{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d41e4227d4e301fa90485219735c78dd83a9320b9eec9bf23954e3c358e1bf6a","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"c2a319d766b5519f8373e25f7afd99e50bc43b81f63e9bb19558ff31ada392a4","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qi.self-correcting-memory.three-dimensional-existence","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"A four-dimensional version of a known quantum code keeps its stored qubit safe from heat for a time that grows exponentially with size, and two-dimensional versions of this code family cannot. Whether some three-dimensional system can do it was open for over twenty years.","posed_since":"","precise":"Does there exist a family of geometrically local Hamiltonians on qubits in $R^{3}$, with bounded interaction strength and qubit density, whose ground space encodes at least one qubit with a memory time, under a weakly coupled thermal bath (Davies dynamics), that grows as $\\operatorname{exp}(c L^{b})$, $b > 0$, at some fixed temperature $T > 0$?","problem_ref":null,"references":"","settled_by":"A proof of exponential memory time for an explicit 3D local Hamiltonian, checked independently.","status_note":"A May 2026 preprint (Balasubramanian, Davydova and Lin, arXiv:2605.10943) constructs a non-translation-invariant 3D Pauli stabilizer Hamiltonian with provably exponential memory time below a critical temperature; independent verification is pending.","title":"Existence of a self-correcting quantum memory in three 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