Model register guide
Measurement Registers
This page collects the symbols used to keep the model's measurement registers separate. The notation distinguishes observed redshift, accumulated path response, depth coordinates, weak-field response, and compactness so the chapters can refer to each register consistently without collapsing them into one scale.
| Symbol | Name | Short meaning | Role in the model |
|---|---|---|---|
| z | Observed redshift | The measured spectral shift of light from a source. | Primary observable that is re-expressed, but not replaced, by the finite-response registers. |
| A = ln(1+z) | Accumulated path response | A logarithmic rewrite of the same observed redshift signal. | Tracks cumulative response along the path through the finite deformable domain. |
| G(d) | Local response rate | The incremental response assigned to path coordinate d. | Defines how accumulated response builds up across distance or path length. |
| χ | Finite-depth coordinate | A normalized depth register inside the model's projected geometry. | Places observables on a compact depth scale used for regime comparisons. |
| X | Normalized transition coordinate | A display coordinate with the boundary transition set to X = 1. | Marks the recovered projection shoulder and separates interior from transition behavior. |
| η | Weak-field compliance coordinate | The ratio gbar/g†. | Measures how gravity departs from ordinary weak-field behavior. |
| u | Compactness register | The dimensionless ratio 2GM/(Rc²). | Tracks approach to compactness-regime behavior and boundary saturation. |