This paper presents a comparative framework documenting modular cortical reorganization across three independent primate lineages — papionins, capuchins, and Paranthropus — that achieved sophisticated cognitive capabilities within small brain size constraints. Drawing on the parameters-of-derived-cortical-organization analysis and integrating Hubbe and Harvati's (2026) morphometric data on Paranthropus cranial variation, we demonstrate that cortical reorganization rather than volumetric expansion is the primary mechanism for cognitive advancement in these lineages. The papionin-capuchin-Paranthropus convergence framework reveals that modular reorganization of existing cortical territory, particularly expansion of prefrontal and temporal association areas at the expense of primary sensory cortex, occurs independently when ecological pressures favor enhanced social cognition and extractive foraging. We propose that the VI trajectory logic — validated across the broader integration-depth framework — predicts which cortical modules will be reorganized based on the functional integration depth of existing neural circuits. This work establishes a comparative research program for studying convergent cognitive evolution under brain-size constraints, with implications for understanding hominin cognitive diversity beyond the genus Homo.