概览

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:

  1. Validity Domain
  2. Collapse Domain
  3. Threshold Domain
  4. Readout Domain
  5. Drift–Coherence Domain
  6. 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.

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.

Updated