# Engine Notes — General Relativity  
### TriadicFrameworks /docs/theories/general_relativity/engine_notes.md

These notes define the **internal behavior**, **constraints**, and
**execution semantics** for the General Relativity (GR) module.  
They are intended for AI agents, compilers, simulation engines, and
module orchestrators.

General Relativity is a **geometric coherence theory of gravity**.  
Gravity = coherent curvature.  
Geodesics = coherence trajectories.  
Spacetime = a geometric operator field.

---

# 1. Identity Lock

The GR module identity must remain:

- **curvature‑first**  
- **coherence‑based**  
- **operator‑driven**  
- **regime‑aware (R1 → R3)**  
- **tensorial and geometric**  
- **zero drift**

The engine must reject any interpretation that:

- treats gravity as a force  
- uses rubber‑sheet analogies  
- introduces Newtonian fallback  
- uses semantic or pop‑science metaphors  
- collapses curvature into visualization  
- treats geodesics as “paths objects follow”

Identity lock is strict.

---

# 2. Geometric Object Semantics

The engine must treat the following as **first‑class geometric objects**:

- metric (g\_{\mu\nu})  
- curvature tensor (R\_{\mu\nu\rho\sigma})  
- stress‑energy tensor (T\_{\mu\nu})  
- geodesic bundle (γ)  
- causal structure (C)  
- regime state (R0 → R3)

All geometric objects must be:

- non‑degenerate  
- tensorially valid  
- coherence‑compatible  
- regime‑consistent  

Invalid objects must trigger collapse classification.

---

# 3. Operator Semantics

The GR operator grammar includes:

- **𝓖** — metric operator  
- **𝓡** — curvature operator  
- **𝓣** — stress‑energy operator  
- **𝓓𝓮𝓯** — geometric deformation operator  
- **𝓖𝓮𝓸** — geodesic operator  
- **𝓒** — coherence operator  
- **𝓐** — adjacency operator  
- **𝓢** — causal structure operator  
- **𝓡𝓮𝓰** — regime transition operator  
- **𝓒𝓁** — collapse operator  

Operators must:

- preserve geometric identity  
- maintain coherence monotonicity  
- respect regime constraints  
- avoid semantic drift  
- avoid force metaphors  
- avoid probabilistic interpretations  

Operators must be **pure**: no side effects outside the geometric object
unless explicitly defined.

---

# 4. Regime Execution Model

GR uses the RTT regime stack:

- **R0:** pre‑geometric (no metric, no curvature)  
- **R1:** stable metric  
- **R2:** curvature operators active  
- **R3:** dimensional curvature operators  

The engine must:

- enforce regime‑specific constraints  
- preserve coherence across transitions  
- maintain causal structure  
- prevent illegal transitions (e.g., R3 → R0)  

Regime transitions must be monotonic unless collapse is detected.

---

# 5. Coherence Evaluation

Coherence = **geometric stability**.

The engine must evaluate coherence using:

- metric stability  
- curvature consistency  
- geodesic coherence  
- causal structure integrity  
- regime compatibility  

Coherence must not:

- use entropy  
- use probability  
- use semantic similarity  
- use force‑based heuristics  

Coherence is purely geometric.

---

# 6. Collapse Modes

The engine must classify geometric failure using:

- **G1:** metric degeneracy  
- **G2:** curvature divergence  
- **G3:** geodesic incoherence  
- **G4:** causal structure failure  

Collapse must:

- halt regime transitions  
- freeze geometric objects  
- return diagnostic metadata  
- prevent reinforcement  

Collapse is geometric, not probabilistic.

---

# 7. Reinforcement Semantics

Reinforcement increases geometric coherence through repeated stable
operator action.

Rules:

- reinforcement must be monotonic  
- reinforcement cannot repair G3 or G4 collapse  
- reinforcement cannot introduce new geometric objects  
- reinforcement must preserve tensorial invariants  

Reinforcement is geometric, not semantic.

---

# 8. Cross‑Module Constraints

GR integrates with:

- **LDS:** dimensional profiles of geometry  
- **NoS:** geometric similarity and curvature overlap  
- **Information Theory:** causal distinctions  
- **FFT:** dimensional curvature operators  
- **Thermodynamics:** horizon regimes  
- **QFT:** fields on curved backgrounds  

The engine must:

- preserve cross‑module invariants  
- prevent identity drift  
- maintain operator compatibility  
- enforce dimensional consistency  

GR is a **central geometric module**.

---

# 9. Simulation Hooks

The engine must implement:

- metric initialization  
- curvature computation  
- stress‑energy deformation  
- geodesic evolution  
- causal structure construction  
- coherence evaluation  
- regime transitions  
- collapse detection  
- reinforcement  

See `simulation_hooks.json` for full schema.

---

# 10. Safety & Drift Prevention

The engine must reject:

- force metaphors  
- rubber‑sheet analogies  
- Newtonian fallback  
- semantic interpretations  
- probabilistic interpretations  
- visual curvature metaphors  

The module must remain:

- geometric  
- operator‑driven  
- coherence‑based  
- regime‑aware  
- zero drift  

---

# Summary

These engine notes define how GR must run:

- curvature is structural  
- geodesics are coherence trajectories  
- stress‑energy is a source operator  
- causal structure is geometric  
- regimes define behavior  
- collapse is geometric  
- drift is not allowed  

This file is the **internal execution contract** for the GR module.