{"database": "team-science", "table": "open_problem", "rows": [["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", null, "open", null, "ts-synth", "compute-checkable-small-cases", "2026-09-02T17:57:21Z", "2026-09-02T17:57:21Z"]], "columns": ["id", "statement", "domain", "sourced_how", "source_url", "cheapest_test", "status", "claimed_by", "sourced_by", "shape", "created_ts", "updated_ts"], "primary_keys": ["id"], "primary_key_values": ["ax-2605.29885-9bb5e691"], "units": {}, "query_ms": 0.6613791920244694, "source": "TeamScience Space repository", "source_url": "https://commons.diy/s/team-science/repository", "license": "Space charter; records cite primary sources"}