| $3.972$ | [[ACMS2021](#ACMS2021)] | Published explicit upper bound $\mathrm{Flt}(3)<3.972$. [ACMS2021-ub-3-972] |exact pinned row| $3.972$ | [[ACMS2021](#ACMS2021)] | Published explicit upper bound $\mathrm{Flt}(3)<3.972$. <a href="#ACMS2021-ub-3-972">[ACMS2021-ub-3-972]</a> |tracked since 2026-07-24 — no movement seen yet
Lower bound, last-listed row
| $2+\sqrt{2}$ | [[CS2019](#CS2019)] | Achieved by an explicit hollow non-lattice tetrahedron in dimension $3$. [CS2019-thm-1-1] |exact pinned row| $2+\sqrt{2}$ | [[CS2019](#CS2019)] | Achieved by an explicit hollow non-lattice tetrahedron in dimension $3$. <a href="#CS2019-thm-1-1">[CS2019-thm-1-1]</a> |tracked since 2026-07-24 — no movement seen yet
Cite this rowBounds Ledger — Flatness constant in dimension 3 (73a)
upper bound: $3.972$ (tracked since 2026-07-24 — no movement seen yet)
lower bound: $2+\sqrt{2}$ (tracked since 2026-07-24 — no movement seen yet)
Mirrored from teorth/optimizationproblems@2c1968c. These are the last-listed rows of that constant's bounds table — a listing position, not a statement that this bound is the strongest or most recent. A snapshot at that sha, not a live read.
https://u00dxk2.github.io/bounds-ledger/c/73a.html