"The existence of anti-halite..."
...Anti-salt? Oh god, now the only thing I can think of is matter/anti-matter collisions and matter-to-energy conversions, but with salt.
Also, regarding the history of crossbows... No one knows who invented it, really. Both China and Ancient Greece started having known examples of crossbows appearing at almost the same time (also, with the theory that Chinese Emperors/Artisans hired Greek artists to teach them how to do sculpting and molding for projects like the Terracotta Army of Qin Shi Huang... albeit like 2-300 years later than the crossbow... it's possible there was fringe trade of culture and products that historically went unnoticed).
China definitely cornered the market on crossbows early on, however. They were fielding entire armies of them while the crossbow was not (yet) widely used in Europe. It wasn't until the era of the Roman Empire and afterwards that the crossbow finally found its niche in Europe and put a hell of a lot of people into the ground.
And, oh, the crossbow as not banned by the Pope. The Pope didn't permit it being used against fellow Christians... Non-Christians could still be murdered quite happily with the crossbow. And plenty of mercenaries and other countries continued to use it against Christians as well.
Also, Zircona, as usual, is right. Kazuma keeping all this entirely Valetta is incredibly shitty and will likely make her feel like she wasn't trust-worthy or capable enough or something along those lines. Valetta is not dumb. If you simply had told her, "I'm doing this" and when she offered her help you said you didn't want her to get her hands dirty with blood and wanted to focus on production of things like the forge, iron production, etc. instead because they're important too... She'd understand. But, no. MC is going to pull a dumb, because misunderstandings need to be misunderstood or whatever.