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.

Model Integrity Notes.

Category	Status	Guardrail
Physically grounded structure	Observed redshift \(z\), accumulated-response bookkeeping \(A=\ln(1+z)\), local GR-compatible limits, register separation, and explicit failure tests.	Keep tied to direct observables, stated equations, and reproducible comparisons.
Model-dependent construction	Finite-boundary path response, projection factors, response-engine mapping, and mass-size conversion tests.	Treat as hypotheses that require stronger covariance tests, independent data, and physical derivation.
Speculative or provisional elements	Compactness interior behavior, saturation laws, and any unified field-equation bridge.	Mark unsupported claims explicitly and prefer omission over invented mechanisms.
K-values	Adjustable/testable diagnostics: \(K_D\), \(K_X\), and \(K_\eta\) are fitted values; \(K_u=1/3\) is a trial compactness parameter.	Do not treat K-values as foundational constants or physical derivations unless independently recovered and theoretically derived.

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 g_bar/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.
K_D, K_X, K_η, K_u	Provisional scaling diagnostics	Fitted or trial exponents used to test possible response weighting.	These values are not foundational constants; they remain provisional until independently recovered and physically derived.