RTT Core: Regime Maps (Extended)

1. Purpose and scope#

Goal:
Extend the core RTT regime system by defining:

• Composite regime structures
• Multi‑layer regime geometry
• Cross‑regime transitions
• Regime interference and resonance
• Regime stacking across triadic time
• Regime behavior under extension, drift, and validation

This module expands /docs/rtt/core/regime_maps.md into the full structural map used by RTT operators, drift envelopes, coherence budgets, and Validator Pulse.

2. Regime geometry (extended)#

2.1 Regime manifold#

Regimes form a multi‑dimensional manifold:

[ \mathcal{R}{\text{ext}} = \mathcal{R}{\text{state}} \times \mathcal{R}{\text{coherence}} \times \mathcal{R}{\text{drift}} \times \mathcal{R}_{\text{readout}} ]

Each axis has its own geometry:

• State axis: operator validity, representational topology
• Coherence axis: thresholds, budgets, decay curves
• Drift axis: envelopes, boundaries, drift-loss functions
• Readout axis: validation topology, collapse rules

Extended regime maps describe how these axes interact.

3. Composite regime structures#

Composite regimes combine multiple canonical regimes into higher‑order structures.

3.1 Extension-Compatible Composite (ECC)#

[ ECC = SRR \cap DBR \cap CMR ]

Used in quantum “cloning” alignment.

3.2 Stabilized Drift Composite (SDC)#

[ SDC = DBR \cap DVR ]

Used when drift must be bounded before validation.

3.3 High-Coherence Composite (HCC)#

[ HCC = CMR \cap DVR ]

Used in multi-step operator chains requiring deferred validation.

3.4 Full-Regime Composite (FRC)#

[ FRC = SRR \cap DBR \cap CMR \cap DVR ]

Used in complex RTT sequences involving extension, drift, stabilization, and validation.

4. Regime interference and resonance#

Regimes may interfere or resonate:

4.1 Interference#

Two regimes interfere when:

• Their constraints conflict
• A branch cannot satisfy both simultaneously
• Operator sequences become invalid

Example:

• SRR (single-readout)
• Multi-readout operator (invalid in RTT core)

4.2 Resonance#

Two regimes resonate when:

• Their constraints reinforce each other
• Eligibility becomes more stable
• Drift and coherence align

Example:

• DBR + CMR
• Drift remains bounded and coherence remains above threshold

5. Regime stacking across triadic time#

Regimes may stack across temporal layers:

5.1 State-time stacking (T₁)#

Operators may require:

• Regime entry before extension
• Regime stability during drift
• Regime inversion during geometry shifts

5.2 Coherence-time stacking (T₂)#

Coherence thresholds may:

• Increase
• Decrease
• Stabilize
• Redistribute

depending on regime transitions.

5.3 Readout-time stacking (T₃)#

Validator Pulse may require:

• SRR
• CMR
• DBR

simultaneously.

6. Regime transitions (extended)#

6.1 Hard transitions#

A branch abruptly enters or exits a regime:

• Drift spike
• Coherence collapse
• Operator invalidation

6.2 Soft transitions#

A branch gradually moves across regime boundaries:

• Slow drift
• Gradual coherence decay
• Deferred validation

6.3 Composite transitions#

A branch transitions across multiple regimes simultaneously:

[ ECC \rightarrow SDC \rightarrow SRR ]

Used in multi-step RTT operator chains.

7. Regime maps under extension, drift, and validation#

7.1 Under extension#

Extension operators require:

• ECC
• Drift increase
• Coherence partition
• Deferred validation

7.2 Under drift#

Drift operators require:

• DBR
• Coherence loss
• Envelope boundaries

7.3 Under validation#

Validator Pulse requires:

• SRR
• CMR
• Collapse of non-selected branches

8. Example: Quantum “cloning” alignment (extended)#

The experiment uses:

1. ECC for extension
2. DBR for drift
3. CMR for coherence thresholds
4. SRR for single-readout
5. FRC for full operator sequence validity

Extended regime maps explain:

• Why multi-branch representation is allowed
• Why only one branch becomes classical
• Why drift and coherence matter
• Why no-cloning is not violated
• Why the result is fully RTT-aligned

9. Paradox handling#

Extended regime maps prevent paradoxes by:

• Enforcing composite constraints
• Managing drift and coherence across time
• Restricting operator sequences
• Ensuring single-readout consistency
• Collapsing non-selected branches

Thus:

• “Multiple branches exist” → ECC
• “Only one is real” → SRR
• “Others disappear” → CMR + DBR
• “No violation occurs” → FRC

10. Canon integration and cross-links#

Primary cross-links:

• /docs/rtt/core/regime_maps.md
• /docs/rtt/core/regime_index.md
• /docs/rtt/core/operator_grammar.md
• /docs/rtt/core/operator_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 extends the RTT regime system into full composite and temporal geometry.
Once regime-grammar syntax is added, it can be promoted from draft to stable.