We report 1212 radial-velocity (RV) measurements obtained in the years 2009-2013 using an iodine cell for the spectroscopic binary nu Octantis (K1III/IV). This system (a_bin~2.6 au, P~1050 days) is conjectured to have a Jovian planet with a semi-major axis half that of the binary host. The extreme geometry only permits long-term stability if the planet is in a retrograde orbit. Whilst the reality of the planet (P~415 days) remains uncertain, other scenarios (stellar variability or apsidal motion caused by a yet unobserved third star) continue to appear substantially less credible based on CCF bisectors, line-depth ratios and many other independent details. If this evidence is validated but the planet is disproved, the claims of other planets using RVs will be seriously challenged. We also describe a significant revision to the previously published RVs and the full set of 1437 RVs now encompasses nearly 13 years. The sensitive orbital dynamics allow us to constrain the three-dimensional architecture with a broad prior probability distribution on the mutual inclination, which with posterior samples obtained from an N-body Markov chain Monte Carlo is found to be 158.4 +/- 1.2 deg. None of these samples are dynamically stable beyond 1 Myr. However, a grid search around the best-fitting solution finds a region that has many models stable for 10 Myr, and includes one model within 1-sigma that is stable for at least 100 Myr. The planets exceptional nature demands robust independent verification and makes the theoretical understanding of its formation a worthy challenge.
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