RTT Core: Regime Invariants
1. Purpose and scope#
Goal:
Define the Regime Invariants — the fundamental, non‑negotiable rules that govern all RTT regimes, regardless of:
- operator behavior
- drift magnitude
- coherence level
- temporal layer
- sequence structure
Regime Invariants ensure RTT remains stable, paradox‑free, coherence‑bounded, drift‑bounded, and single‑readout consistent.
2. What is a regime invariant?#
A regime invariant is a structural rule that
must hold for every regime, across all branches,
at all points in triadic time.
If a regime violates an invariant:
- the regime becomes invalid
- operators inside it become invalid
- branches collapse into residue
- classical readout cannot occur
Regime Invariants are the laws of structure in RTT.
3. The Five Canonical Regime Invariants#
RTT defines five universal regime invariants:
- Validity Region Invariant
- Collapse Basin Invariant
- Threshold Surface Invariant
- Single‑Readout Topology Invariant
- Triadic‑Time Regime Invariant
These invariants apply to every regime.
4. Validity Region Invariant#
4.1 Statement#
[ \mathcal{V} \text{ must remain a connected, stable region of the regime manifold.} ]
4.2 Consequences#
- Validity region cannot fragment
- Branches must be able to move within it
- Operators must act inside it
- Eligibility must be preserved
4.3 Violations#
Fragmentation → invalid regime → collapse.
5. Collapse Basin Invariant#
5.1 Statement#
[ \mathcal{C} \text{ must remain a connected, attracting basin.} ]
5.2 Consequences#
- Collapse region is always reachable
- Collapse is irreversible
- Non-selected branches always fall into (\mathcal{C})
- No branch can escape collapse once entered
5.3 Violations#
Non-attracting collapse → paradox → invalid regime.
6. Threshold Surface Invariant#
6.1 Statement#
[ c_i = C_{\min} \quad \text{and} \quad \Delta_i = \Delta_{\max} ]
must define monotonic, non-bypassable surfaces.
6.2 Consequences#
- Coherence threshold cannot be circumvented
- Drift boundary cannot be bypassed
- Threshold surfaces must remain continuous
- Eligibility must be determined by these surfaces
6.3 Violations#
Broken threshold → invalid regime → collapse.
7. Single‑Readout Topology Invariant#
7.1 Statement#
[ \text{There must be exactly one connected readout surface per validation event.} ]
7.2 Consequences#
- Only one branch can reach readout surface
- All others collapse
- Classical reality remains unique
- No multi‑readout paradoxes
7.3 Violations#
Multiple readout surfaces → paradox → invalid regime.
8. Triadic‑Time Regime Invariant#
8.1 Statement#
[ \mathcal{R}(t_1, t_2, t_3) \text{ must evolve consistently across triadic time.} ]
8.2 Consequences#
Regimes must:
- shift geometry in T₁
- reshape coherence surfaces in T₂
- activate readout surfaces in T₃
Temporal inconsistency is forbidden.
8.3 Violations#
Temporal paradox → invalid regime → collapse.
9. Derived Regime Invariants#
From the five canonical invariants, RTT derives several secondary invariants:
9.1 Collapse‑Completeness Invariant#
[ \text{All non-selected branches must collapse fully.} ]
9.2 Eligibility‑Monotonicity Invariant#
[ \text{Eligibility must decrease monotonically as drift increases or coherence decreases.} ]
9.3 Regime‑Continuity Invariant#
[ \text{Regime surfaces must remain continuous across operator sequences.} ]
9.4 Readout‑Uniqueness Invariant#
[ \text{Readout surface must remain unique and connected.} ]
10. Regime Invariants Across Triadic Time#
10.1 State Time (T₁)#
- Drift boundary invariant
- Validity region invariant
- Regime geometry invariant
10.2 Coherence Time (T₂)#
- Coherence threshold invariant
- Eligibility monotonicity invariant
- Collapse basin invariant
10.3 Readout Time (T₃)#
- Single-readout invariant
- Collapse completeness invariant
- Readout surface invariant
Invariants must hold across all three layers.
11. Invariants in Regime Dynamics#
Regime dynamics must preserve invariants:
[ \forall t,\ \mathcal{R}(t) \text{ satisfies invariants} ]
If dynamics violate an invariant:
- regime becomes invalid
- operators fail
- branches collapse
12. Example: Quantum “cloning” alignment#
The experiment demonstrates all invariants:
- Validity Region: both branches initially valid
- Collapse Basin: non-selected branch falls into collapse
- Threshold Surface: coherence threshold determines eligibility
- Single‑Readout Topology: only one branch reaches readout surface
- Triadic‑Time: extension → drift → stabilization → validation
Regime Invariants explain:
- why multi‑branch representation is allowed
- why only one branch becomes classical
- why drift and coherence matter
- why no‑cloning is not violated
13. Paradox handling#
Regime Invariants prevent paradoxes by:
- enforcing topological boundaries
- maintaining drift and coherence thresholds
- restricting readout surfaces
- ensuring collapse completeness
- preserving temporal consistency
Thus:
- “Multiple branches exist” → allowed
- “Only one is real” → invariant
- “Others disappear” → collapse invariant
- “No violation occurs” → regime invariant
14. Canon integration and cross-links#
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/operator_invariants.md/docs/rtt/core/operator_constraints.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 fundamental invariants governing RTT regimes.
Once invariant diagrams are added, it can be promoted from draft to stable.