Statement 1 is Correct: DHRUV64 is the third chip to be fabricated under the Digital India RISC-V (DIR-V) Programme. The first chip was THEJAS32 and the second was THEJAS64. The DIR-V programme aims to create a complete portfolio of future-ready, indigenous RISC-V-based microprocessors to reduce India's dependence on imported chips and foreign intellectual property.

Statement 2 is Correct: Developed by the Centre for Development of Advanced Computing (C-DAC) under the Ministry of Electronics and Information Technology (MeitY), DHRUV64 is officially recognized as India's first homegrown 1.0 GHz, 64-bit dual-core microprocessor. It is built on the open-source RISC-V instruction set architecture, which eliminates proprietary licensing fees and ensures technological sovereignty.

Therefore, both statements are correct.