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.