  Multiple Landen values (MLVs) are defined as iterated integrals on the
interval $x\in[0,1]$ of the differential forms $A=d\log(x)$, $B=-d\log(1-x)$,
$F=-d\log(1-\rho^2x)$ and $G=-d\log(1-\rho x)$, where $\rho=(\sqrt{5}-1)/2$ is
the golden section. I conjecture that the dimension of the space of ${\mathbb
Z}$-linearly independent MLVs of weight $w$ is a tribonacci number $T_w$,
generated by $1/(1-x-x^2- x^3)=1+\sum_{w>0}T_w x^w$, and that a basis is
provided by all the words in the $\{A,G\}$ sub-alphabet that neither end in $A$
nor contain $A^3$. For $w<9$, I construct a much more efficient basis, for a
MLV datamine, where no prime greater than 11 occurs in the denominators of
3,357,257 coefficients of rational reduction of 49,151 MLVs. Numerical data for
40 primitives then enable fast evaluation of all of these MLVs to 20,000
digits. The datamine provides reductions of Ap\'ery-type sums
$A_w=\sum_{n>0}(-1)^{n+1}n^{-w}/{2n\choose n}$ and 6 ladder-combinations of
depth-1 polylogarithms ${\rm Li}_w(\rho^p)=\sum_{n>0}\rho^{pn}n^{-w}$ with
$p\in\{1,2,3,4,6,8,10,12,20,24\}$ and coefficients given by Landen, Coxeter and
Lewin at $w=2$. I prove that the former evaluate to MLVs and conjecture that
the latter do. Comparison is made between the properties of MLVs and multiple
polylogarithms at roots of unity, encountered in the quantum field theory of
the standard model of particle physics.
