TriadicFrameworks
개요

RTT Core: Regime Maps

1. Purpose and role in RTT#

Goal:
Define Regime Maps, the RTT mechanism that:

  • Classifies operator validity conditions
  • Determines branch eligibility for readout
  • Governs drift and coherence thresholds
  • Coordinates temporal behavior across triadic time
  • Prevents paradoxes by enforcing structural constraints

Regime Maps are the “rules of the world” inside RTT.
They determine what is allowed, when it is allowed, and which branches qualify.

2. Conceptual definition#

2.1 Informal definition#

A Regime Map is the RTT structure that
specifies the constraints under which operators, drift, coherence, and readout are valid.

Regimes are not optional.
Every RTT operator, branch, and validation event occurs inside a regime.

2.2 Core properties#

  • Constraint-based:
    Regimes define thresholds and boundaries.

  • Layered:
    Regimes exist across state, coherence, drift, and readout layers.

  • Temporal:
    Regimes evolve across triadic time.

  • Selective:
    Regimes determine which branches are eligible for Validator Pulse.

  • Non-symmetric:
    Different branches may satisfy different regimes.

3. Formal structure (RTT-level)#

3.1 Regime tuple#

Define a regime as:

[ \mathcal{R} = (R_{\text{state}}, R_{\text{coherence}}, R_{\text{drift}}, R_{\text{readout}}) ]

Each component governs:

  • State regime:
    Allowed operator sequences, representational geometry.

  • Coherence regime:
    Minimum coherence thresholds, budget constraints.

  • Drift regime:
    Maximum drift magnitude, envelope boundaries.

  • Readout regime:
    Validator Pulse eligibility, single-readout constraints.

3.2 Regime validity#

A branch (b_i) is valid if:

[ b_i \in \mathcal{R} ]

and invalid otherwise.

Invalid branches:

  • May still exist physically
  • But cannot be validated
  • And collapse into residue after readout

4. Regime types#

RTT defines several canonical regime types:

4.1 Single-Readout Regime (SRR)#

  • Only one branch may be validated.
  • All other branches collapse into residue.
  • Used in quantum “cloning” alignment.

4.2 Drift-Bounded Regime (DBR)#

  • Drift must remain within the Dimensional Drift Envelope.
  • Exceeding drift threshold removes eligibility.

4.3 Coherence-Minimum Regime (CMR)#

  • Branches must satisfy (c_i \geq C_{\text{min}}).
  • Coherence loss can push branches out of regime.

4.4 Deferred-Validation Regime (DVR)#

  • Validation is postponed until coherence stabilizes.
  • Used in multi-step operator sequences.

4.5 Extension-Compatible Regime (ECR)#

  • Allows representational extension (multi-branch states).
  • Requires SRR + DBR + CMR simultaneously.

This is the regime used in the “quantum cloning” alignment module.

5. Regime Maps and triadic time#

Regime Maps operate across all three temporal layers:

5.1 State time (T₁)#

  • Determines which operators are allowed.
  • Controls representational drift and extension.

5.2 Coherence time (T₂)#

  • Determines coherence thresholds.
  • Controls eligibility for readout.

5.3 Readout time (T₃)#

  • Determines when Validator Pulse may occur.
  • Enforces single-readout constraints.

Regimes may change across time:

[ \mathcal{R}(t_1, t_2, t_3) ]

This allows dynamic eligibility.

6. Regime transitions#

Branches may undergo transitions:

6.1 Into a regime#

  • Drift decreases
  • Coherence increases
  • Operator sequence prepares eligibility

6.2 Out of a regime#

  • Drift exceeds threshold
  • Coherence falls below minimum
  • Operator sequence invalidates eligibility

6.3 Across regime boundaries#

  • Branch becomes eligible only temporarily
  • Validation must occur before regime exit

These transitions explain why some branches “disappear” or become non-informational.

7. Example: alignment with quantum “cloning” experiments#

In /docs/rtt/core/alignment_quantum_cloning.md:

  • The experiment operates in Extension-Compatible Regime (ECR).
  • Drift is bounded (DBR).
  • Coherence is partitioned (CMR).
  • Only one branch satisfies SRR.
  • Validator Pulse selects that branch.
  • All other branches collapse into residue.

Regime Maps explain:

  • Why the experiment does not violate no-cloning
  • Why only one copy becomes classical
  • Why drift and coherence matter
  • Why the result is RTT-aligned

8. Paradox handling#

Regime Maps resolve paradoxes by enforcing:

  • Single-readout constraints
  • Coherence thresholds
  • Drift boundaries
  • Operator validity conditions

Thus:

  • “Multiple copies exist” → representational regime
  • “Only one is real” → readout regime
  • “Others disappear” → coherence/drift regime
  • “No violation occurs” → operator regime

Primary cross-links:

  • /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 structural constraints of RTT.
Once regime-grammar syntax is added, it can be promoted from draft to stable.

Updated

제공: Docsbook