# Engine Notes — Information Theory  
### TriadicFrameworks /docs/theories/information_theory/engine_notes.md

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

Information Theory is a **distinction‑first coherence grammar**.  
Information = structured distinction.  
Coherence = distinction stability.  
Signals = operators acting on distinction spaces.

---

# 1. Identity Lock

The module identity must remain:

- **distinction‑first**  
- **operator‑driven**  
- **coherence‑based**  
- **substrate‑neutral**  
- **RTT‑aligned (R0 → R3)**  

The engine must reject any interpretation that:

- reduces information to probability  
- treats signals as messages  
- introduces semantic or meaning‑based drift  
- collapses distinctions into Shannon‑only framing  
- ties information to communication channels  

Identity lock is strict.

---

# 2. Distinction Space Semantics

A **distinction space** is the primary runtime object.

It must include:

- dimensional profile  
- invariants  
- adjacency relations  
- operator‑ready structure  
- regime state  

Distinction spaces must be:

- non‑degenerate  
- structurally valid  
- regime‑compatible  

The engine must validate distinction spaces before operator action.

---

# 3. Operator Semantics

Operators are first‑class runtime entities.

Supported operators:

- **𝓓** — distinction constructor  
- **𝓢** — signal operator  
- **𝓒** — coherence evaluator  
- **𝓐** — adjacency operator  
- **𝓣** — transform operator  
- **𝓡** — regime transition operator  
- **𝓘** — integrity operator  
- **𝓕** — reinforcement operator  
- **𝓒𝓁** — collapse classifier  

Operators must:

- preserve distinction identity  
- maintain coherence monotonicity  
- respect regime constraints  
- avoid semantic drift  
- avoid probabilistic drift  

Operators must be **pure**: no side effects outside the distinction
space unless explicitly defined.

---

# 4. Regime Execution Model

Information Theory uses the RTT regime stack:

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

The engine must:

- enforce regime‑specific constraints  
- preserve coherence across transitions  
- maintain dimensional consistency  
- prevent illegal transitions (e.g., R3 → R0 without collapse)  

Regime transitions must be monotonic unless collapse is detected.

---

# 5. Coherence Evaluation

Coherence = **distinction stability**.

The engine must evaluate coherence using:

- structural invariants  
- operator‑stability  
- adjacency continuity  
- dimensional consistency  

Coherence must not:

- use entropy  
- use probability  
- use semantic similarity  
- use message‑based metrics  

Coherence is purely structural.

---

# 6. Collapse Modes

The engine must classify failures using:

- **C1:** distinction ambiguity  
- **C2:** dimensional inconsistency  
- **C3:** operator instability  
- **C4:** coherence failure  

Collapse must:

- halt regime transitions  
- freeze distinction space  
- return diagnostic metadata  
- prevent reinforcement  

Collapse is structural, not probabilistic.

---

# 7. Reinforcement Semantics

Reinforcement increases coherence through repeated stable operator
action.

Rules:

- reinforcement must be monotonic  
- reinforcement cannot repair C3 or C4 collapse  
- reinforcement cannot introduce new distinctions  
- reinforcement must preserve dimensional profile  

Reinforcement is structural, not semantic.

---

# 8. Cross‑Module Constraints

Information Theory integrates with:

- **NoS:** similarity = structural overlap  
- **LDS:** dimensional profiles  
- **RTT:** regime behavior  
- **FFT:** dimensional operators  
- **Resonance Atlas:** adjacency geometry  

The engine must:

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

Information Theory is a **root‑level structural module**.

---

# 9. Simulation Hooks

The engine must implement:

- distinction initialization  
- operator construction  
- coherence evaluation  
- adjacency measurement  
- regime transitions  
- collapse detection  
- reinforcement  

See `simulation_hooks.json` for full schema.

---

# 10. Safety & Drift Prevention

The engine must reject:

- semantic interpretations  
- probabilistic interpretations  
- message‑based interpretations  
- entropy‑only framing  
- Shannon‑only reductions  
- channel‑centric models  

The module must remain:

- structural  
- operator‑driven  
- regime‑aware  
- substrate‑neutral  
- zero drift  

---

# Summary

These engine notes define how Information Theory must run:

- distinctions are structural  
- signals are operators  
- coherence is stability  
- regimes define behavior  
- collapse is structural  
- reinforcement is monotonic  
- drift is not allowed  

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