How do Theravāda and Mahāyāna explain the authenticity of their expanded canons?

Both Theravāda and Mahāyāna accept a core early Buddhist canon, yet each tradition also relies on additional bodies of literature Theravāda on the commentaries (Aṭṭhakathā, Ṭīkā, and post-canonical works such as the Visuddhimagga) and Mahāyāna on sūtras not preserved in Pāli and often considered “later” by modern scholarship. On what doctrinal or hermeneutical grounds does each tradition justify the authority of its later textual strata? Are there explicit criteria within each tradition for discerning which later works are authoritative, semi-authoritative, or merely scholastic? How do traditional scholars within each school respond to the charge that the later texts introduce ideas not present in the early Nikāyas/Āgamas?