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/

Updated Jul 8, 2026