Hi!! There are a few issues with your evaluation of the RAND report; you link the brief here but the same applies for the full report, and wrt the distinction, "Overextending and Unbalancing Russia" is the title of the brief and not of the report ("Extending Russia: Competing From Advantageous Ground"), but obviously that's not a big deal. Where the real issue starts is when you move from the correct statement that the report "suggests sending arms to Ukraine" to the incorrect statement "and provoking a war." Both the brief* and the full report** clearly warn that it's necessary to balance military support between weakening Russia "and provoking a war." While this supports the aspect of your argument that Russia was forced by the US/NATO to invade Ukraine, it does not support the aspect arguing that this was done purposefully to overextend Russia.

*"But any increase in U.S. military arms and advice to Ukraine would need to be carefully calibrated to increase the costs to Russia of sustaining its existing commitment without provoking a much wider conflict in which Russia, by reason of proximity, would have significant advantages."

**"The Ukrainian military already is bleeding Russia in the Donbass region (and vice versa). Providing more U.S. military equipment and advice could lead Russia to increase its direct involvement in the conflict and the price it pays for it. Russia might respond by mounting a new offensive and seizing more Ukrainian territory. While this might increase Russia’s costs, it would also represent a setback for the United States, as well as for Ukraine."

"Most of these measures—whether in Europe or the Middle East—risk provoking Russian reaction that could impose large military costs on U.S. allies and large political costs on the United States itself. Increasing military advice and arms supplies to Ukraine is the most feasible of these options with the largest impact, but any such initiative would have to be calibrated very carefully to avoid a widely expanded conflict."