Minimal Deterministic Construction of the Singlet Correlation

This preprint develops a minimal deterministic construction of the singlet correlation without relying on probability axioms. 
Instead of starting from a probabilistic measure, the framework uses a deterministic equidistribution process to reproduce 
the correlation −cos(α−β) exactly. The approach shows that structures usually derived probabilistically can be reconstructed 
as emergent consequences of a deterministic sampler.

Compared to earlier versions, this v3 release is fully self-contained and significantly expanded:
- Appendix D introduces an explicit Python sampler, ensuring reproducibility of the deterministic construction.
- Appendix E provides a formal mathematical response to criticism, demonstrating uniqueness and clarifying the distinction 
  between probabilistic and deterministic readings.
- A vector flowchart is integrated to illustrate the construction in a transparent and accessible way.

Together, these additions make the manuscript mathematically complete and pedagogically clear, while also opening 
perspectives for future applications (e.g. cryptography, didactics, and foundations of quantum theory).