Coherence Map — Information Theory

TriadicFrameworks /docs/theories/information_theory/coherence_map.md#

This file defines the coherence dimensions, coherence levels, collapse modes, and regime behavior for Information Theory.

1. Coherence Dimensions#

Information Theory uses five structural coherence dimensions:

1.1 Distinction Coherence#

Stability of distinctions as structural units.

A distinction is coherent when:

• it remains identifiable
• it does not degenerate
• it preserves its invariants

1.2 Operator Coherence#

Stability of distinctions under operator action.

An operator is coherent when:

• it preserves distinction identity
• it does not introduce ambiguity
• it maintains dimensional consistency

1.3 Adjacency Coherence#

Stability of structural distances between distinctions.

Adjacency is coherent when:

• distances remain consistent
• no adjacency inversion occurs
• no collapse of structural neighborhoods

1.4 Dimensional Coherence#

Stability of dimensional profiles.

Dimensional coherence holds when:

• dimensional profiles remain valid
• no dimensional drift occurs
• transforms preserve dimensional identity

1.5 Regime Coherence#

Stability of distinctions across R0 → R3 transitions.

Regime coherence holds when:

• transitions preserve identity
• transitions preserve coherence
• transitions do not introduce collapse

2. Coherence Levels (C0 → C4)#

Coherence is evaluated on a five‑level structural scale:

C0 — Incoherent#

• distinctions unstable
• operators undefined
• dimensional profile invalid

System cannot support information.

C1 — Weak Coherence#

• distinctions exist but unstable
• adjacency inconsistent
• operator action unreliable

System supports only primitive structure.

C2 — Moderate Coherence#

• distinctions stable
• operators valid
• adjacency mostly consistent

System supports basic information structure.

C3 — Strong Coherence#

• distinctions stable under operators
• adjacency consistent
• dimensional profiles valid
• regime transitions stable

System supports full distinction‑based information.

C4 — Perfect Coherence (Ideal)#

• distinctions fully stable
• operators fully stable
• dimensional and adjacency coherence perfect
• regime transitions lossless

C4 is theoretical; real systems approach C3.

3. Collapse Modes (Structural)#

Collapse occurs when distinctions fail structurally.

C1 — Distinction Ambiguity#

Distinctions lose identity.

C2 — Dimensional Inconsistency#

Dimensional profiles become invalid.

C3 — Operator Instability#

Operators fail to preserve distinctions.

C4 — Coherence Failure#

System‑wide structural collapse.

Collapse is structural, not probabilistic.

4. Regime Behavior (R0 → R3)#

Coherence behaves differently across RTT regimes:

R0 — Pre‑Distinction#

• no stable distinctions
• coherence undefined

R1 — Distinction Stability#

• distinctions stable
• minimal operator coherence

R2 — Operator Geometry#

• operator coherence primary
• adjacency coherence active

R3 — Dimensional Operators#

• dimensional coherence active
• regime coherence required

5. Coherence Evaluation Procedure#

To evaluate coherence:

1. Validate distinction identity
2. Validate operator stability
3. Validate adjacency consistency
4. Validate dimensional profile
5. Validate regime compatibility

If any step fails → classify collapse mode.

6. Summary#

Information Theory coherence is:

• distinction‑first
• operator‑driven
• structural
• regime‑aware
• zero drift

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