  We propose a complete microscopic definition of the Hilbert space of minimal
higher spin de Sitter quantum gravity and its Hartle-Hawking vacuum state. The
fundamental degrees of freedom are $2N$ bosonic fields living on the future
conformal boundary, where $N$ is proportional to the de Sitter horizon entropy.
The vacuum state is normalizable. The model agrees in perturbation theory with
expectations from a previously proposed dS-CFT description in terms of a
fermionic Sp(N) model, but it goes beyond this, both in its conceptual scope
and in its computational power. In particular it resolves the apparent
pathologies affecting the Sp(N) model, and it provides an exact formula for
late time vacuum correlation functions. We illustrate this by computing
probabilities for arbitrarily large field excursions, and by giving fully
explicit examples of vacuum 3- and 4-point functions. We discuss bulk
reconstruction and show the perturbative bulk QFT canonical commutations
relations can be reproduced from the fundamental operator algebra, but only up
to a minimal error term $\sim e^{-\mathcal{O}(N)}$, and only if the operators
are coarse grained in such a way that the number of accessible "pixels" is less
than $\mathcal{O}(N)$. Independent of this, we show that upon gauging the
higher spin symmetry group, one is left with $2N$ physical degrees of freedom,
and that all gauge invariant quantities can be computed by a $2N \times 2N$
matrix model. This suggests a concrete realization of the idea of cosmological
complementarity.
