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a. Introducing the Series LLC

As a first way to increase our speed of formation, we had a closer look at a relatively new variant of the LLC: the Series LLCs.
A Series has a Master and individual Series. Each Series is considered an LLCs in its own right, with its own name and its own Member(s) independent from the Members of the Master LLC and other Series' Members.
An on-chain Series LLC has the exact same legal validity as any other LLC!
Crucially, the assets and liabilities between the Series amongst themselves and between the individual Series and the Master are entirely firewall-ed (though there is not yet sufficient caselaw to confirm this firewall is 100% secure in all States).
It is the Master that spawns the individual Series without the need for extra filing with State Registry: The Series' first Member simply signs an Operating Agreement and all that is required from the Master is to keep a record of each individual Series' chosen name and initial Member.
In this legal construct, the time to spin up a new entity can be reduced to the speed by which a Series contracts with its Master.
However, there's still a signature required, which introduces latency.
To make this at the push of a button, as was our goal, we had to go a step further.

A key discovery

Individual Series need a first Member.
In the analog world, this Member would either be a physical person or an official representing a company who contracts with the Master LLCs by signing the Series Operating Agreement.
Even when digital signing is used, the Master still needs to create a record of the name of the Member of the Series for it to be validly activated.
Our key discovery in this respect was that the first Member of a Series LLC can be a smart contract address.
As a result, a new Series LLC could be formed by signing a cryptographic transaction on blockchain between the owner of a wallet and a Master smart contract that activates the Series Operating agreement.
In this setup, the first Member of the Series LLC is whomever controls the wallet that sends Ether to the Master LLC smart contract address that spins-up the Series LLC.
Proof of existence of the new LLC is the smart contract created to hold the Series LLC Operating Agreement. Proof of ownership comes from the public key that shows the address of the first Member who sent the transaction to the Master smart contract.