The market is made of Doppler's audited contracts on Robinhood Chain; multiply adds one router in front of them. What each guarantees:
DopplerHookInitializer (0x4e34…a544). The v4 hook of every pool, and the owner of its liquidity. A pool created with fee beneficiaries is Locked: no exit, no withdraw, no migration. The only functions that could alter a live pool are gated on the token's governance timelock, and every multiply coin is launched with the no-op governance, whose timelock is the burn address. Nobody can call them.
Rehype hook (0x5f9e…3215). Takes the fee, converts it, forwards it. Its schedule (flat or decaying) is written once at launch.
Launch router (0xB9De…5Acd). Enforces the shape of every launch: supply, opening market cap, fee range, protection schedule, fee destination, Doppler's 5%. It is upgradeable so its address can stay stable for indexers; an upgrade can only change future launches, because the router has no function that reaches a pool once it exists.
A rug in the ordinary sense (someone withdraws the pool and walks) is not a thing that can happen here. Not for the creator, not for multiply.cash, not for Doppler. There is no LP token to unstake and no timelock that eventually opens.