Scale-Resolved Correlation as a Control Variable in Emergent Connectivity

This repository accompanies the research note:

Scale-Resolved Correlation as a Control Variable in Emergent Connectivity
Kirandeep Kaur, Independent Researcher (2026)
Contact: kiran@oxfordprioritymortgage.com

Manuscript

Scale-Resolved Correlation as a Control Variable in Emergent Connectivity
Kirandeep Kaur, January 2026

PDF: Paper/scale_resolved_correlation_connectivity.pdf

Repository: https://github.com/Kaydeep0/scale-structure-tests

Summary

Recent work in holography and quantum information suggests that spacetime connectivity emerges from quantum entanglement. This note introduces a scale-resolved correlation profile defined via admissible coarse-graining flows, and proposes that operational connectivity depends on how correlation is distributed across scales, not only on the total amount. An exact theorem is proven in a layered tensor-network model, and numerical simulations demonstrate noise-robust separation of states with identical total mutual information but distinct scale profiles.

Repository Structure

• Paper/

  • scale_resolved_correlation.tex — LaTeX source
  • scale_resolved_correlation.pdf — compiled manuscript
  • figure_*.png — generated figures

• notebooks/

  • scale_resolved_correlation_appendixA_noise_sweep.ipynb — simulation notebook for Appendix A

Reproducing the Simulations

python3 -m venv venv
source venv/bin/activate
pip install numpy matplotlib jupyter
jupyter lab

Open notebooks/scale_resolved_correlation_appendixA_noise_sweep.ipynb and run all cells.

Note: Figures in Paper/ are generated by the notebook.

License

MIT License. See LICENSE for details.