Axioms, or the Laws of Trust

Law I — The Law of Reduction. A Verifier can accept only what reduces to the checking of a signature against a key it already trusts. Everything a program “believes” it believes because a signature verified. Any scheme for proving a behaviour must, at its last step, hand the Verifier a signature to check. This is not a limitation to be lamented; it is the coordinate system in which all our solutions must be expressed.

Law II — The Law of Opacity (Rice’s wall). No Verifier can certify, from an Agent’s code alone, that the code computes a given behaviour. Any nontrivial semantic property of programs is undecidable (Rice’s theorem). Behaviour is semantic; code is syntactic. The gap is not an engineering inconvenience but a theorem.

Law III — The Law of the Terminal Fact. A behaviour is provable to a Verifier if and only if its terminal fact carries a witness. When the fact B observes is itself signed by a key the chain trusts, “trust the behaviour” collapses (by Law I) into “check the witness.” When the terminal fact carries no witness — a human’s honest intent, the fairness of a private coin — no proof of the behaviour exists, and one must retreat to attestation, plurality, or bond.

Law IV — The Law of Conserved Trust. Trust is never created, only relocated. Every construction in this book moves the root of trust from one place (a hot operator key) to another (a hardware vendor, a mathematical assumption, the DNS root, an economic majority). The art is not to eliminate the root — impossible — but to move it somewhere smaller, colder, more plural, or already-assumed.

Scholium to the Laws. The reader will notice that Law III is the conserved quantity of this whole subject, in the sense Newton meant when he found that momentum is conserved across a collision no matter how intricate the impact. No matter how baroque the machinery of a trust scheme, ask only: what is the terminal fact, and does it carry a witness? If yes, the scheme can be made to work; if no, the scheme is secretly smuggling in an attestor, a quorum, or a bond, and you should find it and price it.