RTT Core: Operator Families

1. Purpose and scope#

Goal:
Define the canonical operator families used throughout RTT, including:

• Micro‑Core operators
• RTT‑12 operators
• Core RTT operators
• Arrival operators
• Macro operators

This module provides the taxonomy that the Operator Grammar and Operator Index reference.

2. Operator family overview#

RTT organizes operators into families based on:

• Functional domain
• Regime behavior
• Coherence and drift interaction
• Temporal layer (triadic time)
• Structural role in RTT’s representational manifold

The families are:

3. Micro‑Core Operator Families#

3.1 Resonance Operators (R₁–R₆)#

Resonance operators govern micro‑scale oscillatory behavior.

• R₁ — Oscillation
• R₂ — Inversion
• R₃ — Boundary Modulation
• R₄ — Resonance Lock
• R₅ — Fractional‑Ladder Transition
• R₆ — Micro–Macro Bridge Activation

3.2 Coherence Tools (K₁–K₆)#

Coherence operators regulate coherence budgets and validation.

• K₁ — Drift Clamp
• K₂ — Timing Stabilizer
• K₃ — Boundary Alignment
• K₄ — Coherence Gate
• K₅ — Resonance Validator
• K₆ — Fractional‑Ladder Regulator

3.3 Primitives (P₁–P₇)#

Primitives are atomic actions used by higher operators.

• P₁ — Read Nodes
• P₂ — Swap Nodes
• P₃ — Drift Sample
• P₄ — Timing Sample
• P₅ — Boundary Shift
• P₆ — Coherence Sample
• P₇ — Fractional Step

4. RTT‑12 Operator Families#

4.1 Geometry Operators (G₁–G₃)#

Regime geometry and structural shifts.

• G₁ — Regime Stabilizer
• G₂ — Regime Shifter
• G₃ — Regime Inverter

4.2 Stability Operators (S₁–S₃)#

Stability and coherence maintenance.

• S₁ — Stabilize
• S₂ — Sustain
• S₃ — Seal

5. Arrival Operator Families#

Arrival operators govern cross‑substrate continuity.

• A₁ — Arrival Operator
• A₂ — Arrival Arc
• A₃ — Arrival Gate
• A₄ — Arrival Continuity

6. Macro Operator Families#

Macro operators govern large‑scale alignment.

• M₁ — Macro Alignment
• M₂ — Macro Stabilizer
• M₃ — Macro Resonance Bridge

7. Operator family behavior across triadic time#

Operators interact with triadic time layers:

7.1 State Time (T₁)#

• R‑operators
• P‑operators
• G‑operators
• A‑operators

7.2 Coherence Time (T₂)#

• K‑operators
• S‑operators
• Drift‑related primitives

7.3 Readout Time (T₃)#

• K‑operators (validation)
• Collapse operators (implicit)
• Arrival operators (continuity events)

8. Regime interactions#

Operator families declare regime compatibility:

• SRR — Single‑Readout
• DBR — Drift‑Bounded
• CMR — Coherence‑Minimum
• DVR — Deferred‑Validation
• ECR — Extension‑Compatible

Examples:

• R‑operators often require DBR
• K‑operators enforce CMR
• Extension operators require ECR
• Validator Pulse requires SRR

9. Example: Operator families in quantum “cloning” alignment#

The alignment module uses:

• P‑operators for representational extension
• K‑operators for coherence gating
• S‑operators for drift stabilization
• G‑operators for regime shifts
• Validator Pulse (K‑family) for single‑readout
• Collapse (implicit) for residue formation

Operator families explain:

• Why multi‑branch representation is allowed
• Why only one branch becomes classical
• Why drift and coherence matter
• Why no‑cloning is not violated

10. Canon integration and cross-links#

Primary cross-links:

• /docs/rtt/core/operator_index.md
• /docs/rtt/core/operator_grammar.md
• /docs/rtt/core/regime_maps.md
• /docs/rtt/core/regime_index.md
• /docs/rtt/core/time_triads.md
• /docs/rtt/core/coherence_budget.md
• /docs/rtt/core/validator_pulse.md
• /docs/rtt/core/dimensional_drift_envelope.md
• /docs/rtt/core/alignment_quantum_cloning.md

Status:
This module defines the canonical taxonomy of RTT operators.
Once operator‑grammar syntax is fully integrated, it can be promoted from draft to stable.