic Approximation
We introduce a new categorical and constructive foundation for analytic approximation based on a Contextual Choice Principle (CCP), which enforces locality and compatibility in the construction of mathematical objects. Central to our approach is the Universal Embedding and Linear Approximation Theorem (UELAT), which establishes that functions in broad spaces -- including C(K), Sobolev spaces W^{k,p}(Omega), and distributions D'(Omega) -- can be explicitly approximated by finite-rank linear proj…

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…

Reflective Paper-to-Code Reproduction Enabled by Fine-Grained Verification
Mingyang Zhou, Quanming Yao, Lun Du, Lanning Wei, Da Zheng
https://arxiv.org/abs/2508.16671 https://…

Reflective Paper-to-Code Reproduction Enabled by Fine-Grained Verification
Reproducing machine learning papers is essential for scientific progress but remains challenging for both humans and automated agents. Existing agent-based methods often struggle to fully and accurately reproduce implementation details such as mathematical formulas and algorithmic logic. Previous studies show that reflection with explicit feedback improves agent performance. However, current paper reproduction methods fail to effectively adopt this strategy. This gap mainly arises from the dive…

Nonlinear Continuum of States and Intuitionistic Flows in a Cognitive Space
Faruk Alpay, Taylan Alpay
https://arxiv.org/abs/2509.02613 https://arxiv.org/pd…

Nonlinear Continuum of States and Intuitionistic Flows in a Cognitive Space
We construct a rigorous mathematical framework for an abstract continuous evolution of an internal state, inspired by the intuitive notion of a flowing thought sequence. Using tools from topology, functional analysis, measure theory, and logic, we formalize an indefinitely proceeding sequence of states as a non-linear continuum with rich structure. In our development, a trajectory of states is modeled as a continuous mapping on a topological state space (a potentially infinite-dimensional Banac…

AI's Euclid's Elements Moment: From Language Models to Computable Thought
Xinmin Fang, Lingfeng Tao, Zhengxiong Li
https://arxiv.org/abs/2506.23080

AI's Euclid's Elements Moment: From Language Models to Computable Thought
This paper presents a comprehensive five-stage evolutionary framework for understanding the development of artificial intelligence, arguing that its trajectory mirrors the historical progression of human cognitive technologies. We posit that AI is advancing through distinct epochs, each defined by a revolutionary shift in its capacity for representation and reasoning, analogous to the inventions of cuneiform, the alphabet, grammar and logic, mathematical calculus, and formal logical systems. Th…

SC-TPTP: An Extension of the TPTP Derivation Format for Sequent-Based Calculus
Julie Cailler, Simon Guilloud
https://arxiv.org/abs/2507.11349 https://

SC-TPTP: An Extension of the TPTP Derivation Format for Sequent-Based Calculus
Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe proofs in first-order logic: SC-TPTP. To avoid multiplication of standards, our proposed format over-specifies the TPTP derivation format by focusing on sequent formalisms. By doing so, it provides a high level of detail, is faithful to mathematical tradition, a…