Key Reuse

Public-private key pairs are used extensively in contracts. The public key serves as a unique id, and the private key is what a share holder uses as proof of title to the shares. The short story on key reuse is: don't. In greater depth: A given public key should only show up as receiver of shares once
*While key reuse is just recommended against for some cryptocurrencies, for Assign Onward it is a requirement which, together with atomic assignment makes double spend checking easier, supporting the goal of minimized real world cost of participation.
in a blockchain.
*the chances of competent key generation software accidentally making the same key pair twice is vanishingly small
As a nod to practicality, since so many keys will show up in an active blockchain, the genesis block might place a limit like: no double use of keys to receive shares within the range of all sources of shares' blocks to the recording block, enabling underwriters and error checkers to more practically monitor the allowed/not allowed situation.
*this might also drive up the transaction cost when sourcing from shares very far back in the chain - it's a higher cost in shares, but should be easily offset by coin inflation.
Still, it is more than a best practice asset organizer software should NOT reuse key pairs that are involved in share assignment operations.
*keys used for persistent identities are different from keys used in share assignment operations, persistent identity keys may be used multiple times by their owners - although owners should consider periodically expiring/revoking old keys after using them to sign new ones.