IPD‑12 Composite Operator Grammar
Unified Drift‑Layer Grammar for Multi‑Domain Analysis#
IPD‑12 exposes seven core operators.
The composite grammar defines how they combine, chain, and escalate across domains.
This grammar is used by:
- the IPD‑12 engine triadicframeworks.org
- the IPD‑12 teaching module
- the IPD‑12 multi‑domain drift analyzer
- the IPD‑12 paradox explainer (structural paradox mode) github.com
1. Core Operators (Base Layer)#
| Operator | Purpose | Notes |
|---|---|---|
| map_process() | Capture structural identity | Required for all chains |
| compare_process() | Identify shared structure | Activates multi‑process mode |
| drift() | Detect surface‑level divergence | Bounded drift only |
| detect_divergence() | Identify major coherence breaks | Deep drift |
| drift_tensor() | Multi‑layer drift evaluation | Geometric / Operational / Temporal / Conceptual / Domain |
| align_coherence() | Restore or evaluate coherence | Coherence declared |
| cross_system() | Map relationships across systems | Multi‑domain mode |
These operators appear in the IPD‑12 engine’s operators.json and module page. triadicframeworks.org
2. Composite Operator Families#
IPD‑12 organizes operators into five composite families:
A. Capture Family#
map_process()
compare_process()
B. Drift Family#
drift()
detect_divergence()
C. Tensor Family#
drift_tensor()
D. Coherence Family#
align_coherence()
E. Cross‑System Family#
cross_system()
These families are the backbone of the multi‑domain drift analyzer.
3. Composite Operator Chains#
Composite chains define how operators combine.
Chain 1 — Basic Drift Chain#
map_process() → drift()
Chain 2 — Deep Drift Chain#
map_process() → drift_tensor() → detect_divergence()
Chain 3 — Comparison → Drift → Coherence#
compare_process() → drift() → align_coherence()
Chain 4 — Multi‑Domain Drift Chain#
map_process() → compare_process() → drift_tensor() → cross_system()
Chain 5 — Paradox Detection Chain (RTT‑1)#
Derived from your paradox section in p_Capture.md:
github.com
drift() → align_coherence() → paradox(structural)
Chain 6 — Composite Drift‑Tensor Chain#
Used in the multi‑domain drift analyzer:
map_process() → drift_tensor() → align_coherence() → cross_system()
4. Composite Tensor Grammar#
The composite drift‑tensor evaluates drift across five layers:
| Tensor Layer | Meaning |
|---|---|
| L1: Geometric Drift | Form, shape, structure |
| L2: Operational Drift | Workflow, process flow |
| L3: Temporal Drift | Speed, evolution, pacing |
| L4: Conceptual Drift | Interpretation, meaning |
| L5: Domain Drift | Cross‑domain divergence |
These layers appear in the multi‑domain drift analyzer.
5. Composite Coherence Grammar#
Coherence is declared, not inferred (RTT‑1 teaching mode).
Coherence anchors include:
- shared structure
- shared constraints
- shared operators
- shared regime boundaries
This matches the coherence section in your paradox explainer. github.com
6. Composite Paradox Grammar (RTT‑1)#
IPD‑12 only recognizes structural paradoxes:
shared_coherence ∧ increasing_drift ∧ mutual_dependency
This is exactly the paradox pattern shown in your current tab.
github.com
Paradox is detected, not resolved.
7. Composite Cross‑System Grammar#
cross_system() becomes the multi‑domain operator when:
- ≥ 2 processes
- ≥ 2 domains
- ≥ 1 drift‑tensor layer
- coherence anchors declared
It produces:
- cross‑domain drift maps
- cross‑system coherence maps
- multi‑domain synthesis inputs
8. Composite Grammar Summary#
Composite Operator Set#
map_process()
compare_process()
drift()
detect_divergence()
drift_tensor()
align_coherence()
cross_system()
Composite Chain Set#
Capture → Drift
Capture → Tensor → Divergence
Compare → Drift → Coherence
Capture → Compare → Tensor → Cross‑System
Drift → Coherence → Paradox
Tensor → Coherence → Cross‑System
Composite Layer Set#
Geometric
Operational
Temporal
Conceptual
Domain
This is the complete composite grammar for IPD‑12.