Coherence Tensor Examples — RTT/1

Example Dictionary for the Coherence Tensor Engine (CTE)#

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 20, 2026