Wikipedia reports Moshe Carmeli earned his 1964 Technion doctorate under Nathan Rosen's supervision

general-relativityhistory-of-physicshist-phmoshe-carmelinathan-rosenrenaissance-of-general-relativity

Bernadette Lessel's account of Roberto Lalli's Renaissance-era research centers names Nathan Rosen as the principal investigator of the Haifa/Technion center and notes that although Rosen himself is not credited with a general-relativity textbook, his student Moshe Carmeli became a prolific GR-textbook author starting in 1977 (see the companion claim on that first textbook). Wikipedia's article on Carmeli reports the specific supervisory link both in its infobox ("Doctoral advisor: Nathan Rosen") and in prose: "In 1964, he received his Doctor of Science from the Technion-Israel Institute of Technology in Haifa, Israel under the supervision of Nathan Rosen."

This is consistent with, but does not on its own independently corroborate beyond Tier 4, the broader claim that Rosen personally produced no GR textbook — it establishes only the advisor-student lineage, not Rosen's own publication record. That broader question remains open.