Experiment A: Elliptic Curve Products (E E)
Knneth decomposition and Lefschetz theorem. CAS-6 analysis: Proof of full closure via categorical isomorphism. Computational verification of bases and metrics.
Experiment B: Higher Elliptic Products (E)
Higher-degree cohomology. Exhaustion by divisor products. CAS-6 metrics: Dimension match implying probability 1. Symbolic computations confirming stability.
Experiment C: K3 Surface Products (K3 K3)
Dimensional analysis (404 vs. 400). Transcendental gap as categorical incompleteness. Candidate cycles (diagonals, FM kernels) with rank tests. Computational pipeline for span verification.
Discussion: Closure, Stability, and Emergence in HC
Interpretation of results through formalized CAS-6. Relations to recent advances (e.g., spectral methods, deformation theory). Limitations and heuristic epistemology.
Future Directions
Extensions to Calabi-Yau and higher K3 products. Integration with derived categories and Lean formalization. Computational experiments and philosophical reflections on post-rigorous math.
Conclusion
