| $\dfrac{1}{\sqrt{1+\sqrt{3}}}\,\dfrac{\Gamma(1/3)\Gamma(11/12)}{\Gamma(1/4)}\approx 0.4719$ | [AG1937] | Ahlfors–Grunsky bound; conjectured sharp. [BS2023-AG-conj-B] [BS2023-bounds-B] |exact pinned row| $\dfrac{1}{\sqrt{1+\sqrt{3}}}\,\dfrac{\Gamma(1/3)\Gamma(11/12)}{\Gamma(1/4)}\approx 0.4719$ | <a href="#AG1937">[AG1937]</a> | Ahlfors–Grunsky bound; conjectured sharp. <a href="#BS2023-AG-conj-B">[BS2023-AG-conj-B]</a> <a href="#BS2023-bounds-B">[BS2023-bounds-B]</a> |tracked since 2026-07-24 — no movement seen yet
Lower bound, last-listed row
| $\dfrac{\sqrt{3}}{4}+2\times 10^{-4}$ | [CG1996] | Best recorded lower bound (as quoted in the survey literature). [BS2023-bounds-B] |exact pinned row| $\dfrac{\sqrt{3}}{4}+2\times 10^{-4}$ | <a href="#CG1996">[CG1996]</a> | Best recorded lower bound (as quoted in the survey literature). <a href="#BS2023-bounds-B">[BS2023-bounds-B]</a> |tracked since 2026-07-24 — no movement seen yet
Cite this rowBounds Ledger — Bloch’s constant (57a)
upper bound: $\dfrac{1}{\sqrt{1+\sqrt{3}}}\,\dfrac{\Gamma(1/3)\Gamma(11/12)}{\Gamma(1/4)}\approx 0.4719$ (tracked since 2026-07-24 — no movement seen yet)
lower bound: $\dfrac{\sqrt{3}}{4}+2\times 10^{-4}$ (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/57a.html