Kontsevich's conjecture on transformations of period integrals

A period is a number admitting an integral representation whose functions and domains of integration are algebraic with coefficients in $\bar{\mathbb{Q}}$. The relevant transformations are: additivity of domains and integrands, invertible algebraic changes of variables (with the corresponding Jacobian in several variables), and the Newton–Leibniz formula in one variable, replaced by Stokes' formula in several variables. Kontsevich's conjecture. If a period has two integral representations, then one can pass from one formula to another using only rules (1)–(3), with all functions and domains of integration algebraic with coefficients in $\bar{\mathbb{Q}}$. This conjecture asserts that the standard calculus and Stokes transformation rules account for every equality between integral representations of periods; the supplied text presents it as a widely held belief, but the candidate is marked resolved by the parser.