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
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
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.
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Paper/scale_resolved_correlation.tex— LaTeX sourcescale_resolved_correlation.pdf— compiled manuscriptfigure_*.png— generated figures
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notebooks/scale_resolved_correlation_appendixA_noise_sweep.ipynb— simulation notebook for Appendix A
python3 -m venv venv
source venv/bin/activate
pip install numpy matplotlib jupyter
jupyter labOpen notebooks/scale_resolved_correlation_appendixA_noise_sweep.ipynb and run all cells.
Note: Figures in Paper/ are generated by the notebook.
This repository is dual-licensed for noncommercial use:
| Content | License |
|---|---|
Code (.py, scripts, notebooks) |
PolyForm Noncommercial 1.0.0 |
| Paper, figures, LaTeX, written content | CC BY-NC-SA 4.0 |
Commercial use requires a separate license. See COMMERCIAL-LICENSING.md for details and contact information.
If you use this work, please cite:
Kaur, Kirandeep. "Scale-Resolved Correlation as a Control Variable in Emergent Connectivity." 2026. https://github.com/Kaydeep0/scale-structure-tests