What Is Identifiable on Old Babylonian Mathematical Tablets?

Old Babylonian mathematical tablets preserve finished numbers, not the scratch-pad sequences that produced them. For Plimpton 322 especially, mutually incompatible historio- graphical models (parametric triples, scribal-school reciprocals, table generation, sexagesimal- ratio trigonometry, cadastral catalogues) can generate the same surviving cells. The question is not which school is historically true, but how much of a protocol the clay itself identifies. The corpus comprises seven representative artefacts: Plimpton 322, CBS 10201, YBC 7289, BM 13901 Pb 1, the paired witnesses CBS 1215 / VAT 6505, MS 3971 #3, and the cadastral plan Si.427. That predicament—recovering a hidden computational procedure from a short table whose intermediate working has vanished, and whose remaining cells may contain discrete slips rather than smooth error—is the inverse problem addressed, in another field, by Two- Part Minimum Description Length scoring of candidate programs. Legras (2026a) gives a frozen form of that rule: each hypothesis is written in an agreed vocabulary of operations and charged for how long the writing is, plus how much of the table it still fails to explain. The present paper asks whether the same rule, once the vocabulary is restricted to attested Old Babylonian operations (DSL1), can measure identifiability on diplomatic encodings of clay. Technical derivations remain in the companion; what follows is the historical application. At the level of the tablet numbers, leading models of Plimpton 322 remain indistinguish- able: the data-fit gap |∆Ldata| = 0.300 bits is the difference between two diagnostic labels for the same cell, not a measurement that the clay decides. Under the baseline DSL1 codebook, Robson’s reciprocal-curriculum compilation is the shorter writing (∆L = 8.585 bits). That ranking is grammar-contingent: it occupies most of an independent sensitivity volume, but it can near parity if doubling is treated as an atomic cheap operation. Across the corpus, numerical invariants and some algebraic relations are identifiable; the chronological order of erased intermediate steps is not. The result is a map of identifiability, not a verdict on Babylonian mathematical culture.