Worlds Next Door: A Candidate Giant Planet Imaged in the Habitable Zone of α Centauri A. II. Binary Star Modeling, Planet and Exozodi Search, and Sensitivity Analysis by Aniket Sanghi, Charles Beichman, Dimitri Mawet, William O. Balmer, Nicolas Godoy, Laurent Pueyo, Anthony Boccaletti, Max Sommer, Alexis Bidot, Elodie Choquet, Pierre Kervella, Pierre-Olivier Lagage, Jarron Leisenring, Jorge Llop-Sayson, Michael Ressler, Kevin Wagner, Mark Wyatt

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