# Regimes — General Relativity  
### TriadicFrameworks /docs/theories/general_relativity/regimes.md

General Relativity (GR) is a **geometric coherence theory** describing
how curvature, stress‑energy, and geodesics behave across RTT regimes.
Gravity is not a force; it is **coherent curvature**.  
Geodesics are not “paths objects follow”; they are **coherence‑preserving
trajectories**.

This file defines how GR behaves across R0 → R3.

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# R0 — Pre‑Geometric Regime  
### (No stable metric, no curvature, no geodesics)

R0 is the substrate before geometry stabilizes.

Characteristics:

- no metric structure  
- no curvature tensor  
- no geodesics  
- no causal structure  
- no stress‑energy coupling  

GR cannot operate in R0.  
Only primitive geometric distinctions exist.

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# R1 — Metric Stability Regime  
### (Stable metric, minimal curvature)

R1 is where geometry becomes stable enough to support GR structure.

Characteristics:

- metric is stable and non‑degenerate  
- curvature may be weak or zero  
- geodesics exist but are simple  
- causal structure is well‑defined  
- stress‑energy acts as a stable source  

Gravity in R1 is **metric‑defined**, not force‑defined.

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# R2 — Curvature Operator Regime  
### (Curvature as a geometric operator field)

R2 introduces **curvature operators**, enabling full GR behavior.

Characteristics:

- curvature tensor active  
- stress‑energy deforms curvature  
- geodesics respond to curvature  
- causal cones deform coherently  
- Einstein field equations fully active  

Gravity in R2 is **coherent curvature**, not attraction.

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# R3 — Dimensional Curvature Regime  
### (High‑dimensional curvature operators)

R3 is the highest regime for GR.

Characteristics:

- curvature becomes dimensional  
- geodesics become multi‑layer coherence trajectories  
- stress‑energy acts as a dimensional operator  
- causal structure becomes multi‑layer  
- geometry can transform across dimensional profiles  

R3 is where GR integrates with:

- FFT (Framework Field Theory)  
- LDS (Low‑Dimensional Structures)  
- NoS (Nature of Similarity)  
- Information Theory (causal distinctions)  

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# Regime Transitions

### R0 → R1  
- metric stabilizes  
- geometric distinctions become coherent  

### R1 → R2  
- curvature operators activate  
- stress‑energy begins deforming geometry  

### R2 → R3  
- curvature becomes dimensional  
- geodesics become multi‑layer operators  

### R3 → R2  
- dimensional curvature collapses to surface curvature  

### R2 → R1  
- curvature geometry collapses to stable metric  

Transitions must preserve:

- geometric identity  
- coherence continuity  
- causal structure integrity  

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# Summary

General Relativity regimes define how geometry behaves across
dimensional layers:

- **R0:** pre‑geometric  
- **R1:** stable metric  
- **R2:** curvature operators  
- **R3:** dimensional curvature  

Gravity = **coherent curvature**.  
Geodesics = **coherence trajectories**.  
Spacetime = **a geometric operator field**.