# Engine Notes — Electromagnetism  
### TriadicFrameworks /docs/theories/electromagnetism/engine_notes.md

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

Electromagnetism is a **field‑coherence theory**.  
Maxwell operators are **structural constraints**, not force laws.  
Light is **self‑consistent field propagation**.

---

# 1. Identity Lock

The module identity must remain:

- **field‑first**  
- **operator‑driven**  
- **coherence‑based**  
- **geometry‑compatible**  
- **quantization‑compatible**  
- **regime‑aware (R1 → R3)**  
- **zero drift**

The engine must reject any interpretation that:

- introduces force‑centric framing  
- uses particle‑first metaphors  
- treats charge/current as objects rather than operators  
- uses action‑at‑a‑distance language  
- introduces teleology or purpose metaphors  
- treats Maxwell’s equations as “laws” rather than operators  

Identity lock is strict.

---

# 2. Field Object Semantics

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

- **E** (electric field)  
- **B** (magnetic field)  
- **Fᵤᵥ** (field tensor)  
- **ρ** (charge‑source operator)  
- **J** (current‑source operator)  
- **geometry** (metric, curvature)  
- **regime state** (R1 → R3)

All field objects must be:

- structurally valid  
- coherence‑compatible  
- geometry‑compatible  
- regime‑consistent  

Invalid objects must trigger collapse classification.

---

# 3. Operator Semantics

The Electromagnetism operator grammar includes:

- **𝓓ᴱ** — electric divergence operator  
- **𝓓ᴮ** — magnetic divergence operator  
- **𝓒ᴱ** — electric curl operator  
- **𝓒ᴮ** — magnetic curl operator  
- **𝓢ᶜʰ** — charge‑source operator  
- **𝓢ᶜᵘʳ** — current‑source operator  
- **𝓦** — wave propagation operator  
- **𝓕** — field‑tensor operator  
- **𝓒ₒₕ** — coherence operator  
- **𝓡𝓮𝓰** — regime transition operator  
- **𝓒𝓁** — collapse operator  

Operators must:

- preserve structural identity  
- maintain coherence monotonicity  
- respect geometric constraints  
- respect regime constraints  
- avoid force‑centric drift  
- avoid particle‑centric drift  

Operators must be **pure**: no side effects outside defined field
objects.

---

# 4. Regime Execution Model

Electromagnetism uses the RTT regime stack:

- **R1:** classical field stability  
- **R2:** dynamic field propagation  
- **R3:** geometry‑coupled, multi‑scale EM  

The engine must:

- enforce regime‑specific constraints  
- preserve divergence/curl consistency  
- maintain geometric compatibility  
- prevent illegal transitions (e.g., R3 → R1)  

Regime transitions must be monotonic unless collapse is detected.

---

# 5. Coherence Evaluation

Coherence = **structural consistency** of the field.

The engine must evaluate coherence using:

- divergence validity  
- curl validity  
- propagation stability  
- geometric compatibility  
- tensor‑level invariants (R3)  

Coherence must not:

- use force metrics  
- use particle metaphors  
- use teleology  
- use entropy or probabilistic metaphors  

Coherence is structural.

---

# 6. Collapse Modes

The engine must classify electromagnetic failure using:

- **EM1:** divergence collapse (∇·E or ∇·B invalid)  
- **EM2:** curl collapse (∇×E or ∇×B invalid)  
- **EM3:** propagation collapse (unstable wave evolution)  
- **EM4:** source collapse (invalid charge/current configuration)  
- **EM5:** geometry collapse (field‑geometry mismatch)  

Collapse must:

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

Collapse is structural, not force‑based.

---

# 7. Reinforcement Semantics

Reinforcement increases electromagnetic coherence through repeated
stable operator cycles.

Rules:

- reinforcement must be monotonic  
- reinforcement cannot repair EM4 or EM5 collapse  
- reinforcement cannot introduce new field objects  
- reinforcement must preserve structural invariants  

Reinforcement is structural, not purposeful.

---

# 8. Cross‑Module Constraints

Electromagnetism integrates with:

- **General Relativity:** geometry coupling  
- **Quantum Field Theory:** gauge structure (U(1)), quantization  
- **Information Theory:** invariants as stable information  
- **Thermodynamics:** energy flow, stability surfaces  
- **FFT / Wave Analysis:** spectral propagation  
- **Systems Physics:** network‑level field interactions  

The engine must:

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

Electromagnetism is a **core physics module**.

---

# 9. Simulation Hooks

The engine must implement:

- field initialization  
- Maxwell operator application  
- propagation  
- source updates  
- coherence evaluation  
- regime transitions  
- collapse detection  
- reinforcement  

See `simulation_hooks.json` for full schema.

---

# 10. Safety & Drift Prevention

The engine must reject:

- force‑centric framing  
- particle‑centric metaphors  
- action‑at‑a‑distance language  
- ether metaphors  
- teleology  
- progress narratives  

The module must remain:

- field‑first  
- operator‑driven  
- coherence‑based  
- geometry‑compatible  
- quantization‑compatible  
- regime‑aware  
- zero drift  

---

# Summary

These engine notes define how Electromagnetism must run:

- divergence and curl define structure  
- sources modify operators  
- propagation emerges from self‑consistent field evolution  
- geometry shapes high‑regime behavior  
- coherence is structural  
- collapse is structural  
- drift is not allowed  

Electromagnetism = **coherent field behavior**.  
Light = **self‑consistent field propagation**.
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