Arbitrage
The corridor is not held by decree. It is held by people who profit from holding it — at both edges.
Two loops at two edges
At the cost of entry
When the market price rises above the mint price by more than the costs, minting is cheaper than buying: mint a position, close it — the closing is above backing, so it is free and raises backing for everyone — and sell. The price returns under the ceiling, and the ceiling keeps rising.
At backing
When the market price falls below backing by more than the redemption fee and the costs, buying on the market and redeeming in the contract pays: the price returns over the floor. The redemption multiplier widens this band in drawdowns, so the floor never becomes a cliff.
How wide the band stays
Inside the corridor the price settles into a band whose width is roughly the cost of a round trip: two pool fees, the transfer fee, slippage, and gas — cents on Arbitrum. At a 1 % pool tier that is about two per cent; at 0.3 %, under one. The pool’s fee tier is, in effect, a parameter of the corridor.
The liquidity provider
A concentrated-liquidity position needs a range; the corridor is one, with edges the contract publishes and defends. The provider earns fees from every arbitrage and every trade inside the band and re-ranges as the corridor rises. What that earns, phase by phase, with numbers, is in the study.
States of the market
Steady inflow
New positions close above backing; the floor rises; the price sits near the ceiling. Volume high, both loops busy. The provider’s best phase.
Stagnation
Few new positions. In Phase 2 the ceiling keeps rising while the floor stands still; the corridor widens from above. Volume thin; the price drifts down.
Outflow
Holders redeem. The pool shrinks; backing does not, because redemption is neutral. Volume comes from redemption arbitrage at the floor.
Volatile collateral
If the reserve holds volatile currencies, the floor moves with them. Both edges then move for reasons outside the protocol.
The study
Both loops with their break-even conditions, the band as a function of the fee tier, the provider’s position value and impermanent loss inside a bounded range, three phases with numbers, and the choice of tier.