This dataset provides the complete evidence bundle for the Intuitivism Diagrammatic Core (IDC), a diagrammatic framework for representing and verifying algebraic equivalence within a commutative-ring structure. The archive is designed as a fully reproducible validation pipeline and includes: • Formal computational validation of algebraic axioms• Randomized symbolic stress testing of expressions• Diagram-to-expression (JSON) roundtrip verification• Monte Carlo simulations of randomized controlled trial (RCT) designs• A synthetic human-pilot dataset for validating the statistical analysis workflow• Sensitivity analysis under reduced IDC advantage and improved baseline conditions• Overlap analysis quantifying performance similarity between IDC and traditional symbolic algebra (TSA)• Failure-case analysis identifying conditions in which IDC performs worse• Figures, structured reports, metadata, and full audit outputs All results in this archive are reproducible using the included data and documentation. The human-pilot dataset is synthetic and does not contain real human-subject data. It is included to validate the analysis pipeline, simulate expected study behavior, and support the design of a future empirical pilot study. This dataset demonstrates that IDC is formally consistent, computationally verifiable, and statistically modeled across a range of assumptions. It establishes readiness for empirical validation but does not claim real-world performance superiority. Independent human-subject experimentation and replication are required for empirical confirmation.