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Description
In this talk we discuss a remarkable property of a special kind of Feynman integrals: their final results are entirely determined by singularity structures and symbology. Exhibiting parity-odd behavior under flipping sign of their leading singularities, the symbol-level results of these integrals are uniquely fixed up to an overall constant solely by the parity-odd ansatz derived from symbol alphabet predictions and integrable conditions. This uniqueness property further constrains all singularities, particularly algebraic singularities, to manifest in characteristic patterns. Leveraging this property, we predict simplified forms for selected higher-point/higher-loop integrals and explicitly compute representative examples, including a special super-component of nine-point two-loop N^2MHV scattering amplitude, as well as basis integrals of five-point half-BPS correlators in N=4 super Yang-Mills theory.
