The conjectured S-type retrograde planet in nu Octantis: more evidence including four years of iodine-cell radial velocitiesAuthors:Ramm et alAbstract: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 planet's exceptional nature demands robust independent verification and makes the theoretical understanding of its formation a worthy challenge.