Intuitivism Diagrammatic Core (IDC): Formal Validation and Synthetic Pilot Evaluation of a Diagrammatic Algebra Framework

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.