The precision ladder

Zeq claims ≤0.1% on every result. That figure isn't a hope or a benchmark — it's the top of a ladder of guarantees, each rung holding up the one above it. Here's the whole ladder, bottom to top.

The rungs

1 · An exact clock

The Zeqond is exactly 777,000,777 integer nanoseconds, and phase is computed in big-integer arithmetic — so the time base never drifts. Nano-zeqond precision.

2 · A bounded modulation

KO42 modulates with amplitude α = 10⁻³, and because f·τ = 1 exactly, one whole cycle fits each Zeqond and averages to zero — so the clock stamp can't bias the value beyond 0.1%. KO42.

3 · Real formulas, bound constants

Solvers evaluate the operator's actual equation over CODATA-2018 constants in float64 — the physics is standard, not approximated. The solvers.

4 · An enforced gate

Every result's uncertainty is checked against the 0.1% bound before it returns; a solver that can't meet it is flagged, never quietly passed. Step 5, VERIFY.

5 · Independent recompute

The cited closed form is re-evaluated on a separate code path and checked to agree — a result its own equation can't reproduce is caught.

6 · Public conformance

Anyone can re-run a node against a content-addressed corpus of golden vectors; one mutated constant fails a vector. Conformance.

Why a ladder, not a number

A single "≤0.1%" printed on a datasheet is a claim. A ladder is a structure you can climb and inspect: the exactness at the bottom (an integer clock) is what makes the bound at the top (0.1%) clean rather than approximate, and every rung in between is checkable. You don't have to believe the top figure — you can descend the ladder and verify each rung, right down to hashing a node's golden vectors yourself.

That's the difference between precise and provably precise. Zeq aims for the second, and the ladder is how it gets there.

The rungs​