Registers a builder code for the signing account. The server calls FeeManager.registerBuilderCode(account) and stores the supplied slug/name against the assigned builder_id. Gas sponsored by API service.

fee_recipient is always the signing account — it is derived, never accepted from the client. Up to 10 builders per account; a request past that cap is rejected without sending a transaction.

Prerequisites:

1. GET /v1/auth/nonce — one-time nonce (5 min TTL, shared with the Login flow)
2. GET /v1/auth/eip712-domain — EIP-712 domain (name, version, chainId, verifyingContract = Authorization contract)

Typed data:

RegisterBuilder(address account,string slug,string name,uint256 nonce,uint32 deadline)

Sign as standard EIP-712 typed data (e.g. ethers signTypedData) with nonce = the hex nonce parsed as a uint256.

Signature: 64-byte EIP-2098 compact (r + yParityAndS) or 65-byte (r+s+v, auto-converted).