Every framework in this atlas that denies an afterlife does so from outside the traditions that assert one. Cārvāka is the exception: a school that argued the case in Sanskrit, inside Indian philosophy, against Vedic ritualists and Buddhists and Jains simultaneously, and was taken seriously enough that the major schools felt obliged to answer it for well over a thousand years.
Its positions are austere. Only the four gross elements — earth, water, fire, air — are real; ether is rejected because it cannot be perceived. Only perception is a reliable means of knowledge, and inference, which is how everyone else gets to invisible souls and unseen karmic mechanisms, is unreliable because it always smuggles in an unverified general premise. There is no ātman distinct from the body. Consciousness is a property that emerges when the elements are combined in a living body, as the intoxicating power emerges when certain ingredients are mixed although none of them is intoxicating alone — an analogy the opponents quote constantly, and one that is recognizably a claim about emergence. When the body dies the combination ends and consciousness ends with it. There is therefore no rebirth, no karmic ledger carrying forward, no svarga and no naraka, and no mokṣa, since there is no bondage of the kind the other schools describe.
What follows is a critique of religion as economics. The Vedic rituals do not deliver their promised results; the priests who perform them eat well; and if an animal sacrificed at a rite really went to heaven, the school asked, why does the sacrificer not offer his own father? The famous verse attributed to Bṛhaspati advises that while life is yours, live joyfully, and that nobody escapes death — and adds, with deliberate provocation, that one should borrow money to drink ghee, since the body once burned does not return. Read as hedonism that is thin. Read as an argument, it is the point being made in its rudest available form: the debt cannot be collected from someone who does not exist.
The school's literature is essentially lost. The Bṛhaspati Sūtra survives only in fragments quoted by opponents, and the fullest presentation is the opening chapter of Mādhava's fourteenth-century Sarvadarśanasaṃgraha — which sets Cārvāka out first precisely as the position to be demolished before the real work begins. Almost everything known is therefore filtered through people arguing against it, which means the hedonism may be caricature and the epistemology may be the serious part.
It belongs in the atlas because it demonstrates that the Indian traditions' shared premises were contested at home, by Indians, with arguments. The wheel of rebirth is not what everyone in India believed. It is what most of them believed, over the objections of people who said the whole structure rested on an inference nobody could check.