The foundational statement is the rule cited by Rav and Shmuel in Pesachim 29b-30a: anything Torah-forbidden that becomes mixed with its own type, so that it cannot be distinguished, is not nullified by any amount, while a mixture with a different type is only forbidden if its flavor is detectable — and this is why leavened bread during Pesach remains forbidden even in a minuscule quantity when mixed with matza of its own type.
Mishnah Avodah Zarah 5:8-9 generalizes this principle explicitly, stating that a substance of its own type is forbidden in any amount while a substance of a different type requires only enough to impart flavor, and it lists items that are forbidden and render mixtures forbidden in any amount regardless of type — wine used for a libation, an item of idolatry, hides of a stabbed animal, a stoned ox, a heifer whose neck was broken, birds of a leper, hair of a nazirite, the firstborn donkey, meat cooked with milk, the scapegoat, and non-sacred animals slaughtered in the Temple courtyard.
A separate category of total non-nullification, even in a thousand, is drawn in Nedarim 58a-58b: any item "that has a permitter," meaning its prohibition is temporary and will lapse on its own (such as untithed produce, second tithe, consecrated items, or new grain before the omer), is never nullified by mixture with permitted items, because there is no need to rely on nullification when the prohibition will end by itself; by contrast, items with no such built-in permitter, like teruma, challah, orlah, and mixed species of the vineyard, were given a fixed measure by the Sages. Beitzah 3b applies this same logic to an egg of uncertain festival-status, ruling that since its prohibition is temporary it is not nullified even by a thousand eggs, and drawing a further distinction for items normally sold by count, which are not nullified even under rabbinic prohibition, all the more so under Torah law.
A third category, items that are inherently significant ("chashuv") and thus never batul regardless of type, is catalogued in Mishnah Orlah 3:1-9, which lists cracked-shell nuts, pomegranates of Badan, sealed casks, beet stalks, cabbage-heads, and Greek gourds — later codified by Mishneh Torah, Forbidden Foods 15:1-8 and Mishneh Torah, Forbidden Foods 16:1-3 as the seven items that are forbidden in any amount when mixed with their own type, and brought likewise in Shulchan Arukh, Yoreh De'ah 110:1 and Tur, Yoreh De'ah 110.
Shulchan Arukh, Yoreh De'ah 101:1-2 extends this non-nullification to a piece of meat that is fit to be honored (a guest dish), ruling that such a piece is not nullified even by a thousand, equating its status to that of a berayah (a complete creature), and the gloss there adds that this holds even for rabbinic prohibitions.
The later commentators work out the scope and boundaries of these non-nullified categories: Arukh HaShulchan, Yoreh De'ah 110:1-30 explains that the non-nullification of a significant item is only rabbinic in force, so that doubts about its significance are resolved leniently; Beit Yosef, Yoreh De'ah 110:17 discusses how, once such a non-nullified mixture is itself further diluted or one piece is lost at sea, the whole becomes permitted; and Siftei Kohen on Shulchan Arukh, Yoreh De'ah 110:1-8 and Turei Zahav on Shulchan Arukh, Yoreh De'ah 110:1-4 debate whether the chashuv-item rule applies only within its own type or also across types, and whether an item merely sold by count (like an egg) is included.
Torat HaBayit HaAroch, The Fourth House, The First Gate 6 traces the underlying Gemara analysis of the list of items forbidden in any amount, noting the question of whether the governing criterion is that the item is sold by count or that it is forbidden for benefit, and that some items require both factors together.
Among the Zevachim sources, Zevachim 73b:5 records a case of sacrificial birds whose categories became intermixed where, even at a ratio of one in ten thousand, all must be destroyed, extending the concept of total non-nullification into the sacrificial domain.
Modern treatment of these same categories appears in Rav Eliezer Melamed (Peninei Halakhah, Kashrut 34:9), which organizes the non-nullified classes as a berayah, a piece fit to be honored, and significant items sold by count, none of which are nullified even in a thousand whether mixed with their own type or another type, adding that chametz on Pesach and items of idolatry are likewise never nullified due to their extra severity; and in Rav Eliezer Melamed (Peninei Halakhah, Kashrut 34:11), which clarifies that this status attaches only to foods customarily sold by individual count due to their importance, not to foods sold by weight or volume, or counted merely for pricing convenience.
Separately, Pesachim 21b:10-11 addresses a related but distinct question — not nullification but scope of prohibition, establishing that Torah prohibitions phrased only in terms of eating are nevertheless understood to forbid deriving benefit as well, which is a different doctrinal strand from the any-amount nullification question.
Sefer HaChinukh 229:1 likewise addresses a distinct principle, that the Torah prohibition against theft applies even to less than a peruta in value even though the biblical penalty does not, illustrating the general concept of a prohibition that applies below a halachic threshold, though this is not the same doctrine as non-nullification in a mixture.
Vayikra 7:18 and Bamidbar 15:22-31 are pesukim bearing on piggul and intentional transgression respectively, and do not themselves address the mechanics of nullification in mixtures.
Shulchan Arukh, Yoreh De'ah 102:1 confirms the Nedarim principle in practical form, ruling that an egg laid on a holiday, if mixed with other eggs, is never nullified even by a thousand, because its prohibition is temporary and will lapse the next day, while if mixed with a different type of food it is nullified by sixty.