Why does silver disappear at New Year? How is royal tax calculated?

Outside Empire Village mode, a living king taxes the territory at New Year unless relations have been broken. Population brackets select a per-person rate for the entire population, not just people beyond the bracket. Current code has two definite assignment-order faults: sufficient coins cause the deduction to become zero; insufficient savings are cleared before subtracting them from remaining tax, so treasury silver can be overcharged. The separate tax audit reproduces these branches. They are current execution results, not intended normal rules.