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RTT Core: Operator Behaviors

1. Purpose and scope#

Goal:
Define the behavioral characteristics of RTT operators across:

  • Representational manifolds
  • Drift envelopes
  • Coherence budgets
  • Regime constraints
  • Triadic time layers
  • Validator Pulse interactions

This module explains how operators behave, not just what they are. It is the dynamic counterpart to /docs/rtt/core/operator_grammar.md and /docs/rtt/core/operator_families.md.

2. Behavioral dimensions#

RTT operators exhibit behavior across five canonical dimensions:

  1. Representational Behavior
  2. Coherence Behavior
  3. Drift Behavior
  4. Regime Behavior
  5. Readout Behavior

These dimensions determine how operators affect branches, manifolds, and classical outcomes.

3. Representational Behavior#

3.1 Extension Behavior#

Operators may:

  • Create new branches
  • Expand representational manifolds
  • Partition coherence
  • Increase drift

Example: EXTEND operator

3.2 Contraction Behavior#

Operators may:

  • Merge branches
  • Reduce representational complexity
  • Stabilize coherence
  • Reduce drift

Example: SEAL operator (S‑family)

3.3 Reconfiguration Behavior#

Operators may:

  • Rotate regime geometry
  • Shift representational coordinates
  • Invert branch eligibility

Example: G₂ — Regime Shifter

4. Coherence Behavior#

4.1 Coherence Partition#

Operators may divide coherence across branches:

[ c_i \rightarrow c_i' + c_j' ]

Used in extension operators.

4.2 Coherence Stabilization#

Operators may stabilize coherence:

  • Reduce decay
  • Clamp drift
  • Increase eligibility

Example: K₂ — Timing Stabilizer

4.3 Coherence Consumption#

Validator Pulse consumes coherence:

[ c_k \rightarrow 0 ]

All other branches collapse.

4.4 Coherence Decay#

Drift increases coherence loss:

[ c_i' = c_i - f(\Delta_i) ]

Example: DRIFT operator.

5. Drift Behavior#

5.1 Drift Increase#

Operators may increase drift:

  • Extension
  • Regime inversion
  • Boundary modulation

5.2 Drift Reduction#

Operators may reduce drift:

  • Stabilization
  • Coherence gating
  • Boundary alignment

5.3 Drift Envelope Interaction#

Operators must respect:

  • Drift boundaries
  • Envelope curvature
  • Stability surfaces

Branches exceeding drift envelope lose eligibility.

6. Regime Behavior#

Operators declare regime compatibility:

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

6.1 Regime Entry#

Operators may push branches into a regime:

  • Stabilization
  • Coherence increase
  • Drift reduction

6.2 Regime Exit#

Operators may push branches out of a regime:

  • Drift spike
  • Coherence collapse
  • Invalid operator sequence

6.3 Regime Transition#

Operators may cause transitions:

[ ECC \rightarrow SDC \rightarrow SRR ]

Used in multi-step RTT sequences.

7. Readout Behavior#

7.1 Readout Eligibility#

Operators determine whether branches satisfy:

  • Coherence thresholds
  • Drift boundaries
  • Regime constraints

7.2 Readout Triggering#

Validator Pulse triggers readout:

  • Consumes coherence
  • Collapses non-selected branches
  • Produces classical information

7.3 Readout Deferral#

Some operators defer readout:

  • Stabilization
  • Drift reduction
  • Coherence recovery

Example: DEFER operator.

8. Operator Behavior Across Triadic Time#

Operators interact with triadic time layers:

8.1 State Time (T₁)#

  • Extension
  • Drift
  • Regime shifts
  • Boundary modulation

8.2 Coherence Time (T₂)#

  • Coherence partition
  • Coherence decay
  • Coherence stabilization

8.3 Readout Time (T₃)#

  • Validation
  • Collapse
  • Continuity (Arrival operators)

Operators may trigger transitions across layers.

9. Composite Operator Behaviors#

Operators often combine behaviors:

9.1 Extension + Drift + Deferred Readout#

Used in multi-branch creation:

  • Increase drift
  • Partition coherence
  • Defer readout

9.2 Stabilization + Coherence Gate + Regime Entry#

Used in preparation for validation:

  • Reduce drift
  • Increase coherence
  • Enter SRR

9.3 Validation + Collapse#

Used in classical readout:

  • Consume coherence
  • Collapse non-selected branches

10. Example: Quantum “cloning” alignment#

The experiment uses:

  • Extension Behavior: create two branches
  • Coherence Behavior: partition coherence
  • Drift Behavior: increase drift but remain bounded
  • Regime Behavior: operate in ECR + SRR
  • Readout Behavior: validate one branch, collapse the other

Operator Behaviors explain:

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

11. Paradox handling#

Operator Behaviors prevent paradoxes by:

  • Enforcing regime constraints
  • Managing coherence budgets
  • Bounding drift
  • Restricting readout
  • Collapsing non-selected branches

Thus:

  • “Multiple branches exist” → extension behavior
  • “Only one is real” → readout behavior
  • “Others disappear” → collapse behavior
  • “No violation occurs” → regime behavior

Primary cross-links:

  • /docs/rtt/core/operator_grammar.md
  • /docs/rtt/core/operator_index.md
  • /docs/rtt/core/operator_families.md
  • /docs/rtt/core/regime_maps.md
  • /docs/rtt/core/regime_maps_extended.md
  • /docs/rtt/core/regime_geometry.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 behavioral dynamics of RTT operators.
Once operator-behavior diagrams are added, it can be promoted from draft to stable.

Updated

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