The upgrade authority is burned. Nobody can rewrite a published root, reopen a closed epoch, or touch what's sitting unclaimed. It closes on schedule whether anyone's watching or not.
I built a distributor that never sweeps unclaimed value back to anyone. Airdrops and vesting contracts have always had the same failure: what nobody claims sits in a treasury, or gets clawed back by whoever's running it. root doesn't have a treasury.
Every epoch, every wallet's entitlement gets hashed into a leaf, and the whole epoch collapses into one root published on chain. Claiming just means proving your leaf against that root, log₂(n) hashes, nothing else required. Anyone can call rollover() once a window closes and keep a fixed reward for folding what's unclaimed into the next epoch's pool.