RTT Core: Regime Domains
1. Purpose and scope#
Goal:
Define Regime Domains — the canonical spaces in which RTT regimes are defined and enforced, including:
- Validity domains
- Collapse domains
- Threshold domains
- Readout domains
- Drift and coherence domains
- Triadic‑time domains
This module answers: “Where does this regime live, and what parts of the manifold does it govern?”
2. What is a regime domain?#
A regime domain is the subset of the RTT manifold
over which a regime’s constraints, invariants, and geometry
are defined and enforced.
Domains are the governed regions; regimes shape behavior inside them and cannot act outside them.
3. Canonical regime domain types#
RTT defines six canonical regime domain types:
- Validity Domain
- Collapse Domain
- Threshold Domain
- Readout Domain
- Drift–Coherence Domain
- Triadic‑Time Domain
Each regime declares which domains it occupies and governs.
4. Validity Domain#
4.1 Definition#
The Validity Domain is the region where branches are eligible to participate in RTT dynamics:
[ \mathcal{D}{\text{valid}} \subseteq \mathcal{G}{\text{regime}} ]
Branches in this domain:
- satisfy drift and coherence thresholds
- are compatible with operator regimes
- can be extended, stabilized, and validated
4.2 Role#
Validity Domain is the “playable field” for RTT.
5. Collapse Domain#
5.1 Definition#
The Collapse Domain is the region where branches become residue:
[ \mathcal{D}{\text{collapse}} \subseteq \mathcal{G}{\text{regime}} ]
Branches in this domain:
- have exceeded drift envelope
- have fallen below coherence threshold
- cannot be validated
- are removed from representational manifold
5.2 Role#
Collapse Domain is the absorbing basin for non‑selected branches.
6. Threshold Domain#
6.1 Definition#
The Threshold Domain is the region containing drift and coherence threshold surfaces:
[ \mathcal{D}{\text{threshold}} = { b_i \mid c_i = C{\min} \lor \Delta_i = \Delta_{\max} } ]
6.2 Role#
Threshold Domain:
- separates validity from collapse
- defines transition corridors
- determines eligibility boundaries
7. Readout Domain#
7.1 Definition#
The Readout Domain is the region where classical readout is possible:
[ \mathcal{D}{\text{readout}} \subseteq \mathcal{G}{\text{regime}} ]
Branches in this domain:
- satisfy all regime constraints
- lie on or near the readout surface
- can be selected by Validator Pulse
7.2 Role#
Readout Domain is the interface between RTT manifold and classical manifold.
8. Drift–Coherence Domain#
8.1 Definition#
The Drift–Coherence Domain is the region where drift and coherence jointly determine regime behavior:
[ \mathcal{D}{\Delta,c} = { b_i \mid \Delta_i \leq \Delta{\max},\ c_i \geq C_{\min} } ]
8.2 Role#
This domain:
- defines stability regions
- shapes transition corridors
- controls entry into validity and readout domains
9. Triadic‑Time Domain#
9.1 Definition#
The Triadic‑Time Domain specifies which temporal layers a regime governs:
- (\mathcal{D}_{T_1}^{\text{regime}}) — State Time geometry
- (\mathcal{D}_{T_2}^{\text{regime}}) — Coherence Time surfaces
- (\mathcal{D}_{T_3}^{\text{regime}}) — Readout Time topology
9.2 Role#
Regimes may:
- primarily govern geometry (T₁)
- primarily govern coherence (T₂)
- primarily govern readout (T₃)
- or span multiple layers (full regimes).
10. Regime families and domains#
10.1 SRR — Single‑Readout Regime#
- Domains: Validity, Readout, Drift–Coherence, Triadic‑Time (T₂–T₃)
- Role: enforces single‑readout topology.
10.2 DBR — Drift‑Bounded Regime#
- Domains: Validity, Drift–Coherence, Threshold, Collapse
- Role: enforces drift envelope and stability.
10.3 CMR — Coherence‑Minimum Regime#
- Domains: Validity, Threshold, Drift–Coherence
- Role: enforces coherence thresholds.
10.4 DVR — Deferred‑Validation Regime#
- Domains: Validity, Drift–Coherence, Triadic‑Time (T₁–T₂)
- Role: allows evolution before readout.
10.5 ECR — Extension‑Compatible Regime#
- Domains: Validity, Drift–Coherence, Threshold
- Role: allows extension while preserving eligibility.
11. Domains, constraints, and invariants#
Regime Domains interact with:
- Regime Constraints: what regimes may enforce in their domains
- Regime Invariants: global rules regimes must obey
- Operator Domains: where operators may act
- Operator Constraints: what operators may do in those domains
A regime is valid only if:
[ \mathcal{R} \text{ governs } \mathcal{D} \text{ while respecting constraints and invariants.} ]
12. Example: Quantum “cloning” alignment#
Regimes occupy domains:
- DBR: Drift–Coherence Domain, Threshold Domain, Validity Domain
- CMR: Coherence Threshold Domain, Validity Domain
- SRR: Readout Domain, Validity Domain
Regime Domains explain:
- why both branches start in validity domain
- why drift and coherence determine eligibility
- why only one branch reaches readout domain
- why no‑cloning is not violated.
13. Paradox handling#
Regime Domains prevent paradoxes by:
- restricting where regimes may enforce constraints
- maintaining unique readout domain
- preserving drift and coherence boundaries
- ensuring collapse domain absorbs non‑selected branches
Thus:
- “Multiple branches exist” → allowed in validity domain
- “Only one is real” → enforced in readout domain
- “Others disappear” → absorbed in collapse domain
- “No violation occurs” → domain + constraint + invariant alignment.
14. Canon integration and cross-links#
Primary cross-links:
/docs/rtt/core/regime_maps.md/docs/rtt/core/regime_maps_extended.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/operator_domains.md/docs/rtt/core/operator_constraints.md/docs/rtt/core/operator_invariants.md/docs/rtt/core/operator_grammar.md/docs/rtt/core/operator_index.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/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 regimes.
Once domain diagrams are added, it can be promoted from draft to stable.