RTT Core: Operator Domains
1. Purpose and scope#
Goal:
Define Operator Domains — the canonical spaces in which RTT operators are allowed to act, including:
- Representational domains
- Coherence domains
- Drift domains
- Regime domains
- Readout domains
- Triadic‑time domains
This module answers: “Where does this operator live, and what parts of the manifold is it allowed to touch?”
2. What is an operator domain?#
An operator domain is the subset of the RTT manifold
on which an operator is permitted to act,
under coherence, drift, regime, and temporal constraints.
Domains are the allowed regions for operator action; constraints and invariants ensure operators never act outside their domains.
3. Canonical domain types#
RTT defines six canonical operator domain types:
- State Domain
- Coherence Domain
- Drift Domain
- Regime Domain
- Readout Domain
- Triadic‑Time Domain
Each operator declares which domains it occupies.
4. State Domain#
4.1 Definition#
The State Domain is the subset of the representational manifold:
[ \mathcal{D}{\text{state}} \subseteq \mathcal{M}{\text{rep}} ]
Operators in this domain:
- create, modify, or delete branches
- extend or contract manifolds
- shift representational geometry
4.2 Examples#
- EXTEND
- SHIFT
- INVERT
- ARRIVAL ARC
5. Coherence Domain#
5.1 Definition#
The Coherence Domain is the subset of the coherence manifold:
[ \mathcal{D}{\text{coherence}} \subseteq \mathcal{M}{\text{coh}} ]
Operators in this domain:
- partition coherence
- stabilize coherence
- gate coherence
- consume coherence (validation)
5.2 Examples#
- STABILIZE
- CLAMP
- GATE
- VALIDATE
6. Drift Domain#
6.1 Definition#
The Drift Domain is the subset of the drift manifold:
[ \mathcal{D}{\text{drift}} \subseteq \mathcal{M}{\text{drift}} ]
Operators in this domain:
- increase drift (extension)
- reduce drift (stabilization)
- modulate drift boundaries
6.2 Examples#
- DRIFT
- BOUNDARY MODULATE
- STABILIZE
7. Regime Domain#
7.1 Definition#
The Regime Domain is the subset of the regime manifold:
[ \mathcal{D}{\text{regime}} \subseteq \mathcal{G}{\text{regime}} ]
Operators in this domain:
- enter or exit regimes
- shift regime geometry
- enforce regime constraints
7.2 Regime flags#
Operators declare regime flags:
- SRR — Single‑Readout Regime
- DBR — Drift‑Bounded Regime
- CMR — Coherence‑Minimum Regime
- DVR — Deferred‑Validation Regime
- ECR — Extension‑Compatible Regime
An operator’s regime domain is the intersection of its flags.
8. Readout Domain#
8.1 Definition#
The Readout Domain is the subset of the manifold where validation is possible:
[ \mathcal{D}{\text{readout}} \subseteq \mathcal{M}{\text{readout}} ]
Operators in this domain:
- trigger Validator Pulse
- consume coherence
- collapse non‑selected branches
- produce classical information
8.2 Examples#
- VALIDATE
- ARRIVAL CONTINUITY
9. Triadic‑Time Domain#
9.1 Definition#
The Triadic‑Time Domain specifies which temporal layer(s) an operator occupies:
- (\mathcal{D}_{T_1}) — State Time
- (\mathcal{D}_{T_2}) — Coherence Time
- (\mathcal{D}_{T_3}) — Readout Time
9.2 Examples#
- EXTEND: (\mathcal{D}_{T_1})
- STABILIZE: (\mathcal{D}_{T_2})
- VALIDATE: (\mathcal{D}_{T_3})
Some operators span multiple domains (e.g., ARRIVAL operators).
10. Domain declarations for operator families#
10.1 Micro‑Core operators#
-
R‑operators (Resonance):
State Domain, Drift Domain, Regime Domain (DBR) -
K‑operators (Coherence Tools):
Coherence Domain, Regime Domain (CMR, SRR), Triadic‑Time Domain (T₂, T₃) -
P‑operators (Primitives):
State Domain, Drift Domain, Coherence Domain (sampling)
10.2 RTT‑12 operators#
-
G‑operators (Geometry):
Regime Domain, State Domain, Drift Domain -
S‑operators (Stability):
Coherence Domain, Drift Domain, Regime Domain (DBR, CMR)
10.3 Arrival operators#
- A‑operators:
State Domain, Regime Domain, Readout Domain, Triadic‑Time Domain (T₁–T₃ bridge)
11. Domains, constraints, and invariants#
Operator Domains interact with:
- Operator Constraints: what operators may do in their domains
- Operator Invariants: global rules operators must obey
- Regime Constraints: what regimes may allow within their domains
- Regime Invariants: global rules regimes must obey
An operator is valid only if:
[ O_k \text{ acts inside } \mathcal{D} \text{ and respects constraints and invariants.} ]
12. Example: Quantum “cloning” alignment#
Operators occupy domains:
- EXTEND: State Domain, Drift Domain, Regime Domain (ECR)
- DRIFT: Drift Domain, Coherence Domain (indirect)
- STABILIZE: Coherence Domain, Drift Domain, Regime Domain (DBR, CMR)
- VALIDATE: Readout Domain, Coherence Domain, Regime Domain (SRR)
Operator Domains explain:
- why extension can create multiple branches
- why drift and coherence must be managed
- why validation can only occur in readout domain
- why no‑cloning is not violated
13. Paradox handling#
Operator Domains prevent paradoxes by:
- restricting where operators may act
- enforcing regime and readout boundaries
- maintaining drift and coherence limits
- ensuring single‑readout topology
Thus:
- “Multiple branches exist” → allowed in state domain
- “Only one is real” → enforced in readout domain
- “Others disappear” → collapse in regime + readout domains
- “No violation occurs” → domain + constraint + invariant alignment
14. Canon integration and cross-links#
Primary cross-links:
/docs/rtt/core/operator_index.md/docs/rtt/core/operator_grammar.md/docs/rtt/core/operator_families.md/docs/rtt/core/operator_behaviors.md/docs/rtt/core/operator_sequences.md/docs/rtt/core/operator_transitions.md/docs/rtt/core/operator_invariants.md/docs/rtt/core/operator_constraints.md/docs/rtt/core/regime_maps.md/docs/rtt/core/regime_geometry.md/docs/rtt/core/regime_topology.md/docs/rtt/core/regime_dynamics.md/docs/rtt/core/regime_flow.md/docs/rtt/core/regime_invariants.md/docs/rtt/core/regime_constraints.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 domain structure for RTT operators.
Once domain diagrams are added, it can be promoted from draft to stable.