Preface — the question, honestly stated

An on-chain program is a curious kind of mind. It is immortal, deterministic, and blind. It cannot see the world; it can only see numbers presented to it and check, against a public key, whether a number is a valid signature. From this single faculty — “this account carried a signature that verifies” — Solana builds its entire notion of authority. A program does not know who you are; it knows only that something able to sign for a certain public key consented to this transaction.

Into this world of keys we wish to introduce a deed: the act of verifying that a domain’s DNS record _solana.authority.<domain> contains a public key k. Today the system smuggles that deed onto the chain by proxy. A trusted human — the postmaster — performs the deed off-chain and then signs, and the chain accepts the signature as a token standing in for the deed. This is the whole of the self-service automation tension: to make the deed automatic, someone must place the postmaster’s whole key — authorize, deactivate, sweep, retune — hot on an internet-facing host, because the chain has no way to trust the deed itself, only the key that vouches for it.

The commissioning question is therefore this:

How may an off-chain agent prove to an on-chain program — a mind that reasons only in public-key cryptography — that it possesses a behaviour, in the same unforgeable way one proves possession of a private key, so that the program may accept a call which presumes that behaviour?

The correspondent’s own first conjecture was elegant: invent a language in which behaviours are written as canonical byte-sequences, and let an agent prove it has behaviour B by exhibiting that hash(agent) = hash(B) — the private key made implicit in the agent’s own binary structure. We will honour that conjecture by taking it apart precisely (it fails, and instructively), and then by rebuilding its true form, which turns out to be realisable.

Method. In imitation of the Principia I proceed by Definitions, then Laws, then Books of Propositions with their proofs and Scholia (commentaries, several drawn from the literature of imagined machines, since the commission invited Asimov and Star Trek to the table). Book I is theory; Book II is the taxonomy of solutions; Book III applies the whole to the concrete CreateDomain instruction.