Overview

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.

Updated