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.