Exact critical exponents of directed percolation in 1+1 dimensions
In plain words
Directed percolation is the simplest model of spreading that can die out. In one space dimension its exponents are known to six digits from series expansions, but no exact formula exists and they do not look like simple fractions.
Precise statement
For $1+1$ dimensional directed percolation (bond, site, or the contact process), determine exact values of $\beta \text{ approximately } 0.276486, \nu_{\mathrm{perp}} \text{ approximately } 1.096854 \text{ and } \nu_{\mathrm{par}} \text{ approximately } 1.733847$, or show that they do not come from a solvable structure; the model is not known to be integrable and its critical point lacks conformal invariance in the usual sense because time and space scale differently. An answer is closed forms matching the series values.
What would settle it
An exact solution or an integrable mapping reproducing the series estimates, or a proof excluding a stated class of closed forms.
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