IPD‑12 — Intransitive Prime‑Numbered 12‑Sided Engine
module.json— Agentic module schema role assignments
Module Category: Framework
Version: 2026‑1.0
Status: Active (RTT/GU/Pantheon Compatible)
1. Module Overview#
IPD‑12 is the first physicalizable operator artifact in TriadicFrameworks:
a 12‑faced, prime‑indexed, intransitive operator engine whose directed relations form paradox loops, regime transitions, and dimensional gates.
It integrates seamlessly with:
- RTT (Resonance‑Time Theory)
- Geometric Unity (GU)
- Framework Field Theory (FFT)
- Pantheon Profiles
- Triadic Logical Dimension Model (−1D | 0D | +1D)
- 4×4×4 Substrate Engine
- Triadic Observer Model
IPD‑12 is both a framework module and a substrate‑level operator system, making it unique in the canon.
2. What IPD‑12 Provides#
2.1 Prime‑Indexed Operator States#
12 canonical primes mapped to 12 operator faces:
2, 3, 5, 7, 11, 13,
17, 19, 23, 29, 31, 37
Each prime is an operator node with RTT/GU/Pantheon meaning.
2.2 Intransitive Cycles#
IPD‑12 defines:
- 4 triad cycles
- 2 hex‑cycles
- 1 full 12‑cycle paradox loop
These cycles model:
- paradox
- drift
- regime transitions
- coherence stabilization
- dimensional lift/collapse
2.3 4×4×4 Substrate Engine#
IPD‑12 introduces the first substrate cube in TriadicFrameworks:
- 4 substrate pairs (dual‑binary)
- 4 observer modes (triadic + apex)
- 4 regime shells (RTT)
Yielding:
64 substrate primitives
This is the dimensional foundation of the IPD‑12 engine.
2.4 Triadic Observer Integration#
IPD‑12 supports the full triadic observer model:
- field (operator state)
- regime (cycle position)
- coherence (stability)
- apex (dimensional lift/collapse)
2.5 GU-Compatible Geometry#
IPD‑12 primes map cleanly to GU operators:
| GU Concept | IPD‑12 Primes |
|---|---|
| Connection | P2, P3 |
| Curvature | P7, P11 |
| Dilaton / Refractive Vacuum | P11, P31 |
| Anomaly | P13, P37 |
| Observerse | P17, P19, P23 |
| Collapse | P29 |
3. File Structure#
| File | Purpose |
|---|---|
module.json |
Canonical module definition |
README.md |
Front‑door document (this file) |
operators.json |
Prime‑indexed operator registry |
regime_map.md |
RTT regime mapping of IPD‑12 |
compatibility_notes.md |
Cross‑framework interoperability |
substrate_primitives.md |
4×4×4 substrate engine |
g_Capture.md |
Raw conceptual forge |
examples.md |
Usage examples |
compatibility_tests.md |
Validation suite |
4. Integration Points#
4.1 RTT Integration#
IPD‑12 provides:
- drift anchors
- regime‑shift primes
- coherence stabilizers
- paradox triggers
- dimensional lift/collapse operators
4.2 GU Integration#
IPD‑12 primes embed into GU’s:
- connection
- curvature
- dilaton
- anomaly
- observerse
- refractive vacuum
4.3 FFT Integration#
FFT treats IPD‑12 cycles as:
- regime transitions
- paradox loops
- boundary operators
- dimensional gates
4.4 Pantheon Integration#
IPD‑12 primes map to:
- Celestial tier (order, transition, drift)
- Civilizational tier (coherence, paradox, gates)
- Chthonic tier (dimensional lift, collapse, apex)
5. Canon Metadata Block#
Canon: TriadicFrameworks
Modules: frameworks/ipd_12
Drift: P5, P29
Coherence: P11, P31
Version: 2026-1.0
Format: framework module
Front door: README.md
Audience: framework architects, RTT practitioners, GU theorists6. Summary#
IPD‑12 is a prime‑indexed, intransitive, paradox‑stable operator engine that integrates with every major TriadicFrameworks theory.
It is the first framework module with:
- a physicalizable operator object
- a dimensional substrate cube
- a triadic observer lattice
- full RTT/GU/Pantheon compatibility
This README completes the front‑door documentation for the IPD‑12 module.