Minimal Deterministic Construction of the Singlet Correlation (Extended Version with Philosophical Implications)

This expanded version of the manuscript “Deterministic Emergent Correlations without Probability” includes two additional appendices (Appendix A and Appendix B) that provide rigorous mathematical proofs. In particular, Appendix B contains a lemma on Fourier stability showing that under symmetry, boundary conditions, and isotropic smoothing, the negative cosine correlation is uniquely determined. Together with Appendix A, these results strengthen the theoretical foundation and clarify that the correlation is not assumed ad hoc but emerges from natural physical constraints.

Compared to version 1, this version offers a more complete and self-contained presentation of the deterministic emergent framework.