CORE Vedic corpus and systems of reasoning
The Shruti / Smriti corpus and six orthodox darshanas form the opening grammar of the Indian knowledge system. Shruti refers to revealed and orally transmitted authority: the 4 Vedas, their Brahmanas, Aranyakas and the Upanishadic layer. Smriti refers to remembered and authored tradition: Dharmashastra, Itihasa, Purana, law, ritual manuals and later commentaries. The Upanishadic corpus is usually counted at 108 texts, with 13 principal Upanishads often used for classical Vedanta. The value system begins inside this corpus because knowledge is tied to speech discipline, teacher-student transmission, debate, ritual duty and inner self-knowledge. The six orthodox darshanas are not six religions; they are six knowledge-method families that accept Vedic authority in different ways. Nyaya, associated with Gautama, develops logic and valid means of knowledge. Vaisheshika, associated with Kanada, analyses categories such as substance, quality and action. Samkhya, associated with Kapila, separates purusha and prakriti. Yoga, associated with Patanjali, disciplines mind and practice. Purva Mimamsa, associated with Jaimini, interprets ritual action. Uttara Mimamsa or Vedanta, associated with Badarayana, interprets the Upanishadic teaching on brahman. Rajasthan enters the frame through Bhinmal in present Jalore district, where Brahmagupta later wrote the Brahmasphutasiddhanta in 628 CE. That work belongs to mathematics and astronomy, yet it also shows how Sanskrit learning, calculation, cosmology and commentary remained connected in western India after the older Vedic and Vedanga streams.