| $10^{143}$ | [Bru2002] | Bruiltet proves an explicit inequality of the form $h(p/q)\ge 10^{75}\Rightarrow \lvert \Gamma(1/4)-p/q\rvert > (1/(qe))^{10^{143}}$, which implies $\mu(\Gamma(1/4))\le 10^{143}$. [Bru2002-cor-gamma14] |exact pinned row| $10^{143}$ | <a href="#Bru2002">[Bru2002]</a> | Bruiltet proves an explicit inequality of the form $h(p/q)\ge 10^{75}\Rightarrow \lvert \Gamma(1/4)-p/q\rvert > (1/(qe))^{10^{143}}$, which implies $\mu(\Gamma(1/4))\le 10^{143}$. <a href="#Bru2002-cor-gamma14">[Bru2002-cor-gamma14]</a> |tracked since 2026-07-24 — no movement seen yet
Lower bound, last-listed row
| $2$ | Trivial (Dirichlet) | Every irrational number has irrationality exponent at least $2$. |tracked since 2026-07-24 — no movement seen yet
Cite this rowBounds Ledger — The irrationality measure of $\Gamma(1/4)$ (7b)
upper bound: $10^{143}$ (tracked since 2026-07-24 — no movement seen yet)
lower bound: $2$ (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/7b.html