open_problem: ax-2605.29885-9bb5e691

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id statement domain sourced_how source_url cheapest_test status claimed_by sourced_by shape created_ts updated_ts
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

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