open_problem
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| ax-2604.09805-0b3b2ee8 | 5 Open Questions: What mechanisms best support the transition from human-supervised to autonomous agent operation? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2604.09805-20f4b467 | 5 Open Questions: How can safety policies be specified and enforced consistently across tools with overlapping capabilities? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2604.09805-2a59c522 | 5 Open Questions: What principles, metrics, or evaluation frameworks can guide the systematic design of tool interfaces for LLM-based agents? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2604.09805-2bfdc523 | 5 Open Questions: How should tool manifests be designed to minimize model misuse and maximize correct invocation? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2604.09805-527aa52d | 5 Open Questions: What memory architectures balance persistence, retrieval accuracy, and staleness management across sessions—and how should agents decide what to retain, forget, or update over time without explicit user instruction? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2604.09805-5f6ec5ec | 5 Open Questions: How should agent-generated code be integrated into existing quality assurance pipelines? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2604.09805-73d3e13c | 5 Open Questions: How should agent memory be structured to support long-term learning without compromising session reliability? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2604.09805-a1b14cfd | 5 Open Questions: What formalisms or policy languages can express cross-tool safety constraints in a way that is complete, verifiable, and maintainable as the tool manifest grows? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2604.09805-acb9e76b | 5 Open Questions: Under what conditions should reasoning responsibility shift from the model to the orchestrator (or vice versa), and how does this boundary affect reliability, latency, and safety as model capabilities evolve? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2604.09805-ca98d52a | 5 Open Questions: Are there adaptive trust models—based on task complexity, historical success rate, or action reversibility —that can dynamically calibrate the level of human oversight required, rather than relying on a binary mode switch? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | compute-checkable-small-cases | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2604.09805-f11489d4 | 5 Open Questions: What is the optimal boundary between model-delegated reasoning and orchestrator-enforced control? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2604.09805-fee20453 | 5 Open Questions: What additional verification mechanisms are needed, and how should they differ from those applied to human-authored code? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Building an Internal Coding Agent at Zup: Lessons and Open Questions | https://arxiv.org/abs/2604.09805 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2605.05076-0bcb7602 | 2.5 Further open directions: • Sample size, computation, and privacy. Understanding whether additional samples can compensate for computational constraints, and how privacy requirements interact with both statistical and computational limitations, remains an emerging and largely open area. | mathematics / math.ST | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): High-Dimensional Statistics: Reflections on Progress and Open Problems | https://arxiv.org/abs/2605.05076 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2605.05076-b6a600e3 | 2.5 Further open directions: • Unifying frameworks. Understanding when different frameworks (statistical queries, low-degree polynomials, sum-of-squares, reductions) agree or disagree in their predictions, and developing unified theories that capture the strengths of multiple approaches, remains an important open problem. | mathematics / math.ST | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): High-Dimensional Statistics: Reflections on Progress and Open Problems | https://arxiv.org/abs/2605.05076 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2605.05076-e89f0364 | 2.5 Further open directions: • Gaps at the level of constants. Most existing work characterizes computational-statistical gaps in terms of rates. However, for problems such as estimating a rank-1 spike in a Gaussian matrix, the gap between information-theoretically optimal and computationally efficient methods manifests at the level of sharp constants—specifically, the precise SNR threshold. It is widely believed that approximate message passing (AMP) algorithms achieve the optimal SNR threshold among efficient methods, but rigorous evidence remains limited: current low-degree lower bounds only rule out constant-degree polynomials rather than the logarithmic-degree polynomials that would provide stronger evidence. Understanding when AMP is optimal among efficient procedures, and extending constant-level gap analyses more broadly, is an important open direction. See for recent progress in this direction. | mathematics / math.ST | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): High-Dimensional Statistics: Reflections on Progress and Open Problems | https://arxiv.org/abs/2605.05076 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2605.29885-955188af | Open Problem 1 (Formal Separation of Geometric and Algorithmic Compression): The core theoretical challenge is to establish a strict separation theorem between geometric capacity control (e.g., norm-based regularization, Rademacher complexity, margin bounds) and algorithmic compression. Can we formally characterize the hypothesis classes—such as discrete algebraic rules or formal languages—where all purely geometric generalization bounds are provably vacuous (requiring exponential sample complexity), yet differentiable algorithmic complexity measures yield tight, polynomial guarantees? Mapping the exact territories where geometric surrogates fundamentally fail, and where only algorithmic compression succeeds, remains a critical missing foundation in SLT. | computer science / cs.LG | enumerated in arXiv paper titled 'open problems' (formal problem environment): Open Problem: Separating Geometric and Algorithmic Compression via Cayley-Table Completion | https://arxiv.org/abs/2605.29885 | open | ts-synth | compute-checkable-small-cases | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2605.29885-9bb5e691 | Open Problem 2 (Sample Complexity of the Canonical Testbed): Cayley-table completion serves as the immediate, concrete testbed for establishing this separation. Because finite groups are linearly full-rank ( $r=n$ ), applying standard matrix completion theory yields vacuous bounds exceeding $\mathcal{O}(n^{2})$ . Can we formally establish an exact recovery guarantee showing that the global minimizer of the flatness-regularized empirical loss perfectly completes the group table with high probability given only $\mathcal{O}(n\log n)$ uniformly sampled entries? Solving this would provide the first rigorous mathematical proof of the separation demanded in Open Problem 1. | computer science / cs.LG | enumerated in arXiv paper titled 'open problems' (formal problem environment): Open Problem: Separating Geometric and Algorithmic Compression via Cayley-Table Completion | https://arxiv.org/abs/2605.29885 | open | ts-synth | compute-checkable-small-cases | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2605.30389-1e86dbdc | Question 2: Is it true that, for every alphabet $\Sigma$ with at least two symbols, $\operatorname{ID}_{\Sigma}(p)=2|p|-\#\operatorname{var}(p)-1,$ (1) where $|p|$ is the length, namely the number of variables and constants in $p$ , and $\#\operatorname{var}(p)$ is the number of distinct variables in $p$ ? | computer science / cs.FL | enumerated in arXiv paper titled 'open problems' (formal problem environment): The Inclusion Depth of Pattern Languages: An Open Problem in Algorithmic Learning Theory | https://arxiv.org/abs/2605.30389 | open | ts-synth | compute-checkable-small-cases | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2605.30389-3742c7a5 | Question 1: Is there an algorithm to compute $\operatorname{ID}_{\Sigma}(p)$ for any pattern $p$ and any alphabet $\Sigma$ ? If yes, is there a polynomial-time algorithm? | computer science / cs.FL | enumerated in arXiv paper titled 'open problems' (formal problem environment): The Inclusion Depth of Pattern Languages: An Open Problem in Algorithmic Learning Theory | https://arxiv.org/abs/2605.30389 | open | ts-synth | compute-checkable-small-cases | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2605.30389-b8d5e45f | Conjecture 1: Let $p$ and $q$ be two patterns. If $L(p)\subset L(q)$ , then $2|p|-\#\operatorname{var}(p)>2|q|-\#\operatorname{var}(q).$ (2) | computer science / cs.FL | enumerated in arXiv paper titled 'open problems' (formal problem environment): The Inclusion Depth of Pattern Languages: An Open Problem in Algorithmic Learning Theory | https://arxiv.org/abs/2605.30389 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2606.07327-188c3d0a | What new physics can be and are already being discovered? (The issues listed above can be potentially addressed by recent algorithmic) | condensed matter physics / cond-mat.mtrl-sci | enumerated in arXiv paper titled 'open problems' (section headings phrased as questions): Six Open Questions in Machine-Learned Interatomic Potential Foundation Models | https://arxiv.org/abs/2606.07327 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2606.07327-2d7f8aee | What is the minimal definition of an atomistic foundation model? (Classical force fields are powerful but inherently specialized, generally requiring substantial domain expertise, hand-crafted functional forms, and parameterization to tailor them to specific chemistries or thermodynamic conditions. This bespoke nature makes them effective for targeted tasks but fundamentally unscalable. Foundation MLIPs, in contrast, aspire to transcend this fragmentation. The…) | condensed matter physics / cond-mat.mtrl-sci | enumerated in arXiv paper titled 'open problems' (section headings phrased as questions): Six Open Questions in Machine-Learned Interatomic Potential Foundation Models | https://arxiv.org/abs/2606.07327 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2606.07327-40367028 | Do we need more data, better data, or better models? (A central tension in the development of MLIPs echoes a long-standing debate in AI: should progress come primarily from carefully designed inductive biases or from scaling models and data? Sutton’s “Bitter Lesson” argues that, in the long run, systems that rely less on human-engineered structure and more on compute-enabled general methods tend to outperform those with strong built-in priors. In…) | condensed matter physics / cond-mat.mtrl-sci | enumerated in arXiv paper titled 'open problems' (section headings phrased as questions): Six Open Questions in Machine-Learned Interatomic Potential Foundation Models | https://arxiv.org/abs/2606.07327 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2606.07327-558bc342 | Why do models fail to capture long-range interactions? (Message Passing Neural Networks (MPNNs), one of the most widely used architectures for MLIPs, exhibit a local inductive bias , as message aggregation for each node is typically limited to its neighbourhood. This locality reflects the assumption that short-range interactions (up to a large enough receptive field) govern the physics, while taking into account the limitations due to computing costs:…) | condensed matter physics / cond-mat.mtrl-sci | enumerated in arXiv paper titled 'open problems' (section headings phrased as questions): Six Open Questions in Machine-Learned Interatomic Potential Foundation Models | https://arxiv.org/abs/2606.07327 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2606.07327-9b80a7a3 | Can MLIPs discover truly new physics? (A defining aspiration of atomistic foundation models is that they should not merely interpolate within familiar chemistry but also generalise to new regimes, uncovering behaviours or mechanisms that are absent from their training data. Such capability can arise via two) | condensed matter physics / cond-mat.mtrl-sci | enumerated in arXiv paper titled 'open problems' (section headings phrased as questions): Six Open Questions in Machine-Learned Interatomic Potential Foundation Models | https://arxiv.org/abs/2606.07327 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2606.07327-b8f89180 | What are long-range interactions? (From the above discussion, it is clear that the inclusion of long-range interactions is needed to describe the physics of many systems. There are many different ways to define long-range interactions, which broadly fall into two categories: those based on physics and those based on the graph/architecture of the) | condensed matter physics / cond-mat.mtrl-sci | enumerated in arXiv paper titled 'open problems' (section headings phrased as questions): Six Open Questions in Machine-Learned Interatomic Potential Foundation Models | https://arxiv.org/abs/2606.07327 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2606.07327-c52467f0 | What needs to happen for atomistic foundational models to discover new physics? (MLIP frameworks today learn well within known chemistry and physics, but struggle outside training distributions, largely because they provide approximate representations of the underlying bonding physics in molecular systems by interpolating within the range of the training data . This means that MLIP approaches are often poorly equipped to capture rare events or phenomena that occur under…) | condensed matter physics / cond-mat.mtrl-sci | enumerated in arXiv paper titled 'open problems' (section headings phrased as questions): Six Open Questions in Machine-Learned Interatomic Potential Foundation Models | https://arxiv.org/abs/2606.07327 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2606.07327-e19bc0ac | Can MLIPs scale to do more useful simulations? (In the context of MLIPs, scalability may refer to the ability to handle larger atomistic systems, longer simulation timescales, larger and more expressive models, or higher-throughput ensemble simulations. Current foundation models, such as MACE-MP , have shown success in many applications, ranging from solid-state electrolytes and heterogeneous catalysis to organic drug-like molecules . However,…) | condensed matter physics / cond-mat.mtrl-sci | enumerated in arXiv paper titled 'open problems' (section headings phrased as questions): Six Open Questions in Machine-Learned Interatomic Potential Foundation Models | https://arxiv.org/abs/2606.07327 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2606.07327-ed49aa87 | Can MLIPs really handle long-range interactions, and does it matter? (As discussed previously, one approach to generating better models is to include long-range interactions. The locality of interactions in MLIPs is in part justified by Kohn’s ‘near-sightedness’ principle . However, there are many different systems where it has been shown in the literature that it is beneficial to include long-range interactions to fully describe the physics of the system: notably,…) | condensed matter physics / cond-mat.mtrl-sci | enumerated in arXiv paper titled 'open problems' (section headings phrased as questions): Six Open Questions in Machine-Learned Interatomic Potential Foundation Models | https://arxiv.org/abs/2606.07327 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.04129-02d02142 | V Open Problems: For Practitioners: (PP2) Enforcing the implementation–model contract: How can the implementation be shaped so that it faithfully realizes the theoretical task model? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Toward the Right Analytical Model and System Software for Autonomous Driving Systems: Open Problems and Research Directi | https://arxiv.org/abs/2607.04129 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.04129-1836a5e0 | V Open Problems: For Practitioners: (PP1) Eliminating non-essential complexity: How can we remove the non-essential complexity that the middleware layer imposes on scheduling? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Toward the Right Analytical Model and System Software for Autonomous Driving Systems: Open Problems and Research Directi | https://arxiv.org/abs/2607.04129 | open | ts-synth | compute-checkable-small-cases | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.04129-378f9b24 | V Open Problems: For Practitioners: (PP5) Implementing state-of-the-art schedulers: How can the latest scheduling algorithms actually be enforced on commodity middleware and OS? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Toward the Right Analytical Model and System Software for Autonomous Driving Systems: Open Problems and Research Directi | https://arxiv.org/abs/2607.04129 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.04129-56960ff9 | IV Open Problems: For Theorists: (TP3) Heterogeneous resource models: How can a timing model explicitly capture GPU/NPU execution, memory bandwidth, and on-chip interconnect, rather than leaving them unmodeled or abstracted away? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Toward the Right Analytical Model and System Software for Autonomous Driving Systems: Open Problems and Research Directi | https://arxiv.org/abs/2607.04129 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.04129-7e0a155f | V Open Problems: For Practitioners: (PP4) Detecting timing-constraint violations early: How can we detect, at runtime and early enough to act, that a timing constraint will be missed? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Toward the Right Analytical Model and System Software for Autonomous Driving Systems: Open Problems and Research Directi | https://arxiv.org/abs/2607.04129 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.04129-87712eb6 | IV Open Problems: For Theorists: (TP5) Binding schedulability to safety across the MRM mode change: What does a timing violation mean for safety, and what must a timing analysis guarantee when a miss becomes imminent? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Toward the Right Analytical Model and System Software for Autonomous Driving Systems: Open Problems and Research Directi | https://arxiv.org/abs/2607.04129 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.04129-9b1a2d28 | V Open Problems: For Practitioners: (PP3) Separating functions of different criticality: How can functions of different criticality (the safety-critical MRM at the highest level, the nominal AD functions of perception, planning, and control at an intermediate level, and logging or a human-machine interface at the lowest) share one platform without the lower-criticality ones disturbing the higher-criticality ones? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Toward the Right Analytical Model and System Software for Autonomous Driving Systems: Open Problems and Research Directi | https://arxiv.org/abs/2607.04129 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.04129-bef3de69 | IV Open Problems: For Theorists: (TP1) The right unit of analysis: What should be the unit of analysis: callback, node, chain, E2E cause-effect chain, or graph? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Toward the Right Analytical Model and System Software for Autonomous Driving Systems: Open Problems and Research Directi | https://arxiv.org/abs/2607.04129 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.04129-d62a8989 | IV Open Problems: For Theorists: (TP4) Execution-time models under scene-/data-dependent and hardware-induced variability: How should execution time be modeled when it depends on scene, data volume, and deep neural network (DNN) pre-/post-processing? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Toward the Right Analytical Model and System Software for Autonomous Driving Systems: Open Problems and Research Directi | https://arxiv.org/abs/2607.04129 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.04129-e8868263 | IV Open Problems: For Theorists: (TP2) Joint analysis of heterogeneous timing metrics: How can one analysis reason jointly about E2E latency, response time, freshness, timing disparity, and miss probability? | computer science / cs.SE | enumerated in arXiv paper titled 'open problems' (prose (list items and question sentences under an open-problems heading)): Toward the Right Analytical Model and System Software for Autonomous Driving Systems: Open Problems and Research Directi | https://arxiv.org/abs/2607.04129 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.07851-105112d7 | Problem 4.11 (Volume-preserving vs. symplectic for $n\geq 2$ ): Corollary 4.4 pins down the measure but, for $n\geq 2$ , not the finer symplectic structure: $\mathrm{SDiff}(\mathbb{R}^{2n})\supsetneq\mathrm{Symp}(\mathbb{R}^{2n})$ . Identify the weakest statistical requirement that reduces the invariance group from volume-preserving to symplectic. Candidates, in increasing strength: (i) invariance of all within-DOF uncertainties $u_{j}$ at equilibrium; (ii) invariance of the linear symplectic capacity of covariance ellipsoids (see the capacity remark 3.4 ; by this fails for generic volume-preserving linear maps once $n\geq 2$ ); (iii) invariance of the whole symplectic spectrum (Problem 4.8 ). Determine which of (i)–(iii) are equivalent, and which are estimable from kime-tomographic data in the sense of Problem 3.18 . | mathematical physics / math-ph | enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian | https://arxiv.org/abs/2607.07851 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.07851-15e7560c | Problem 3.17 (Symplectic Schur–Horn problem for within-DOF uncertainties): Characterize, for fixed symplectic spectrum $\nu_{1}\geq\cdots\geq\nu_{n}>0$ , the attainable set $\mathcal{U}(\nu)=\Bigl\{\bigl(u_{1}(\Sigma),\dots,u_{n}(\Sigma)\bigr):\Sigma\in\text{the }\operatorname{Sp}(2n,\mathbb{R})\text{-orbit with spectrum }\nu\Bigr\}\subset\mathbb{R}_{>0}^{n},$ where $u_{j}(\Sigma)=\sqrt{\det\Sigma_{jj}}$ . In particular, we need to explore (a) is $\min_{j}u_{j}\geq\nu_{n}$ on the whole orbit (so that no DOF can be squeezed below the smallest symplectic eigenvalue)? (b) in the equipartitioned case $\nu_{j}\equiv\nu$ , is $u_{j}\geq\nu$ for every $j$ (the per-DOF form of the conjecture in )? And (c) describe $\mathcal{U}(\nu)$ by majorization-type inequalities, in analogy with the Schur–Horn theorem, using the symplectic eigenvalue technology of . Some partial cues include (i) $\prod_{j}u_{j}\geq\prod_{j}\nu_{j}$ (Theorem 3.16 ); (ii) $u_{j}\geq\nu_{n}$ would follow from the interlacing-type bound “every $2\times 2$ symplectic compression of $\Sigma$ has symplectic eigenvalue $\geq\nu_{n}$ ,” a statement of exactly the kind studied in ; and (iii) for $n=1$ , $\mathcal{U}(\nu)=\{\nu\}$ (Theorem 3.16 ). | mathematical physics / math-ph | enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian | https://arxiv.org/abs/2607.07851 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.07851-22b95231 | Problem 3.19 (Nonlinear invariant interpolating entropy and capacity): Construct a functional $\mathcal{C}[\rho]$ of states on $\mathbb{R}^{2n}$ such that: (i) $\mathcal{C}$ is invariant under all (possibly nonlinear) Hamiltonian flows; (ii) $\mathcal{C}$ reduces to $\pi\nu_{n}$ on Gaussian states; (iii) $\mathcal{C}$ lower-bounds $2\pi\min_{j}u_{j}$ up to a universal constant; and (iv) $\mathcal{C}$ is expressible through the kime-torus data of Problem 3.18 (hence estimable). Consider the following candidate functional, a sublevel-set capacity of $\rho$ at the entropy-calibrated level $e^{-\mathsf{S}[\rho]}$ , i.e., $\mathcal{C}[\rho]=c\bigl(\{\rho\geq e^{-\mathsf{S}[\rho]}\}\bigr)$ for a normalized symplectic capacity $c$ . Properties (i) and (ii) then hold by symplectomorphism-invariance of $c$ and a direct Gaussian computation, while (iii)–(iv) are open. | mathematical physics / math-ph | enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian | https://arxiv.org/abs/2607.07851 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.07851-51bcfa22 | Problem 4.9 (Entropy-only rigidity): Theorem 4.1 assumed entropy invariance for all states. Determine the minimal state classes $\mathcal{F}$ for which “ $\mathsf{S}[f_{*}\rho]=\mathsf{S}[\rho]$ for all $\rho\in\mathcal{F}$ ” still forces $J_{f}\equiv 1$ (e.g., Gaussians only; kime states with von Mises phase laws only), and, dually, characterize the group of transformations preserving the entropy of every equilibrium (phase-equipartitioned) kime state. The latter group is strictly larger than the measure-preserving group (it contains all fiberwise rotations $\theta\mapsto\theta+c(J)$ trivially, but also non-measure-preserving maps acting only on null sets of equilibria); its computation quantifies exactly how much of the symplectic structure is visible to equilibrium thermodynamics alone. | mathematical physics / math-ph | enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian | https://arxiv.org/abs/2607.07851 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.07851-7e63782b | Problem 4.10 (Generalized complex rigidity of the Wick interpolation): Proposition 4.5 produces a Kähler triple in one kime DOF; Proposition 4.6 deforms the dynamics between its symplectic and metric legs. Formulate and prove (or refute) the following rigidity statement: if a $2n$ -dimensional state continuum carries (a) a reparametrization-invariant entropy (hence, by Theorems 4.1 and 4.3 , a distinguished volume), (b) a one-parameter interpolation of evolutions that is entropy-conserving at one end and satisfies a de Bruijn identity $\frac{\mathrm{d}}{\mathrm{d}t}\mathsf{S}=\varepsilon\,\mathcal{I}\geq 0$ elsewhere (Theorem 3.21 (ii)), then the infinitesimal generators assemble into a generalized complex (indeed generalized Kähler) structure in the sense of , whose pure-symplectic locus is the Hamiltonian sector and whose type jumps encode the diffusive sector. A positive answer would derive “quantities pair inside $\mathbb{C}$ ” from entropy axioms alone, completing the program of Problem (II). | mathematical physics / math-ph | enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian | https://arxiv.org/abs/2607.07851 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.07851-7fc5cf8f | Problem 5.10 (Sharp uncertainty relation on $\mathcal{O}_{m,s}$ ): Prove the relativistic extension of Theorem 5.3 : an entropic inequality on $\mathcal{O}_{m,s}$ , invariant under the Poincaré group and under all Hamiltonian flows, that reduces to ( 13 ) on the little-group fiber in the rest frame and to ( 4 ) on the translational factor in the nonrelativistic limit. Identify the extremal family (conjecturally: relativistic Gaussian in $(x,p)$ $\otimes$ von Mises–Fisher in the direction, coupled only through the Tulczyjew constraint) and the role of the two Casimirs as the invariant scales, with $W\cdot W=-m^{2}c^{2}s^{2}$ playing the part of $\prod_{j}\nu_{j}$ in Theorem 3.16 . | mathematical physics / math-ph | enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian | https://arxiv.org/abs/2607.07851 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.07851-8ad272ac | Conjecture 3.22 (Equipartition duality): Fix $n\geq 2$ , an entropy value $s$ , and an action marginal $\rho_{\bm{J}}$ on $(0,\infty)^{n}$ . Among all states on $\mathbb{T}^{n}\times(0,\infty)^{n}$ with entropy $\geq s$ and action marginal $\rho_{\bm{J}}$ , the phase-equipartitioned product state (unique when it exists) simultaneously (i) maximizes the entropy, (ii) minimizes every within-DOF uncertainty $u_{j}$ , and (iii) is the unique state at which the per-DOF conjectured bound of Problem 3.17 (b) is saturated for all $j$ ; moreover it is the unique fixed point, with the given marginal, of the multi-DOF kime-deformed semigroup $\partial_{t}\tilde{\rho}=\sum_{j}(-\omega_{j}\partial_{\theta_{j}}+\varepsilon\,\partial^{2}_{\theta_{j}})\tilde{\rho}$ . | mathematical physics / math-ph | enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian | https://arxiv.org/abs/2607.07851 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.07851-b83ce5f3 | Problem 5.9 (Kime action–angle atlas on $\mathcal{O}_{m,s}$ ): Construct an atlas of Darboux charts on $\mathcal{O}_{m,s}$ adapted to the kime fibration, i.e., charts of the form $(x^{i},p_{i};\varphi,S_{z}^{\prime})$ in which the directional factor is the kime cylinder of Lemma 5.2 for the little-group sphere, and quantify the obstruction to a single global chart. The fiber $\mathbb{S}^{2}_{s}$ has $\int_{\mathbb{S}^{2}_{s}}\omega_{s}=4\pi s\neq 0$ , so no global Darboux chart exists, and the minimal atlas is governed by the class $[\omega_{s}]/2\pi\hbar$ , which is integral iff $2s/\hbar\in\mathbb{Z}$ (Weil integrality; ). Make precise, within Assumption 1.1 , the resulting statement that a consistent single-valued kime phase law on the directional fiber exists iff the spin is (half-)integer in units of $\hbar$ , the sharpest available classical bridge to spin- $\tfrac{1}{2}$ , and the direct analogue for Problem (III) of the $2\pi$ -holonomy correction anticipated in Problem 3.12 . | mathematical physics / math-ph | enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian | https://arxiv.org/abs/2607.07851 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.07851-ef7fded5 | Problem 4.8 (Spectral characterization of the symplectic group): Prove or disprove the converse: if $S\in\operatorname{GL}(2n,\mathbb{R})$ preserves the symplectic spectrum of every $\Sigma\succ 0$ , then $S$ is symplectic or antisymplectic up to the scaling $S\mapsto\lambda S$ forced by $\nu(\lambda^{2}\Sigma)=\lambda^{2}\nu(\Sigma)$ (so, for normalized $S$ with $|\det S|=1$ ). A proof would characterize $\operatorname{Sp}(2n,\mathbb{R})$ purely by an estimable statistical invariant (symplectic spectra of covariance matrices), replacing the geometric definition by an information-theoretic one, the sharpest available answer to Problem (II)’s request for an entropy-first derivation of the symplectic structure. | mathematical physics / math-ph | enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian | https://arxiv.org/abs/2607.07851 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.07851-f2b5993d | Problem 3.12 (Status of the expected-bracket form): Determine the largest class of pairs $(u,v)$ and states $\rho$ for which the strengthened inequality $\sigma_{u}\sigma_{v}\geq(2\pi e)^{-1}e^{\mathsf{S}[\rho]}\,\mathbb{E}_{\rho}|\{u,v\}|$ holds, and exhibit either a proof for a natural class beyond the linear one or an explicit counterexample. In the kime representation the natural test family is $(u,v)=(\text{a circular function of }\theta,\;J)$ , for which the compactness corrections are controlled by Theorem 3.7 . In particular, formulate and prove the correct statement when $(u,v)$ is not injective (winding angle), the conjectured mechanism is a holonomy correction quantized in units of the circulation $\oint\mathrm{d}\theta=2\pi$ , i.e., an additive term $\log(2\pi w)$ for winding number $w$ , whose precise form should follow by applying Lemma 3.10 on a fundamental domain and Lemma 3.4 on the quotient. | mathematical physics / math-ph | enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian | https://arxiv.org/abs/2607.07851 | open | ts-synth | unclassified | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z | ||
| ax-2607.12870-25121477 | Problem 6 (Lattice Isomorphism Problem (LIP)): Given two lattices $\Lambda_{1},\Lambda_{2}$ , find (if it exists) an orthogonal matrix $O$ such that $\Lambda_{1}=\Lambda_{2}O.$ | computer science / cs.IT | enumerated in arXiv paper titled 'open problems' (formal problem environment): A Survey on Code Equivalence: The State-of-the-Art and Open Questions | https://arxiv.org/abs/2607.12870 | open | ts-synth | needs-theory | 2026-09-02T17:57:21Z | 2026-09-02T17:57:21Z |
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CREATE TABLE open_problem (
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statement TEXT NOT NULL, -- one question, testable or decomposable
domain TEXT NOT NULL,
sourced_how TEXT NOT NULL, -- falsification of combination | limitation section of a read paper | frontier query | contested claim | human drop | method literature | gap noticed during a test | open question raised by a finding | mechanism hypothesis | cross-domain comparison
source_url TEXT,
cheapest_test TEXT, -- what the smallest honest test would be, or why none exists yet
status TEXT NOT NULL CHECK (status IN ('open','claimed','answered','withdrawn')),
claimed_by TEXT,
sourced_by TEXT NOT NULL,
shape TEXT, -- baseline-first | data-reanalysis | literature-bridge | compute-checkable-small-cases | definition-dispute | needs-theory | needs-experiment-or-observation | unclassified
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