What changed
Polkadot: shared security was the paper. Slots were the market.
A relay chain checking many chains is a design. Who rents a slot, and for how long, is a later rule.
Original thesis
Many chains share one security budget. A relay validates the state transitions. A parachain does not have to recruit its own validator set.
What changed
Slot auctions, leases and crowdloans were how scarce relay capacity was sold. They are not the security proof. Governance and a treasury sit beside the paper.
What remains useful
Cite the paper for shared security. Cite a current parameter page for who occupies a slot. Do not treat a lease price as the mechanism.