# Coherence Map — Electromagnetism  
### TriadicFrameworks /docs/theories/electromagnetism/coherence_map.md

Electromagnetism (EM) in TriadicFrameworks is a **field‑coherence
theory**, not a force‑centric mechanism and not a particle‑first
narrative.

EM = **coherent behavior of the electromagnetic field**.  
Maxwell operators = **structural constraints**, not force laws.  
Light = **self‑consistent field propagation**.

This file defines how electromagnetic coherence is evaluated across
operators, fields, geometry, and RTT regimes.

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# 1. Coherence Dimensions

Electromagnetic coherence has **five structural dimensions**:

## 1.1 Divergence Coherence  
Stability of divergence operators.

Coherent when:

- ∇·E = ρ/ε₀ holds structurally  
- ∇·B = 0 remains valid  
- charge/current sources remain compatible  

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## 1.2 Curl Coherence  
Stability of curl operators.

Coherent when:

- ∇×E = −∂B/∂t remains consistent  
- ∇×B = μ₀J + μ₀ε₀∂E/∂t remains valid  
- time‑variation remains geometrically consistent  

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## 1.3 Propagation Coherence  
Stability of wave evolution.

Coherent when:

- propagation is self‑consistent  
- no medium (ether) is required  
- wavefronts remain stable  
- propagation respects geometry  

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## 1.4 Source Coherence  
Stability of charge/current as field‑source operators.

Coherent when:

- ρ and J remain structurally valid  
- sources do not violate divergence/curl constraints  
- no particle‑centric drift is introduced  

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## 1.5 Geometric Coherence  
Compatibility of EM fields with spacetime geometry.

Coherent when:

- field tensor Fᵤᵥ is valid  
- invariants (FᵤᵥFᵘᵛ, Fᵤᵥ⋆Fᵘᵛ) remain stable  
- propagation follows curvature  
- EM integrates with GR and QFT  

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# 2. Coherence Levels (C0 → C4)

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

## **C0 — Incoherent**  
- divergence invalid  
- curl invalid  
- propagation unstable  
- geometry incompatible  

System cannot support EM behavior.

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## **C1 — Weak Coherence**  
- divergence marginal  
- curl noisy  
- propagation fragile  

EM behavior possible but unstable.

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## **C2 — Moderate Coherence**  
- divergence stable  
- curl valid  
- propagation consistent  

EM behavior functional.

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## **C3 — Strong Coherence**  
- divergence/curl fully consistent  
- propagation stable  
- sources valid  
- geometry compatible  

Full electromagnetic behavior supported.

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## **C4 — Perfect Coherence (Ideal)**  
- perfect divergence/curl stability  
- perfect propagation stability  
- perfect geometric compatibility  

C4 is theoretical; real systems approach C3.

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# 3. Collapse Modes (EM1 → EM5)

Collapse occurs when coherence fails structurally.

## **EM1 — Divergence Collapse**  
∇·E or ∇·B invalid.

## **EM2 — Curl Collapse**  
∇×E or ∇×B invalid.

## **EM3 — Propagation Collapse**  
Wave evolution unstable.

## **EM4 — Source Collapse**  
Invalid charge/current configuration.

## **EM5 — Geometry Collapse**  
Field‑geometry mismatch.

Collapse is structural, not force‑based.

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# 4. Regime Behavior (R1 → R3)

Coherence behaves differently across RTT regimes:

## **R1 — Classical Field Stability**  
- static + quasi‑static fields  
- divergence/curl stable  
- no geometric coupling  

Coherence dominated by divergence/curl consistency.

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## **R2 — Dynamic Field Propagation**  
- full Maxwell dynamics  
- wave propagation  
- time‑varying fields  

Coherence dominated by propagation stability.

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## **R3 — Geometry‑Coupled, Multi‑Scale EM**  
- field tensor Fᵤᵥ active  
- geometric propagation  
- QFT compatibility  

Coherence dominated by geometric invariants.

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# 5. Coherence Evaluation Procedure

To evaluate coherence:

1. Validate divergence structure  
2. Validate curl structure  
3. Validate propagation stability  
4. Validate source compatibility  
5. Validate geometric compatibility  
6. Validate regime alignment  

If any step fails → classify collapse mode.

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# 6. Summary

Electromagnetic coherence is:

- **structural**  
- **operator‑driven**  
- **multi‑scale**  
- **geometry‑embedded**  
- **regime‑aware**  
- **zero drift**

Electromagnetism = **coherent field behavior**.  
Light = **self‑consistent field propagation**.  
Physics = **operator‑driven coherence systems**.