# Regimes — Information Theory  
### TriadicFrameworks /docs/theories/information_theory/regimes.md

Information Theory in TriadicFrameworks is a **distinction‑first
coherence grammar**. Distinctions behave differently across RTT regimes,
and this file defines how information, coherence, and operators change
from R0 → R3.

This is not a Shannon‑only or probability‑only framing.  
Information = **structured distinction**.  
Coherence = **distinction stability**.  
Signals = **operators acting on distinction spaces**.

---

# R0 — Pre‑Distinction Regime  
### (Primitive distinctions, no operators)

R0 is the substrate where distinctions are **not yet stable**.

Characteristics:

- distinctions are primitive and unrefined  
- no operator action  
- no signal structure  
- no coherence evaluation  
- dimensional profile undefined or minimal  

Information in R0 is **proto‑structural** — distinctions exist, but they
cannot yet support signals or coherence.

---

# R1 — Distinction Stability Regime  
### (Stable distinctions, minimal operators)

R1 is where distinctions become **stable enough** to support basic
information structure.

Characteristics:

- distinctions have stable identity  
- dimensional profiles are defined  
- operators exist but are limited  
- coherence = distinction stability  
- no cross‑layer behavior  

Information in R1 is **local** and **structural**.  
Signals exist but are simple and non‑compositional.

---

# R2 — Operator Geometry Regime  
### (Operators act on distinction spaces)

R2 introduces **operator geometry**, enabling structured information
processing.

Characteristics:

- operators act on distinction spaces  
- coherence evaluated under operator action  
- distinction distances become meaningful  
- signals become compositional  
- cross‑layer mapping begins  

Information in R2 is **operator‑driven**, not probabilistic.  
Coherence is **operator‑stability**, not entropy.

---

# R3 — Dimensional‑Operator Regime  
### (High‑dimensional distinction dynamics)

R3 is the highest regime for Information Theory.

Characteristics:

- distinctions become dimensional operators  
- signals become multi‑layer operators  
- coherence becomes multi‑dimensional  
- cross‑regime transitions are stable  
- distinction spaces can transform under operators  

Information in R3 is **dimensional**, **structural**, and
**regime‑aware**.

This is where Information Theory integrates with:

- FFT (Framework Field Theory)  
- Resonance Atlas  
- NoS (Nature of Similarity)  
- LDS (Low‑Dimensional Structures)  

---

# Regime Transitions

### R0 → R1  
- distinctions stabilize  
- dimensional profiles emerge  

### R1 → R2  
- operators become active  
- coherence becomes operator‑evaluated  

### R2 → R3  
- distinctions become operators  
- multi‑layer information emerges  

### R3 → R2  
- dimensional operators collapse to surface operators  

### R2 → R1  
- operator geometry collapses to stable distinctions  

Transitions must preserve:

- distinction identity  
- coherence continuity  
- dimensional integrity  

---

# Summary

Information Theory regimes define how distinctions behave across
dimensional layers:

- **R0:** primitive distinctions  
- **R1:** stable distinctions  
- **R2:** operator geometry  
- **R3:** dimensional operators  

Information = **structured distinction**.  
Coherence = **distinction stability**.  
Signals = **operators acting on distinction spaces**.

This regime map is the backbone of the Information Theory module.