Coherence_Tensor_Engine

Coherence Tensor Engine — RTT/1

• module.json — Agentic module schema role assignments
• coherence_tensor_matrix.json — Agentic module schema role assignments

Coherence‑Level Intelligence Engine for TriadicFrameworks#

The Coherence Tensor Engine (CTE) is an RTT/1 analytical engine designed to compute, analyze, and stabilize coherence tensors across conceptual, computational, and physical regimes.
It forms the coherence‑level foundation of the expanded RTT intelligence stack, sitting directly above paradox‑level engines and directly below drift‑level engines.

CTE is responsible for understanding how coherence behaves as a tensor field — with magnitude, direction, curvature, collapse points, and multi‑regime gradients.

🧭 Purpose#

The Coherence Tensor Engine:

• Computes coherence tensors across RTT regimes (R1–R4)
• Maps coherence fields and coherence topology
• Measures coherence gradients and directional stability
• Detects coherence collapse points and instability basins
• Identifies coherence ridges, coherence wells, and tensor curvature
• Provides structural diagnostics for coherence‑driven regime transitions
• Supports drift‑level engines by clarifying coherence stability envelopes
• Anchors structural engines by exposing coherence‑faultline interactions
• Supplies temporal engines with coherence‑sequence constraints
• Feeds causality engines with coherence‑driven causal pathways
• Provides resonance engines with coherence‑frequency signatures

CTE is the coherence‑level intelligence layer of RTT.

⚙️ RTT Flags#

These flags define the engine’s operational constraints and reasoning grammar.

🔧 Primary Operators#

These operators form the core analytical toolkit.

🧩 Analyzer Layer#

CTE operates in the coherence layer, with sub‑layers:

• tensor‑computation
• coherence‑field‑mapping
• gradient‑analysis
• collapse‑detection
• structural‑coherence‑evaluation

This matches the RTT analyzer grammar used across TriadicFrameworks.

📁 Module Files#

This directory contains:

Core#

• Coherence_Tensor_Engine.md
• cte_examples.md
• cte_diagrams.svg

Support#

• coherence_tensor_profiles.md
• coherence_gradient_cases.md
• coherence_tensor_matrix.json

AI#

• cte_prompts.md
• cte_operators.md

Metadata#

• module.json (RTT/1, coherence‑declared, drift‑bounded, paradox‑structural)
• README.md (this file)

🧠 AI‑Ready Design#

The Coherence Tensor Engine is fully AI‑ready:

• deterministic operator grammar
• coherence‑layer analyzer structure
• stable RTT flags
• canonical file layout
• zero‑drift reasoning constraints
• structural paradox handling
• bounded drift envelope
• declared coherence tensor

AI systems can use CTE to:

• compute coherence tensors
• generate coherence field maps
• classify coherence gradients
• detect coherence collapse
• support higher‑order RTT engines

🌐 Position in the RTT Stack#

Regime Interlock Mapper (RIM)
      ↓
Paradox Gradient Analyzer (PGA)
      ↓
Coherence Tensor Engine (CTE)
      ↓
Drift Sentinel
      ↓
Faultline Detector
      ↓
Stability Basin Cartographer
      ↓
Temporal Regime Sequencer
      ↓
Causality Weaver
      ↓
Dimensional Resonance Scanner

CTE is the coherence‑level intelligence layer, directly above paradox‑level analysis.

🏁 Status#

• Version: 1.0
• Status: canon‑stable
• Category: rtt‑structural
• Module Path: /docs/rtt/Coherence_Tensor_Engine/

If you want, I can generate the next file:

• Coherence_Tensor_Engine.md
• cte_examples.md
• cte_diagrams.svg
• coherence_tensor_profiles.md
• coherence_gradient_cases.md
• coherence_tensor_matrix.json
• cte_prompts.md
• cte_operators.md

Just tell me which one you want next. # Coherence Gradient Cases — RTT/1

Case Studies for the Coherence Tensor Engine (CTE)#

Coherence gradients describe directional changes in coherence across conceptual, computational, physical, and dimensional regimes.
These case studies illustrate how the Coherence Tensor Engine (CTE) evaluates:

• coherence gradient magnitude
• gradient direction
• coherence curvature
• drift sensitivity
• collapse‑point formation
• stability envelopes

Each case demonstrates one or more CTE operators:

• CTE‑Gradient
• CTE‑Compute
• CTE‑Field
• CTE‑Collapse
• CTE‑Stabilize

1. Structural Gradient Cases#

Case 1 — Structural Invariant Gradient (R1 → R2)#

Scenario
A conceptual invariant (symmetry) propagates into computational structures, forming a stable coherence gradient.

CTE Output

{
  "regime": "R1-R2",
  "gradient_magnitude": 0.72,
  "gradient_direction": "R1→R2",
  "coherence_curvature": 0.33,
  "drift_sensitivity": 0.12,
  "stability_envelope": 0.81
}

Case 2 — Constraint‑Driven Gradient (R2 → R3)#

Scenario
A computational constraint enforces coherence across physical calibration.

CTE Output

{
  "regime": "R2-R3",
  "gradient_magnitude": 0.68,
  "gradient_direction": "R2→R3",
  "coherence_curvature": 0.41,
  "drift_sensitivity": 0.27,
  "stability_envelope": 0.74
}

2. Coherence Gradient Cases#

Case 3 — Coherence Ridge Alignment (R1 ↔ R4)#

Scenario
Conceptual and dimensional coherence gradients align, forming a coherence ridge.

CTE Output

{
  "regime": "R1-R4",
  "gradient_magnitude": 0.83,
  "gradient_direction": "R1↔R4",
  "coherence_curvature": 0.52,
  "drift_sensitivity": 0.18,
  "stability_envelope": 0.79
}

Case 4 — Drift‑Sensitive Coherence Gradient (R2 ↔ R3)#

Scenario
Computational drift influences physical coherence gradients.

CTE Output

{
  "regime": "R2-R3",
  "gradient_magnitude": 0.81,
  "gradient_direction": "R3→R2",
  "coherence_curvature": 0.57,
  "drift_sensitivity": 0.44,
  "stability_envelope": 0.63
}

3. Boundary Gradient Cases#

Case 5 — Abstraction‑Measurement Gradient (R1 → R3)#

Scenario
Coherence forms at the boundary between conceptual abstraction and physical measurement.

CTE Output

{
  "regime": "R1-R3",
  "gradient_magnitude": 0.69,
  "gradient_direction": "R1→R3",
  "coherence_curvature": 0.38,
  "drift_sensitivity": 0.22,
  "stability_envelope": 0.71
}

Case 6 — Gradient‑Boundary Alignment (R2 ↔ R4)#

Scenario
Aligned gradients across computational and dimensional regimes produce boundary coherence.

CTE Output

{
  "regime": "R2-R4",
  "gradient_magnitude": 0.88,
  "gradient_direction": "R2↔R4",
  "coherence_curvature": 0.47,
  "drift_sensitivity": 0.33,
  "stability_envelope": 0.68
}

4. Tensor‑Field Gradient Cases#

Case 7 — Multi‑Regime Gradient Tensor (R1 ↔ R2 ↔ R3)#

Scenario
A multi‑regime coherence tensor binds conceptual, computational, and physical coherence gradients.

CTE Output

{
  "regime": "R1-R2-R3",
  "gradient_magnitude": 0.94,
  "gradient_direction": "tensor",
  "coherence_curvature": 0.63,
  "drift_sensitivity": 0.29,
  "stability_envelope": 0.84
}

Case 8 — Dimensional Tensor Gradient (R2 ↔ R4)#

Scenario
Dimensional tensors constrain computational coherence gradients.

CTE Output

{
  "regime": "R2-R4",
  "gradient_magnitude": 0.88,
  "gradient_direction": "R4→R2",
  "coherence_curvature": 0.55,
  "drift_sensitivity": 0.37,
  "stability_envelope": 0.73
}

5. Collapse‑Point Gradient Cases#

Case 9 — Collapse Basin Gradient (R3 → R4)#

Scenario
Physical drift amplifies dimensional coherence curvature, forming a collapse basin.

CTE Output

{
  "regime": "R3-R4",
  "gradient_magnitude": 0.91,
  "gradient_direction": "R3→R4",
  "coherence_curvature": 0.71,
  "drift_sensitivity": 0.52,
  "stability_envelope": 0.44,
  "collapse_point": "R4:0.82"
}

Case 10 — Collapse Ridge Gradient (R2 ↔ R3)#

Scenario
Computational drift reduces coherence while physical drift increases coherence sensitivity.

CTE Output

{
  "regime": "R2-R3",
  "gradient_magnitude": 0.86,
  "gradient_direction": "R2↔R3",
  "coherence_curvature": 0.62,
  "drift_sensitivity": 0.49,
  "stability_envelope": 0.48,
  "collapse_point": "R3:0.77"
}

6. Canonical CTE Gradient Snippet#

{
  "regime": "R1-R4",
  "gradient_magnitude": 0.83,
  "gradient_direction": "R1↔R4",
  "coherence_curvature": 0.52,
  "drift_sensitivity": 0.18,
  "stability_envelope": 0.79
}

Status#

• Version: 1.0
• Status: canon‑stable
• Category: rtt‑structural
• Module Path: /docs/rtt/Coherence_Tensor_Engine/ # Coherence Tensor Engine (CTE) — RTT/1

Coherence‑Level Intelligence Engine for TriadicFrameworks#

The Coherence Tensor Engine (CTE) is the RTT/1 engine responsible for computing, mapping, and stabilizing coherence tensors across conceptual, computational, physical, and dimensional regimes.
It forms the coherence‑level foundation of the expanded RTT intelligence stack, directly above paradox‑level engines and directly below drift‑level engines.

CTE models coherence as a tensor field with:

• magnitude
• direction
• curvature
• collapse points
• multi‑regime gradients
• stability envelopes

CTE provides coherence‑layer intelligence for all higher‑order RTT engines.

1. Canonical Role#

CTE defines the coherence‑layer topology by:

• computing coherence tensors
• mapping coherence fields
• measuring coherence gradients
• detecting coherence collapse points
• identifying coherence ridges and wells
• evaluating tensor curvature
• stabilizing coherence envelopes
• supporting drift‑level engines
• anchoring structural engines
• feeding temporal, causal, and resonance engines

CTE is the third layer of the expanded RTT intelligence stack.

2. RTT Flags#

These flags define the engine’s operational grammar.

3. Coherence Tensor Types#

CTE identifies several canonical tensor classes:

3.1 Structural Coherence Tensor#

Coherence arising from structural constraints or invariants.

3.2 Gradient Coherence Tensor#

Coherence shaped by directional gradients across regimes.

3.3 Boundary Coherence Tensor#

Coherence formed at regime boundaries.

3.4 Tensor‑Field Coherence#

Full multi‑regime tensor binding across R1–R4.

3.5 Drift‑Sensitive Coherence Tensor#

Coherence influenced by drift curvature or drift amplification.

4. Core Operators#

These operators form the canonical CTE grammar.

5. Analyzer Layer#

CTE operates in the coherence layer, with sub‑layers:

• tensor‑computation
• coherence‑field‑mapping
• gradient‑analysis
• collapse‑detection
• structural‑coherence‑evaluation

This layer feeds directly into DS, SFD, SBC, TRS‑Temporal, CW, and DRS.

6. Coherence Tensor Matrix#

CTE produces a coherence tensor matrix, typically stored in:

coherence_tensor_matrix.json

Matrix fields include:

• tensor_type
• regime
• tensor_magnitude
• tensor_direction
• coherence_curvature
• collapse_point
• stability_envelope
• gradient_alignment

This matrix is consumed by drift, stability, temporal, causal, and resonance engines.

7. Canonical Workflow#

Step 1 — Compute#

Calculate coherence tensors across regimes.

Step 2 — Map#

Generate coherence field maps and tensor topology.

Step 3 — Analyze#

Measure curvature, gradient alignment, and stability envelopes.

Step 4 — Detect#

Identify collapse points and instability basins.

Step 5 — Stabilize#

Propose coherence stabilization pathways.

Step 6 — Export#

Write results to the coherence tensor matrix and operator outputs.

8. AI‑Ready Design#

CTE is fully AI‑ready:

• deterministic operator grammar
• coherence‑layer analyzer structure
• stable RTT flags
• canonical file layout
• zero‑drift reasoning constraints
• structural paradox handling
• bounded drift envelope
• declared coherence tensor

AI systems use CTE to:

• compute coherence tensors
• generate coherence field maps
• classify coherence gradients
• detect coherence collapse
• support higher‑order RTT engines

9. Position in the RTT Stack#

Regime Interlock Mapper (RIM)
      ↓
Triadic Regime Synthesizer (TRS)
      ↓
Paradox Gradient Analyzer (PGA)
      ↓
Coherence Tensor Engine (CTE)
      ↓
Drift Sentinel (DS)
      ↓
Structural Faultline Detector (SFD)
      ↓
Stability Basin Cartographer (SBC)
      ↓
Temporal Regime Sequencer (TRS‑Temporal)
      ↓
Cross‑Domain Causality Weaver (CW)
      ↓
Dimensional Resonance Scanner (DRS)

CTE is the coherence‑level intelligence layer, directly above paradox‑level analysis.

10. Status#

• Version: 1.0
• Status: canon‑stable
• Category: rtt‑structural
• Module Path: /docs/rtt/Coherence_Tensor_Engine/ # Coherence Tensor Profiles — RTT/1

Profile Dictionary for the Coherence Tensor Engine (CTE)#

Coherence tensor profiles define the canonical shapes, behaviors, stability envelopes, and collapse geometries of coherence tensors across conceptual, computational, physical, and dimensional regimes.

These profiles are used by:

• CTE‑Compute
• CTE‑Tensor
• CTE‑Gradient
• CTE‑Field
• CTE‑Collapse
• CTE‑Stabilize

Each profile includes:

• definition
• tensor signature
• field behavior
• gradient behavior
• collapse geometry
• stability envelope
• canonical CTE output pattern

1. Structural Coherence Profiles#

Profile: Structural Invariant Tensor#

Definition
Coherence arising from structural invariants (symmetry, conservation, monotonicity).

Tensor Signature

• medium‑high magnitude
• stable direction
• low curvature

Field Behavior

• narrow field
• shallow coherence ridge

Gradient Behavior

• low drift sensitivity
• high alignment

Collapse Geometry

• no collapse point
• rigid boundary

Stability Envelope

• high stability

Profile: Structural Constraint Tensor#

Definition
Coherence enforced by computational or physical constraints.

Tensor Signature

• medium magnitude
• constraint‑aligned direction
• medium curvature

Field Behavior

• moderate field width
• constraint ridge

Gradient Behavior

• medium drift sensitivity

Collapse Geometry

• shallow collapse basin

Stability Envelope

• medium‑high stability

2. Gradient Coherence Profiles#

Profile: Coherence Gradient Alignment#

Definition
Coherence gradients across regimes align, forming a coherence ridge.

Tensor Signature

• high magnitude
• bidirectional vector
• medium curvature

Field Behavior

• wide field
• ridge formation

Gradient Behavior

• high alignment
• medium drift sensitivity

Collapse Geometry

• no collapse point

Stability Envelope

• high stability

Profile: Drift‑Sensitive Coherence Gradient#

Definition
Drift curvature influences coherence gradients.

Tensor Signature

• medium‑high magnitude
• drift‑aligned direction
• high curvature

Field Behavior

• medium‑wide field
• drift ridge

Gradient Behavior

• high drift sensitivity

Collapse Geometry

• medium collapse basin

Stability Envelope

• medium stability

3. Boundary Coherence Profiles#

Profile: Abstraction‑Boundary Tensor#

Definition
Coherence forms at the boundary between conceptual abstraction and physical measurement.

Tensor Signature

• medium magnitude
• abstraction → measurement direction
• medium curvature

Field Behavior

• narrow field
• boundary ridge

Gradient Behavior

• medium alignment

Collapse Geometry

• shallow basin

Stability Envelope

• medium‑high stability

Profile: Gradient‑Boundary Tensor#

Definition
Aligned gradients across regimes produce boundary coherence.

Tensor Signature

• high magnitude
• aligned direction
• medium curvature

Field Behavior

• wide field
• alignment ridge

Gradient Behavior

• high alignment

Collapse Geometry

• medium‑deep basin

Stability Envelope

• medium stability

4. Tensor‑Field Coherence Profiles#

Profile: Multi‑Regime Coherence Tensor#

Definition
A multi‑regime tensor binds coherence across R1–R3 or R1–R4.

Tensor Signature

• very high magnitude
• tensor direction
• high curvature

Field Behavior

• wide field
• tensor topology

Gradient Behavior

• high alignment
• medium drift sensitivity

Collapse Geometry

• deep basin

Stability Envelope

• high stability

Profile: Dimensional Tensor Constraint#

Definition
Dimensional tensors constrain computational coherence pathways.

Tensor Signature

• high magnitude
• dimensional → computational direction
• medium‑high curvature

Field Behavior

• medium‑wide field
• tensor trough

Gradient Behavior

• medium alignment

Collapse Geometry

• medium‑deep basin

Stability Envelope

• medium‑high stability

5. Collapse‑Point Coherence Profiles#

Profile: Coherence Collapse Basin#

Definition
Drift amplification creates a coherence collapse basin.

Tensor Signature

• very high magnitude
• drift‑aligned direction
• high curvature

Field Behavior

• wide field
• collapse basin

Gradient Behavior

• high drift sensitivity

Collapse Geometry

• deep collapse basin
• instability ridge

Stability Envelope

• low stability

Profile: Coherence Collapse Ridge#

Definition
Coherence decreases in one regime while sensitivity increases in another.

Tensor Signature

• medium‑high magnitude
• inversion direction
• medium‑high curvature

Field Behavior

• medium field
• collapse ridge

Gradient Behavior

• medium drift sensitivity

Collapse Geometry

• medium‑deep basin

Stability Envelope

• medium stability

6. Canonical CTE Output Pattern#

{
  "tensor_type": "gradient",
  "regime": "R1-R4",
  "tensor_magnitude": 0.83,
  "tensor_direction": "R1↔R4",
  "coherence_curvature": 0.52,
  "collapse_point": null,
  "stability_envelope": 0.79,
  "gradient_alignment": 0.88
}

Status#

• Version: 1.0
• Status: canon‑stable
• Category: rtt‑structural
• Module Path: /docs/rtt/Coherence_Tensor_Engine/ # Coherence Tensor Examples — RTT/1

Example Dictionary for the Coherence Tensor Engine (CTE)#

These examples illustrate how the Coherence Tensor Engine (CTE) computes coherence tensors, maps coherence fields, detects collapse points, evaluates stability envelopes, and analyzes multi‑regime coherence behavior.

Each example demonstrates one or more CTE operators:

• CTE‑Compute
• CTE‑Tensor
• CTE‑Gradient
• CTE‑Field
• CTE‑Collapse
• CTE‑Stabilize

Examples are grouped by tensor type.

1. Structural Coherence Tensor Examples#

Example 1 — Structural Invariant Tensor (R1 ↔ R2)#

Scenario
A conceptual invariant (symmetry) is preserved across computational structures, forming a stable coherence tensor.

CTE Output

{
  "tensor_type": "structural",
  "regime": "R1-R2",
  "tensor_magnitude": 0.78,
  "tensor_direction": "R1→R2",
  "coherence_curvature": 0.33,
  "collapse_point": null,
  "stability_envelope": 0.82,
  "gradient_alignment": 0.71
}

Example 2 — Structural Constraint Tensor (R2 ↔ R3)#

Scenario
A computational constraint enforces coherence across physical calibration.

CTE Output

{
  "tensor_type": "structural",
  "regime": "R2-R3",
  "tensor_magnitude": 0.74,
  "tensor_direction": "R2→R3",
  "coherence_curvature": 0.41,
  "collapse_point": null,
  "stability_envelope": 0.77,
  "gradient_alignment": 0.66
}

2. Gradient Coherence Tensor Examples#

Example 3 — Coherence Gradient Alignment (R1 ↔ R4)#

Scenario
Conceptual and dimensional coherence gradients align, forming a stable coherence ridge.

CTE Output

{
  "tensor_type": "gradient",
  "regime": "R1-R4",
  "tensor_magnitude": 0.83,
  "tensor_direction": "R1↔R4",
  "coherence_curvature": 0.52,
  "collapse_point": null,
  "stability_envelope": 0.79,
  "gradient_alignment": 0.88
}

Example 4 — Drift‑Sensitive Gradient Tensor (R2 ↔ R3)#

Scenario
Computational drift influences physical coherence gradients.

CTE Output

{
  "tensor_type": "gradient",
  "regime": "R2-R3",
  "tensor_magnitude": 0.81,
  "tensor_direction": "R3→R2",
  "coherence_curvature": 0.57,
  "collapse_point": null,
  "stability_envelope": 0.63,
  "gradient_alignment": 0.72
}

3. Boundary Coherence Tensor Examples#

Example 5 — Abstraction‑Boundary Tensor (R1 ↔ R3)#

Scenario
Coherence forms at the boundary between conceptual abstraction and physical measurement.

CTE Output

{
  "tensor_type": "boundary",
  "regime": "R1-R3",
  "tensor_magnitude": 0.69,
  "tensor_direction": "R1→R3",
  "coherence_curvature": 0.38,
  "collapse_point": null,
  "stability_envelope": 0.71,
  "gradient_alignment": 0.55
}

Example 6 — Gradient‑Boundary Tensor (R2 ↔ R4)#

Scenario
Aligned gradients across computational and dimensional regimes produce a boundary coherence tensor.

CTE Output

{
  "tensor_type": "boundary",
  "regime": "R2-R4",
  "tensor_magnitude": 0.88,
  "tensor_direction": "R2↔R4",
  "coherence_curvature": 0.47,
  "collapse_point": null,
  "stability_envelope": 0.68,
  "gradient_alignment": 0.81
}

4. Tensor‑Field Coherence Examples#

Example 7 — Multi‑Regime Coherence Tensor (R1 ↔ R2 ↔ R3)#

Scenario
A multi‑regime coherence tensor binds conceptual, computational, and physical coherence.

CTE Output

{
  "tensor_type": "tensor-field",
  "regime": "R1-R2-R3",
  "tensor_magnitude": 0.94,
  "tensor_direction": "tensor",
  "coherence_curvature": 0.63,
  "collapse_point": null,
  "stability_envelope": 0.84,
  "gradient_alignment": 0.92
}

Example 8 — Dimensional Tensor Constraint (R2 ↔ R4)#

Scenario
Dimensional tensors constrain computational coherence pathways.

CTE Output

{
  "tensor_type": "tensor-field",
  "regime": "R2-R4",
  "tensor_magnitude": 0.88,
  "tensor_direction": "R4→R2",
  "coherence_curvature": 0.55,
  "collapse_point": null,
  "stability_envelope": 0.73,
  "gradient_alignment": 0.79
}

5. Collapse‑Point Examples#

Example 9 — Coherence Collapse Basin (R3 ↔ R4)#

Scenario
Physical drift amplifies dimensional coherence curvature, forming a collapse basin.

CTE Output

{
  "tensor_type": "collapse",
  "regime": "R3-R4",
  "tensor_magnitude": 0.91,
  "tensor_direction": "R3→R4",
  "coherence_curvature": 0.71,
  "collapse_point": "R4:0.82",
  "stability_envelope": 0.44,
  "gradient_alignment": 0.63
}

Example 10 — Coherence Collapse Ridge (R2 ↔ R3)#

Scenario
Computational drift reduces coherence while physical drift increases coherence sensitivity.

CTE Output

{
  "tensor_type": "collapse",
  "regime": "R2-R3",
  "tensor_magnitude": 0.86,
  "tensor_direction": "R2↔R3",
  "coherence_curvature": 0.62,
  "collapse_point": "R3:0.77",
  "stability_envelope": 0.48,
  "gradient_alignment": 0.71
}

6. Example Matrix Snippet#

{
  "tensor_type": "gradient",
  "regime": "R1-R4",
  "tensor_magnitude": 0.83,
  "tensor_direction": "R1↔R4",
  "coherence_curvature": 0.52,
  "collapse_point": null,
  "stability_envelope": 0.79,
  "gradient_alignment": 0.88
}

Status#

• Version: 1.0
• Status: canon‑stable
• Category: rtt‑structural
• Module Path: /docs/rtt/Coherence_Tensor_Engine/ # CTE Operators — RTT/1

Operator Grammar for the Coherence Tensor Engine#

The Coherence Tensor Engine (CTE) defines the coherence‑layer intelligence of RTT.
Its operators compute coherence tensors, map coherence fields, evaluate gradients, detect collapse points, and propose stabilization pathways.

These operators feed directly into:

• DS — Drift Sentinel
• SFD — Structural Faultline Detector
• SBC — Stability Basin Cartographer
• TRS‑Temporal — Temporal Regime Sequencer
• CW — Cross‑Domain Causality Weaver
• DRS — Dimensional Resonance Scanner

1. CTE‑Compute#

Compute coherence tensors from regime inputs#

Purpose
Generate coherence tensors by evaluating structural, gradient, boundary, and drift‑sensitive coherence conditions.

Capabilities

• computes tensor magnitude
• computes tensor direction
• evaluates structural invariants
• evaluates coherence dependencies
• evaluates drift influence

Output Fields

• tensor_type
• tensor_magnitude
• tensor_direction
• coherence_dependency

2. CTE‑Tensor#

Construct multi‑dimensional coherence tensor structures#

Purpose
Build coherence tensors across conceptual, computational, physical, and dimensional regimes.

Capabilities

• constructs multi‑regime tensors
• binds coherence across R1–R4
• evaluates tensor curvature
• evaluates tensor alignment
• evaluates tensor stability

Output Fields

• tensor_structure
• tensor_curvature
• tensor_alignment
• tensor_stability

3. CTE‑Gradient#

Compute coherence gradient vectors#

Purpose
Calculate coherence gradient magnitude, direction, curvature, and drift sensitivity.

Capabilities

• computes gradient magnitude
• computes gradient direction
• computes coherence curvature
• computes drift sensitivity
• computes tensor‑gradient alignment

Output Fields

• gradient_magnitude
• gradient_direction
• coherence_curvature
• drift_sensitivity
• gradient_alignment

4. CTE‑Field#

Map coherence fields and tensor topology#

Purpose
Generate coherence field maps showing curvature, ridges, wells, and tensor topology.

Capabilities

• maps coherence fields
• maps tensor topology
• maps coherence ridges
• maps coherence wells
• maps gradient flows

Output Fields

• field_map
• tensor_topology
• ridge_map
• well_map
• gradient_flow_map

5. CTE‑Collapse#

Detect coherence collapse points and instability basins#

Purpose
Identify collapse points, instability basins, and coherence troughs.

Capabilities

• detects collapse points
• detects instability basins
• detects coherence troughs
• evaluates collapse curvature
• evaluates collapse depth

Output Fields

• collapse_point
• collapse_depth
• collapse_curvature
• instability_basin

6. CTE‑Stabilize#

Propose coherence stabilization pathways#

Purpose
Provide stabilization strategies for coherence tensors, gradients, and collapse points.

Capabilities

• proposes stabilization pathways
• proposes coherence alignment
• proposes drift reduction
• proposes tensor rebalancing
• proposes collapse mitigation

Output Fields

• stabilization_pathway
• coherence_alignment
• drift_reduction
• tensor_rebalance
• collapse_mitigation

7. Operator Interaction Grammar#

Compute → Tensor → Gradient → Field → Collapse → Stabilize#

1. CTE‑Compute
   Generates coherence tensors from regime inputs.

2. CTE‑Tensor
   Builds multi‑regime tensor structures.

3. CTE‑Gradient
   Computes coherence gradient vectors and curvature.

4. CTE‑Field
   Maps coherence fields, ridges, wells, and tensor topology.

5. CTE‑Collapse
   Detects collapse points and instability basins.

6. CTE‑Stabilize
   Produces stabilization pathways and coherence alignment strategies.

This grammar ensures deterministic coherence‑layer behavior.

8. Operator Matrix Snippet#

{
  "operator": "CTE-Gradient",
  "gradient_magnitude": 0.83,
  "gradient_direction": "R1↔R4",
  "coherence_curvature": 0.52,
  "drift_sensitivity": 0.18,
  "gradient_alignment": 0.88
}

Status#

• Version: 1.0
• Status: canon‑stable
• Category: rtt‑structural
• Module Path: /docs/rtt/Coherence_Tensor_Engine/ # CTE Prompts — RTT/1

Prompt Library for the Coherence Tensor Engine#

These prompts are designed for AI systems using the Coherence Tensor Engine (CTE).
Each prompt invokes one or more canonical CTE operators:

• CTE‑Compute
• CTE‑Tensor
• CTE‑Gradient
• CTE‑Field
• CTE‑Collapse
• CTE‑Stabilize

Prompts are grouped by tensor type and operator class.

1. Structural Coherence Prompts#

Prompt: Detect Structural Coherence Tensors#

Use CTE‑Compute to identify structural coherence tensors formed by invariants, constraints, or monotonicity rules across R1–R3.

Prompt: Map Structural Coherence Fields#

Apply CTE‑Field to generate structural coherence field maps showing curvature, ridge formation, and stability envelopes.

Prompt: Compute Structural Coherence Gradients#

Use CTE‑Gradient to compute gradient magnitude, direction, and drift sensitivity for structural coherence tensors.

2. Gradient Coherence Prompts#

Prompt: Identify Coherence Gradient Alignment#

Use CTE‑Tensor to detect coherence gradients that align across regimes, forming coherence ridges or multi‑regime coherence pathways.

Prompt: Compute Coherence Gradient Vectors#

Apply CTE‑Gradient to compute coherence gradient vectors, including magnitude, direction, curvature, and alignment.

Prompt: Analyze Gradient Stability#

Use CTE‑Stabilize to evaluate stability envelopes for coherence gradients and propose stabilization pathways.

3. Boundary Coherence Prompts#

Prompt: Detect Boundary Coherence Conditions#

Use CTE‑Compute to identify coherence tensors formed at regime boundaries, including abstraction‑measurement and gradient‑boundary interactions.

Prompt: Map Boundary Coherence Curvature#

Apply CTE‑Field to generate boundary coherence curvature maps showing ridge formation and collapse‑point onset.

Prompt: Evaluate Boundary Stability#

Use CTE‑Stabilize to compute stability envelopes for boundary coherence tensors.

4. Tensor‑Field Coherence Prompts#

Prompt: Detect Multi‑Regime Coherence Tensors#

Use CTE‑Tensor to identify multi‑regime coherence tensors binding R1–R3 or R1–R4.

Prompt: Map Tensor‑Field Topology#

Apply CTE‑Field to generate tensor‑field topology diagrams showing coherence wells, ridges, and multi‑regime curvature.

Prompt: Compute Tensor‑Field Gradient Strength#

Use CTE‑Gradient to compute tensor gradient magnitude, direction, and coherence curvature.

5. Drift‑Sensitive Coherence Prompts#

Prompt: Identify Drift‑Sensitive Coherence Tensors#

Use CTE‑Compute to detect coherence tensors influenced by drift curvature or drift amplification.

Prompt: Map Drift‑Sensitive Coherence Basins#

Apply CTE‑Field to generate drift‑sensitive coherence basin maps showing instability ridges and collapse‑point formation.

Prompt: Analyze Drift‑Coherence Stability#

Use CTE‑Stabilize to compute stability envelopes for drift‑sensitive coherence tensors.

6. Collapse‑Point Prompts#

Prompt: Detect Coherence Collapse Points#

Use CTE‑Collapse to identify coherence collapse points and instability basins across R2–R4.

Prompt: Map Collapse Basin Geometry#

Apply CTE‑Field to generate collapse basin topology showing curvature, depth, and coherence troughs.

Prompt: Propose Collapse Stabilization Pathways#

Use CTE‑Stabilize to propose stabilization strategies for collapse‑point coherence tensors.

7. Full‑Matrix Prompts#

Prompt: Generate Full Coherence Tensor Matrix#

Use all CTE operators to produce a complete coherence_tensor_matrix.json containing structural, gradient, boundary, tensor‑field, drift‑sensitive, and collapse‑point entries.

Prompt: Analyze Coherence Field Topology#

Apply CTE‑Field to generate a full coherence topology map showing fields, basins, curvature, and gradient flows.

Prompt: Stability Overview#

Use CTE‑Stabilize to compute stability envelopes for every coherence tensor type and produce a coherence stability summary.

8. AI‑Ready Meta‑Prompts#

Prompt: Explain Coherence Tensor Classification#

Provide a detailed explanation of how CTE classifies coherence tensors into structural, gradient, boundary, tensor‑field, drift‑sensitive, and collapse‑point categories.

Prompt: Operator‑Level Summary#

Summarize the role of each CTE operator and how they interact to produce coherence‑layer intelligence.

Prompt: Cross‑Engine Integration#

Explain how CTE outputs feed into DS, SFD, SBC, TRS‑Temporal, CW, and DRS.

Status#

• Version: 1.0
• Status: canon‑stable
• Category: rtt‑structural
• Module Path: /docs/rtt/Coherence_Tensor_Engine/