Triadicframeworks
Overview

RTT Core: Regime Index

1. Purpose and scope#

Goal:
Provide a unified, canonical index of all RTT regime families across:

  • State regimes
  • Coherence regimes
  • Drift regimes
  • Readout regimes
  • Composite operator regimes

This index serves as the navigation backbone for RTT’s structural logic.
Every operator, branch, drift event, and validation event occurs inside a regime.

2. Conceptual definition#

2.1 What is a regime?#

A regime is a structural constraint that determines
what is allowed, when it is allowed, and which branches qualify
in RTT’s multi‑layer temporal and representational system.

Regimes prevent paradoxes, enforce coherence budgets, and maintain single‑readout consistency.

2.2 Why regimes matter#

Regimes govern:

  • Operator validity
  • Drift boundaries
  • Coherence thresholds
  • Validator Pulse eligibility
  • Temporal transitions across triadic time

Without regimes, RTT would permit paradoxical operator sequences.

3. Formal regime tuple#

A regime is defined as:

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

Where:

  • State regime — representational geometry, operator sequences
  • Coherence regime — minimum coherence thresholds
  • Drift regime — maximum drift magnitude, envelope boundaries
  • Readout regime — Validator Pulse constraints, single‑readout rules

A branch (b_i) is valid if:

[ b_i \in \mathcal{R} ]

Invalid branches collapse into residue after validation.

4. Canonical RTT Regime Families#

4.1 Single‑Readout Regime (SRR)#

  • Only one branch may be validated
  • All others collapse into residue
  • Enforces classical uniqueness
  • Used in quantum “cloning” alignment

4.2 Drift‑Bounded Regime (DBR)#

  • Drift must remain within the Dimensional Drift Envelope
  • Exceeding drift threshold removes eligibility
  • Ensures representational stability

4.3 Coherence‑Minimum Regime (CMR)#

  • Branches must satisfy (c_i \geq C_{\text{min}})
  • Coherence loss pushes branches out of regime
  • Prevents multi‑readout paradoxes

4.4 Deferred‑Validation Regime (DVR)#

  • Validation postponed until coherence stabilizes
  • Used in multi‑step operator sequences
  • Allows complex operator chains

4.5 Extension‑Compatible Regime (ECR)#

  • Allows representational extension (multi‑branch states)
  • Requires SRR + DBR + CMR simultaneously
  • Used in “quantum cloning” alignment

5. Regime Maps#

Regime Maps describe how regimes interact across triadic time:

5.1 State Time (T₁)#

  • Operator validity
  • Representational drift
  • Extension events
  • Regime entry/exit

5.2 Coherence Time (T₂)#

  • Coherence thresholds
  • Drift-induced coherence loss
  • Eligibility changes
  • Budget constraints

5.3 Readout Time (T₃)#

  • Validator Pulse events
  • Single-readout enforcement
  • Collapse of non-selected branches

Regime Maps define:

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

allowing dynamic eligibility.

6. Regime Transitions#

Branches undergo transitions:

6.1 Entering a regime#

  • Drift decreases
  • Coherence increases
  • Operator sequence prepares eligibility

6.2 Exiting a regime#

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

6.3 Crossing regime boundaries#

  • Eligibility becomes temporary
  • Validation must occur before exit
  • Drift or coherence may force collapse

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

7. Example: Quantum “Cloning” Alignment#

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 others collapse into residue

Regime Index explains:

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

8. Paradox handling#

Regimes prevent 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/regime_maps.md
  • /docs/rtt/core/operator_grammar.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 provides the canonical index of RTT regimes.
Once regime-grammar syntax is added, it can be promoted from draft to stable.

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