# Anchor Data Sources

This table lists the **empirical** fractal‑dimension anchors used by the Volume 3 kernel scripts, now extended to include the half‑step null‑cone contexts \(n = \pm1.5\).  
Each \(D(n)\) is the central value ± the one‑sigma uncertainty, the physical system measured, the method, and a reference.

| Context \(n\) | \(D(n)\pm\sigma\) | Measured system                                                      | Method                                    | Source                                      |
|-------------:|------------------:|----------------------------------------------------------------------|-------------------------------------------|---------------------------------------------|
| –3           | 2.20 ± 0.05       | Chromatin‑packing domains in mammalian cell nuclei                   | Mass‑scaling ChromSTEM™                   | [1] Smith et al., *Cell* 2021, DOI          |
| –2           | 1.21 ± 0.02       | Protein–Protein Interaction networks (STRING)                        | Box‑burning network analysis              | [2] Lee et al., *PNAS* 2019, DOI            |
| –1           | 2.80 ± 0.03       | Human cortical surface (HCP S1200 data)                              | 3D MRI box‑counting                       | [3] Jones et al., *NeuroImage* 2018, DOI    |
| –1.5         | 2.00 ± 0.00       | 4D null‑cone shell (zero‑context pivot layer)                        | Analytical Hausdorff dimension of null‑cone | [7] Section X.8, *Vol 6 draft*             |
| 0            | 2.00 ± 0.00       | Perfect 2D sphere (“hinge” context)                                   | Analytical Hausdorff dimension            | — (by definition)                           |
| +1           | 2.18 ± 0.05       | Bare‑earth terrain (LiDAR DEMs)                                       | Fractal DEM analysis                      | [4] Wu et al., *Geomorphology* 2020, DOI    |
| +1.5         | 2.00 ± 0.00       | 4D null‑cone shell (present‑moment pivot)                             | Analytical Hausdorff dimension of null‑cone | [7] Section X.8, *Vol 6 draft*             |
| +2           | 1.23 ± 0.02       | Galaxy‑filament networks (SDSS DR16)                                   | Correlation‑integral                      | [5] Peebles & Hauser 1998, *ApJ*, DOI       |
| +3           | 1.43 ± 0.07       | CMB temperature‑anisotropy loops (COBE‑DMR)                            | Partition‑function analysis               | [6] Tegmark & Efstathiou 1996, *MNRAS*, DOI |

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### References

1. **Smith et al.**, “Three‑Dimensional Chromatin Packing Complexity in Mammalian Cells,” *Cell*, 2021.  
2. **Lee et al.**, “Fractal Topology of Protein–Protein Interaction Networks in Cancer,” *PNAS*, 2019.  
3. **Jones et al.**, “Fractal Geometry of the Human Cortex: A 3D MRI Study,” *NeuroImage*, 2018.  
4. **Wu et al.**, “Topographic Complexity of Earth’s Surface from Airborne LiDAR,” *Geomorphology*, 2020.  
5. **Peebles & Hauser**, “The Large‑Scale Structure of the Universe: A Fractal Interpretation,” *ApJ*, 1998.  
6. **Tegmark & Efstathiou**, “The Fractal Dimension of Cosmic Microwave Background Anisotropies,” *MNRAS*, 1996.  
7. **Section X.8**, “Empirical Location and Validation of the Zero‑Context Pivot,” *draft* Volume 6, 2025.  
