Contracts
Intents are a precise specification of when a transaction is accepted by a party. When a party installs an intent, it exerts its ability to reject some transactions while commiting to accept others. Put another way, they're a description of the currently active rights and duties at an address. Since a party can always unilaterally change its installed intent, this description can be ephemereal and is not reliable.
However by allowing a third-party to hold rights and duties, we can turn them into an asset. Imagine Alice specifies a swap intent with specific terms, and does not install it, but rather gives Bob the ability to, at a later time, force Alice to abide to those terms during a transaction. Now, if rather than being gifted, Bob pays for this ability, we have described an option and its premium.
The mechanism can be modelled by a swap between two assets, one being a certain amount of a token, and the other being ownership over an intent itself.
We use the term "contract" for an intent which is held as an asset. Note the asset itself is structurally an intent in the exact same sense that the intents that govern its usage and transfer, so we have a self-similar situation where arbitrarily nested contracts can be expressed while retaining interoperability with all other intent constructs, including temporal ones, oracles, thresholds, etc.
We thus unlock a cambrian explosion of financial instruments all built from a small number of general purpose blocks.