The law behind it

Time is not a container. In the reading behind ROX OS, time is an ordering variable: it sequences state changes. Every substrate has a finite capacity to integrate coherent state changes per unit of its own time. We call that capacity σ.

A workload puts a load on the substrate. We call the load λ: for a quantum circuit, the two-qubit gates it asks the machine to carry before the answer is read.

λ ≤ σ

A system stays ordered while the load stays under the capacity. Push more through it than it can integrate and order breaks into noise. On a quantum computer that break is decoherence: not a mystery, a capacity overload.

The ratio IQ = λ / σ tells you where you are. Three zones: laminar under 1, critical at 1, divergent above 1. ROX OS writes the zone on every forecast as the regime — under, at, beyond the edge.

Read the ratio yourself

0.75 IQ = λ / σ

σ on a real machine comes from today's calibration: the mean two-qubit error of the chosen loop sets how many gates the machine carries before the signal falls to the coin flip. λ comes from your circuit. Nothing here is estimated by hand; the forecast step reads both.

Where it is measured

The same law was measured on IBM Heron and IQM chips as a curve with a collapse edge: ratio over depth, the default arm falling to 0.500, the ROX arm holding signal deeper. The edge on a machine, today, is on The edge. The record of runs behind it is on Proof, wins and losses in the same size.

Sources: the product register §8 (axioms, IQ zones), the whitepaper (Zenodo DOI 10.5281/zenodo.22078286). The law is stated as a law and measured as an instrument with a forecasting record; nothing here comes from unpublished patent families.