Two-State Populations

Population Ratio Uses the Same Weights

The population ratio is another view of the same weight ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The ratio uses the same weights

Upper over lower is one over three.

NupperNlower=13\frac{N_{\rm upper}}{N_{\rm lower}}=\frac{1}{3}
Population ratioThe ratio is checked from the same weights.energies=lower=0J|upper=2Jweights=lower=3|upper=1lowerFraction=3/4upperFraction=1/4upperLowerRatio=1/3weightOrigin=explicit integer weights

No new population source is invented

The ratio and fractions share one two-state check.

Nupper:Nlower=1:3N_{\rm upper}:N_{\rm lower}=1:3
Shared sourceA copied ratio cannot replace the weight ledger.energies=lower=0J|upper=2Jweights=lower=3|upper=1lowerFraction=3/4upperFraction=1/4upperLowerRatio=1/3weightOrigin=explicit integer weights