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Open research questions in Computability, Logic, AI Algorithms

77 unresolved questions extracted from the limitations and future-work sections of 501 Computability, Logic, AI Algorithms papers in our library. Each links back to the study that raised it.

What the literature leaves open

  • The need to avoid relativization and natural proofs. The challenge of constructing a Δ₁-definable unary language p∞ that lies in NP but not in P.

    The Principle of Silence and the Provability of NP ≠ P in ZF · 2026 · DOI

  • The challenge of controlling output length in LLMs. The need to balance conciseness and accuracy. The difficulty of evaluating conciseness in LLMs.

    Concise thoughts: Impact of output length on LLM reasoning and cost · 2026 · DOI

  • The gap between the methods used to prove the Riemann Hypothesis and the actualization of the hypothesis. The gap between the catalogue of obstructions by method and the closure of the verdict side.

    Riemann Hypothesis: The Formal Case Is Closed: The Hypothesis Is True Where Actualized, Every Position a Verdict Could Be Attempted From Is Closed Permanently by an Enumeration No Future Method Enlarges, and What Remains Is One Bit That Belongs to the Reader · 2026 · DOI

  • Frameworks of a different nature— cognitive architectures, active-inference-based models, and large-scale connectionist approaches—were not examined, and extending Quinean methodology to less explicit formalizations remains an open challenge (Clark 1997; Chalmers 2012; Humphreys 2016).

    Ontological Commitments in Formal Models of Artificial General Intelligence · 2026 · DOI

  • The paper suggests that future research should focus on developing a complete solution for post-S3 evolution. The paper suggests that future research should explore the implementation details of the proposed framework.

    Architectural Saturation in Agentic AI: Next‑Generation Agentic Intelligence. · 2026 · DOI

  • The paper identifies a gap in formalizing the structural limits of agentic AI. The paper addresses this gap by providing a formal definition of system capability and proving structural closure at S3.

    Architectural Saturation in Agentic AI: Next‑Generation Agentic Intelligence. · 2026 · DOI

  • Traditional formal logic is insufficient for modeling high-dimensional, dynamic, and interconnected systems. There is a need for a formal system that can adapt its reasoning contextually and resolve paradoxes via geometric synthesis.

    Non-Euclidean Logic: 4D Dynamic System Modeling · 2026 · DOI

  • Future research should investigate whether negative information suffices to prove computability. Future research should investigate the applications of the result to the study of differentiable functions.

    Computability of a whitney extension · 2026 · DOI

  • In this paper we proved the computability of Whitney Extension operators WETm for m ≥ 0. Such operators associate every closed set F ⊆ R and every Whitney jet (f (¯k))|¯k|≤m of order m defined of F to total functions g: Rn → R such that • ∂¯k g(x) = f (¯k)(x) on F for all ¯k with |¯k| ≤ m, • g is C∞ on Rn \ F. This is the content of the Computable Whitney Extension Theorem 6.11. For the case m = 0, one obtains the First Computable Whitney Extension Theorem 5.3, where only the continuity of g is concerned. These results have been obtained under the assumption that closed sets are encoded via total representation. This leaves open at least two important questions. The first one concerns the necessity of using total representation to encode closed sets. Although this representation is very natural, in literature closed sets are often represented by negative information only. We conjecture that negative information does not suffice to prove computability, at least for the type of extension that we 33 have investigated. If so, the next goal would be determining the Weihrauch degree of the corresponding operators WET− m, whose definition is obtained by allowing only negative information for closed domains. The second question concerns the possibility of proving computability for operators WET having as input infinite Whitney jets (f (¯k))|¯k|∈N (with closed domains encoded by total or negative representation), and as output total continuous functions g: Rn → R such that ∂¯k g(x) = f (¯k)(x) on F for all ¯k. The extension originally defined by Hassler Whitney covered also this case. The investigation of these open problems will be the subject for future work. Appendix A. Proof of Proposition 4.8 In order to prove Proposition 4.8 we need a general fact about the derivatives of a quotient. Proposition A.1. Let u, v: Rn → R be C m(R) functions and, for every ¯k with |¯k| ≤ m, let ¯l0,..., ¯lt¯k−1 list in lexicographical order all ¯l ≤ ¯k.

    Computability of a whitney extension · 2026 · DOI

  • The paper is not a peer-reviewed paper in rigorous mathematics. The empirical component is limited to a proof-of-concept toy simulation using synthetic high-dimensional point clouds. The study does not claim that production-scale language models literally implement (E8 × E8) symmetry, Metatron geometry, Upanishadic field dynamics, Inter-Universal Teichmüller structures, or sheaf-cohomological obstruction mechanisms.

    Unified Field Theory of Multiverse Semantics: Version Universe Akashic Reading through the Metatron Lattice for Model Collapse · 2026 · DOI

  • The lack of a formal proof of the internal mathematical structure of large language models. The need for a rigorous mathematical framework for understanding model collapse.

    Unified Field Theory of Multiverse Semantics: Version Universe Akashic Reading through the Metatron Lattice for Model Collapse · 2026 · DOI

  • The gap is that the language of second-order arithmetic is not suited to consider objects of arbitrary large cardinality. The gap is that there is a need to study the reverse mathematics of characterization theorems of regular countable second countable spaces.

    Reverse mathematics of regular countable second countable spaces · 2026 · DOI

  • The Descriptive Degeneracy Problem is a fundamental issue in artificial intelligence. Current artificial intelligence systems operate at evolutionary Stage 2–3 of cognitive development.

    COMPUTATIONAL KNOWLEDGE THEORY (CKT): Prime Based Intelligence (PBI). · 2026 · DOI

  • Further study of the implications of the result. Exploration of new perspectives on the P vs NP problem.

    The Principle of Silence and the Provability of NP ≠ P in ZF · 2026 · DOI

  • Exploring the connection between the ACM and quantum gravity. Applying the ACM to other cosmological problems, such as the fine-tuning problem. Investigating the implications of the ACM for our understanding of the multiverse.

    The Informational Measure of Existence — Kolmogorov Complexity as a Cosmological Metric · 2026 · DOI

  • The measure problem in cosmology remains unresolved with conventional approaches. Prior measures fail to provide a normalized and predictive framework. The need for a new approach that can resolve paradoxes and provide a coherent picture of the multiverse.

    The Informational Measure of Existence — Kolmogorov Complexity as a Cosmological Metric · 2026 · DOI

  • These case studies suggest that agentic AI systems can participate meaningfully in research workflows for open problems in computational mathematics, while human validation remains essential.

    Iteris: Agentic Research Loops for Computational Mathematics · 2026

  • The paper suggests further study of the Multiplicative Turing Ensemble (MTE) and its properties. The paper proposes the development of new algorithms and models for complex systems that exhibit multiplicative behavior. The paper suggests the application of the paper's methods to real-world systems.

    Multiplicative Turing ensembles, Pareto's law, and creativity · 2026 · DOI

  • The paper identifies a gap in the study of integer-valued multiplicative dynamics driven by i.i.d. prime multipliers. The paper notes that the macroscopic statistics of these dynamics are not well understood. The paper identifies a need for a natural prior on prime multipliers.

    Multiplicative Turing ensembles, Pareto's law, and creativity · 2026 · DOI

  • Developing more effective exploration strategies for artificial general intelligence. Investigating the application of epistemic exploration to other domains.

    Agent Exploration Toward Artificial General Intelligence · 2026 · DOI

  • The lack of a unified view of epistemic exploration for agentic systems. The need for a framework that can guide the development of more effective exploration strategies.

    Agent Exploration Toward Artificial General Intelligence · 2026 · DOI

  • The lack of a unified solution to the seven Millennium Prize Problems. The gap between high-dimensional AI alignment and the study of quantum field theory, fluid dynamics, and number theory.

    A Unified Geometric Solution to the Seven Millennium Prize Problems via the Yett-Chyren Correspondence (The Yett theoRY) · 2026 · DOI

  • It does not prove or solve any open problem; its aim is to organize the structural barriers in problem-solving — in particular the consistency→existence gap (Gap II) — using five semi-quantitative indicators: d_cat (category-crossing distance), d_sub (subcategory distance), Gap II, R (circularity depth), and B (bottleneck concentration).

    AI‑Tractable Hard Mathematics: Structural Difficulty Patterns and the CVRT Framework · 2026 · DOI

  • The paper identifies a gap in the understanding of dementia as a non-algorithmic universe. The study notes that traditional semiotic tools are insufficient to fully understand the concept of dementia.

    La démence dans Sia, le rêve du python : un univers non algorithmique · 2026 · DOI

  • The construction is limited to graphs without bridges, as a bridge must carry value zero, which is exactly what nowhere-zero flows disallow. The QUBO formulation may not be efficient for large graphs due to the number of variables required.

    A QUBO formulation for nowhere-zero k-flows · 2026 · DOI

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77 open questions have been extracted from the limitations and future-work passages of 501 Computability, Logic, AI Algorithms papers in our library. Each one below links back to the study that raised it, so you can read the original claim in context.

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