# Coherence Map — General Relativity  
### TriadicFrameworks /docs/theories/general_relativity/coherence_map.md

General Relativity (GR) is a **geometric coherence theory of gravity**.
Coherence in GR is the stability of:

- the metric  
- curvature  
- geodesics  
- causal structure  
- regime transitions  

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

This file defines the coherence dimensions, coherence levels, collapse
modes, and regime behavior for GR.

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# 1. Coherence Dimensions

GR uses **five geometric coherence dimensions**:

## 1.1 Metric Coherence  
Stability of the metric as a geometric structure.

A metric is coherent when:

- it is non‑degenerate  
- causal cones remain valid  
- signature remains stable  

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## 1.2 Curvature Coherence  
Stability of curvature as a geometric operator field.

Curvature is coherent when:

- curvature invariants remain stable  
- curvature does not diverge  
- curvature responds consistently to stress‑energy  

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## 1.3 Geodesic Coherence  
Stability of geodesics as coherence trajectories.

Geodesics are coherent when:

- they preserve identity  
- they respond consistently to curvature  
- they maintain causal compatibility  

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## 1.4 Causal Coherence  
Stability of causal structure.

Causal structure is coherent when:

- light cones remain valid  
- no causal inversion occurs  
- adjacency remains consistent  

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## 1.5 Regime Coherence  
Stability across R1 → R3 transitions.

Regime coherence holds when:

- transitions preserve geometric identity  
- curvature operators remain valid  
- dimensional profiles remain consistent  

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# 2. Coherence Levels (C0 → C4)

Coherence is evaluated on a **five‑level geometric scale**:

## **C0 — Incoherent**  
- metric invalid  
- curvature undefined  
- no geodesic structure  

System cannot support GR.

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## **C1 — Weak Coherence**  
- metric barely stable  
- curvature inconsistent  
- geodesics unreliable  

System supports only primitive geometry.

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## **C2 — Moderate Coherence**  
- metric stable  
- curvature mostly consistent  
- geodesics valid  

System supports basic GR structure.

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## **C3 — Strong Coherence**  
- metric stable under deformation  
- curvature consistent  
- geodesics coherent  
- causal structure intact  
- regime transitions stable  

System supports full GR behavior.

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## **C4 — Perfect Coherence (Ideal)**  
- metric perfectly stable  
- curvature fully consistent  
- geodesics perfectly coherent  
- causal structure fully preserved  
- regime transitions lossless  

C4 is theoretical; real systems approach C3.

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# 3. Collapse Modes (Geometric)

Collapse occurs when geometry fails structurally.

## **G1 — Metric Degeneracy**  
Metric becomes singular or invalid.

## **G2 — Curvature Divergence**  
Curvature becomes unbounded or undefined.

## **G3 — Geodesic Incoherence**  
Geodesics lose identity or causal compatibility.

## **G4 — Causal Structure Failure**  
Light cones collapse or invert.

Collapse is geometric, not probabilistic.

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# 4. Regime Behavior (R0 → R3)

Coherence behaves differently across RTT regimes:

## **R0 — Pre‑Geometric**  
- no metric  
- no curvature  
- no geodesics  

Coherence undefined.

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## **R1 — Metric Stability**  
- metric stable  
- causal structure emerges  
- minimal curvature  

Coherence dominated by metric stability.

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## **R2 — Curvature Operators**  
- curvature tensor active  
- stress‑energy deforms geometry  
- geodesics respond coherently  

Coherence dominated by curvature stability.

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## **R3 — Dimensional Curvature**  
- curvature becomes dimensional  
- geodesics become multi‑layer  
- causal structure becomes layered  

Coherence dominated by dimensional consistency.

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# 5. Coherence Evaluation Procedure

To evaluate coherence:

1. Validate metric stability  
2. Validate curvature consistency  
3. Validate geodesic coherence  
4. Validate causal structure  
5. Validate regime compatibility  

If any step fails → classify collapse mode.

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# 6. Summary

GR coherence is:

- **geometric**  
- **operator‑driven**  
- **curvature‑first**  
- **regime‑aware**  
- **zero drift**  

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