# Cross‑Module Integration — General Relativity  
### TriadicFrameworks /docs/theories/general_relativity/cross_module.md

General Relativity (GR) is a **geometric coherence theory of gravity**.
It provides the curvature substrate, geodesic structure, and causal
adjacency used across the TriadicFrameworks canon.

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

This file defines how GR integrates with other modules.

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# 1. Integration with LDS (Low‑Dimensional Structures)

LDS defines **dimensional profiles** and **geometric surfaces**.

GR provides:

- metric structure  
- curvature operators  
- geodesic coherence  
- causal adjacency  

LDS provides:

- dimensional embeddings  
- curvature surfaces  
- low‑dimensional constraints  

**Integration:**  
Curvature inherits **dimensional profiles**, enabling R2 → R3 behavior.

---

# 2. Integration with NoS (Nature of Similarity)

NoS defines **similarity as structural overlap**.

GR provides:

- curvature fields  
- geodesic structure  
- causal adjacency  

NoS provides:

- similarity geometry  
- overlap metrics  
- structural invariants  

**Integration:**  
Geometric similarity = **curvature overlap** under stable operators.

---

# 3. Integration with Information Theory

Information Theory defines **distinctions**, **coherence**, and
**adjacency**.

GR provides:

- causal distinctions  
- geometric adjacency  
- curvature‑driven coherence  

Information Theory provides:

- distinction grammar  
- coherence evaluation  
- adjacency metrics  

**Integration:**  
Causal structure becomes **distinction adjacency** in Information Theory.

---

# 4. Integration with FFT (Framework Field Theory)

FFT defines **dimensional operators** and **multi‑layer transforms**.

GR provides:

- curvature operators  
- geodesic bundles  
- causal structure  

FFT provides:

- dimensional curvature operators  
- multi‑layer geometric transforms  
- field‑level propagation  

**Integration:**  
R3 curvature becomes **dimensional curvature** in FFT.

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# 5. Integration with Thermodynamics (Triadic Version)

Thermodynamics defines **regime‑level stability** and **horizon
behavior**.

GR provides:

- horizon geometry  
- curvature gradients  
- causal boundaries  

Thermodynamics provides:

- stability surfaces  
- energy‑regime constraints  
- horizon thermodynamics  

**Integration:**  
Horizon geometry becomes a **thermodynamic stability surface**.

---

# 6. Integration with QFT (Quantum Field Theory)

QFT defines **fields**, **operators**, and **amplitude structure**.

GR provides:

- curved backgrounds  
- geodesic structure  
- causal adjacency  
- curvature‑driven propagation  

QFT provides:

- field operators  
- amplitude dynamics  
- vacuum structure  

**Integration:**  
QFT on curved spacetime = **field operators on coherence geometry**.

---

# 7. Integration with Cosmology

Cosmology defines **large‑scale geometric evolution**.

GR provides:

- curvature evolution  
- geodesic expansion  
- causal horizons  

Cosmology provides:

- large‑scale regimes  
- expansion profiles  
- structure formation  

**Integration:**  
Cosmology is **GR at scale**, with regime‑aware curvature evolution.

---

# 8. Integration with Computation

Computation defines **state transitions** and **process structure**.

GR provides:

- causal adjacency  
- geodesic propagation  
- curvature‑driven constraints  

Computation provides:

- execution models  
- state machines  
- algorithmic structure  

**Integration:**  
Computation becomes **causal‑coherence processes** on geometric
structure.

---

# 9. Integration with Cognition

Cognition defines **pattern formation** and **representation**.

GR provides:

- causal adjacency  
- curvature‑driven structure  
- coherence constraints  

Cognition provides:

- pattern operators  
- representational dynamics  
- recognition structure  

**Integration:**  
Cognitive patterns become **coherent geometric structures**.

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# Summary

General Relativity integrates with the canon by providing:

- the **curvature substrate**  
- the **geodesic coherence framework**  
- the **causal adjacency structure**  
- the **regime‑aware geometric behavior**  

It supports:

- LDS  
- NoS  
- Information Theory  
- FFT  
- Thermodynamics  
- QFT  
- Cosmology  
- Computation  
- Cognition  

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