regime_map.md

IPD‑12 Regime Map
Intransitive Prime‑Indexed 12‑State Regime Structure
Version: 2026‑1.0
Module: IPD‑12 Framework
Role: Regime / Dimensional Map

1. Purpose#

This document defines the regime‑layer interpretation of the IPD‑12 operator system.
It maps:

• 12 prime‑indexed operator states
• 4 intransitive triads
• 2 hex‑cycles
• 1 full paradox cycle

into RTT‑style Regime‑0 → Regime‑3 layers, and provides GU‑compatible geometric interpretations.

2. Regime Overview (RTT-Compatible)#

Regime‑0 — Substrate / Stability Layer#

Prime states with stabilizing or coherence roles.

• P11 (coherence node)
• P31 (stability node)

These act as the “vacuum” stabilizers for cycle behavior.

Regime‑1 — Divisional / Transition Layer#

Prime states that initiate or mediate transitions.

• P2 (seed)
• P3 (transition)
• P5 (drift anchor)

This triad forms the first intransitive cycle.

Regime‑2 — Functional / Boundary Layer#

Prime states that define functional edges or boundary behavior.

• P7 (regime shift)
• P11 (coherence)
• P13 (paradox trigger)
• P17 (cycle gate)
• P19 (boundary node)

These states form the “middle shell” of IPD‑12.

Regime‑3 — High‑Order / Dimensional Layer#

Prime states associated with dimensional lift, collapse, apex behavior.

• P23 (dimensional lift)
• P29 (collapse anchor)
• P31 (stability)
• P37 (apex)

This is the highest regime shell.

3. Regime Map Diagram (Textual)#

                [ Regime‑3 ]
        P23 — P29 — P31 — P37
           ↑               ↓
                (full 12-cycle)
           ↓               ↑
        P17 — P19 — P13 — P11
                [ Regime‑2 ]
           ↑               ↓
        P7 — P5 — P3 — P2
                [ Regime‑1 ]
           ↑               ↓
                [ Regime‑0 ]
                  P11, P31

4. Intransitive Cycle Mapping#

Triad Cycles → Regime Layers#

Hex Cycles → Regime Shells#

Full 12‑Cycle → Complete Regime Stack#

P2 → P3 → P5 → P7 → P11 → P13 → 
P17 → P19 → P23 → P29 → P31 → P37 → P2

This is the IPD‑12 paradox loop, spanning all regimes.

5. RTT Regime Interpretation#

Regime‑0 (Stability)#

P11, P31

• Coherence stabilizers
• Prime‑gap equilibrium nodes

Regime‑1 (Transition)#

P2, P3, P5

• Drift and transition operators
• Entry points into cycles

Regime‑2 (Functional)#

P7, P11, P13, P17, P19

• Paradox triggers
• Boundary nodes
• Cycle gates

Regime‑3 (Dimensional)#

P23, P29, P31, P37

• Dimensional lift
• Collapse anchors
• Apex operators

6. GU-Compatible Interpretation#

7. Pantheon-Tier Interpretation#

8. Summary#

The IPD‑12 Regime Map provides a complete RTT‑style regime interpretation of the 12 prime‑indexed operator states. It defines how intransitive cycles map to regime transitions, paradox loops, coherence stabilizers, and GU geometric structures.