@@ -12,7 +12,7 @@ for all non-negative $f \colon \mathbb{R} \to \mathbb{R}$.
 
 | Bound | Reference | Comments |
 | ----- | --------- | -------- |
-| $\pi/2 = 1.57059$ | [SS2002] | |
+| $\pi/2 = 1.5707963\dots$ | [SS2002] | |
 | $1.50992$ | [MV2009] | |
 | $1.5053$ | [GGSWT2025] | May 2025 announcement, AlphaEvolve
 | $1.503164$ | [GGSWT2025] | Dec 2025 preprint release, AlphaEvolve
 
@@ -19,7 +19,7 @@ for all non-negative $f,g: [-1,1] \to [0,1]$ with $f+g=1$ on $[-1,1]$ and $\int_
 | $0.4$ | [MRS1956]| |
 | $0.385694$ | Haugland (unpublished, 1993) | |
 | $0.382002$ | [H1996] | |
-| $0.380927$ | [H2016] | |
+| $0.380926$ | [H2016] | |
 | $0.380924$ | [GGSWT2025] | AlphaEvolve |
 | $0.380876$ | [YKLBMWKCZGS2026] | TTT-Discover |
 | $0.380871$ | [T2026] | TogetherAI |
@@ -31,7 +31,7 @@ for all non-negative $f,g: [-1,1] \to [0,1]$ with $f+g=1$ on $[-1,1]$ and $\int_
 | ----- | --------- | -------- |
 | $1/4=0.25$ | [E1955] |  |
 | $1-1/\sqrt{2} \approx 0.292893$ | Scherk (unpublished, 1955) | |
-| $(4-\sqrt{6})/5 \approx 0.310679$ | [S1958] |  |
+| $(4-\sqrt{6})/5 \approx 0.310102$ | [S1958] |  |
 | $\sqrt{4-\sqrt{15}} \approx 0.356393$ | [M1959] |  |
 | $0.379005$ | [W2022] |
 
 
@@ -8,7 +8,6 @@ $C\_{8} = R$ is the least constant such that there are no zeroes $\sigma+it$ of
 
 | Bound | Reference | Comments |
 | ----- | --------- | -------- |
-| $0$ | Trivial | |
 | $34.82$ | [dlVP1899] | Implies the prime number theorem|
 | $19$ | [RS1962] | |
 | $9.64591$ | [S1970] | |
@@ -23,7 +22,7 @@ $C\_{8} = R$ is the least constant such that there are no zeroes $\sigma+it$ of
 
 | Bound | Reference | Comments |
 | ----- | --------- | -------- |
-| $2/\log \gamma_{1} \approx 0.755106$ | - | Optimal assuming RH |
+| $2/\log \gamma\_{1} \approx 0.755106$ | - | Unconditional: $\gamma\_{1} = 14.1347\dots$ is the ordinate of the lowest zero of $\zeta$, and that zero has $\sigma = 1/2$, so any admissible $R$ must satisfy $1/2 \leq 1 - 1/(R\log\gamma\_{1})$. Optimal assuming RH. |
 
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