To determine which piece of additional information does not help identify the nine nations, let's analyze the options against the given data:
1. Germany’s industry GDP is US $1.2 trillion: Knowing Germany's industry GDP as an absolute value helps to position it relative to other nations, but it may not uniquely identify Germany given other countries may have similar or close values.
2. The nation ranked fourth in terms of agriculture GDP has its agriculture GDP valued at US $150 billion: This information can significantly narrow down the possible countries since it provides a clear ranking and GDP value.
3. In terms of percentage contribution to the respective nations’ GDP, France and Japan’s agriculture sectors contribute the same: This information offers a unique insight, allowing direct comparison between France and Japan that could differentiate them from the others.
4. Japan’s industry GDP is US $1.25 trillion: Just like the Germany's industry GDP, knowing Japan’s specific industry GDP is a substantial identifier, depending on how other countries line up with similar metrics. However, as a general absolute metric, it leaves much to interpretation.
5. Both Japan’s and Germany’s industry GDPs are more than US $1 trillion: This information helps differentiate these two countries with a large GDP, but it’s less precise than knowing Japan’s industry GDP as in option 4, as it doesn’t pinpoint a specific figure.
Conclusion: The statement "Germany’s industry GDP is US $1.2 trillion" does not uniquely identify Germany among the nations, as similar GDP values may overlap with other countries. Thus, this option provides the least additional clarity for identifying the nations.