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An operator is a single verb of the language — one equation (F = ma, the Schwarzschild radius, Shannon entropy). A state contract is deployable JSON logic that composes operators and runs on triggers (every Zeqond, cron, on-event, replay), writing Zeqond-stamped rows to your entangled state. Operators are what you compute with; state contracts are what you ship.

Use compute() for one operator evaluated once (a textbook formula → a signed number). Use solve() for the master-equation path, where multiple operators are synchronized onto one timebase and integrated over time. Use multibody() for many interacting bodies (the three-body problem) with pairwise coupling. solve and multibody are where the framework synchronizes physics — the single-operator path is just the simplest case.

Yes. Every platform result returns a CKO envelope with the operator chain, the generated equations, the Zeqond it ran at, and an Ed25519-signed claim plus a ZeqProof HMAC. A third party can re-derive the result offline and check the signature — no account, no secrets, no trust required.

It is the precision bound — the tolerance at which the kernel compiles the physics to a chosen analytic reference (free-fall, SHM, or a model). For textbook operators via compute() the framework is verified to ≤0.1%. For the nonlinear master equation via solve(), errorPct is the integration tolerance to that reference, not a fault.

No key for local compute() — zeq.compute({ domain: "Classical Mechanics", inputs: { m: 5, a: 9.81 } }) returns 49.05 N offline — or for pulse(). The master-equation paths solve() and multibody() run server-side and need a key, as does the hosted signed compute. Get one with the CLI: install via curl -fsSL https://zeqsdk.com/install.sh | sh, then run zeq signup "four memorable words" to mint your account, machine and zeq_ak_ key.

Yes. The framework is fork-able: every domain runs its own sovereign instance of ZeqVM, no central operator required. Run the whole stack locally or fork a new framework domain — see Operate → Self-hosting.