Causal Discontinuity Cases — RTT/1

Case Studies for the Cross‑Domain Causality Weaver (CW)#

Causal discontinuities represent breaks in causal flow, polarity inversions, discontinuity boundaries, causal fractures, and cross‑domain causal collapse across conceptual, computational, physical, and dimensional regimes.

These case studies illustrate how the Cross‑Domain Causality Weaver (CW) evaluates:

• causal magnitude
• causal direction
• causal curvature
• discontinuity depth
• propagation rate
• stability envelope
• causal‑fracture geometry

Each case demonstrates one or more CW operators:

• CW‑Signature
• CW‑Vector
• CW‑Field
• CW‑Discontinuity
• CW‑Weave
• CW‑Stabilize

1. Conceptual Discontinuity Cases#

Case 1 — Conceptual Causal Break (R1)#

Scenario
A conceptual model loses coherence, forming a shallow causal discontinuity.

CW Output

{
  "regime": "R1",
  "causal_magnitude": 0.41,
  "causal_direction": "conceptual",
  "causal_curvature": 0.22,
  "discontinuity_depth": 0.11,
  "propagation_rate": 0.33,
  "stability_envelope": 0.63
}

Case 2 — Conceptual‑Dimensional Discontinuity (R1 ↔ R4)#

Scenario
Conceptual causality collapses under dimensional polarity pressure.

CW Output

{
  "regime": "R1-R4",
  "causal_magnitude": 0.83,
  "causal_direction": "R1↔R4",
  "causal_curvature": 0.52,
  "discontinuity_depth": 0.22,
  "propagation_rate": 0.33,
  "stability_envelope": 0.69
}

2. Computational Discontinuity Cases#

Case 3 — Computational Causal Break (R2)#

Scenario
A computational structure becomes unstable due to calibration drift, forming a causal fracture.

CW Output

{
  "regime": "R2",
  "causal_magnitude": 0.52,
  "causal_direction": "computational",
  "causal_curvature": 0.33,
  "discontinuity_depth": 0.27,
  "propagation_rate": 0.27,
  "stability_envelope": 0.57
}

Case 4 — Computational‑Physical Discontinuity (R2 ↔ R3)#

Scenario
Computational causality collapses under physical measurement sensitivity.

CW Output

{
  "regime": "R2-R3",
  "causal_magnitude": 0.79,
  "causal_direction": "R3→R2",
  "causal_curvature": 0.58,
  "discontinuity_depth": 0.31,
  "propagation_rate": 0.27,
  "stability_envelope": 0.72
}

3. Boundary Discontinuity Cases#

Case 5 — Abstraction‑Measurement Causal Discontinuity (R1 ↔ R3)#

Scenario
Conceptual abstraction contradicts physical measurement, forming a causal discontinuity boundary.

CW Output

{
  "regime": "R1-R3",
  "causal_magnitude": 0.67,
  "causal_direction": "R1→R3",
  "causal_curvature": 0.33,
  "discontinuity_depth": 0.22,
  "propagation_rate": 0.38,
  "stability_envelope": 0.55
}

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

Scenario
Aligned gradients across computational and dimensional regimes collapse into causal instability.

CW Output

{
  "regime": "R2-R4",
  "causal_magnitude": 0.88,
  "causal_direction": "R2↔R4",
  "causal_curvature": 0.47,
  "discontinuity_depth": 0.29,
  "propagation_rate": 0.33,
  "stability_envelope": 0.66
}

4. Causal‑Field Discontinuity Cases#

Case 7 — Multi‑Regime Causal Field Collapse (R1 ↔ R2 ↔ R3)#

Scenario
A multi‑regime causal field collapses under tensor‑level instability.

CW Output

{
  "regime": "R1-R2-R3",
  "causal_magnitude": 0.94,
  "causal_direction": "tensor",
  "causal_curvature": 0.63,
  "discontinuity_depth": 0.37,
  "propagation_rate": 0.41,
  "stability_envelope": 0.78
}

Case 8 — Dimensional Causal Collapse (R2 ↔ R4)#

Scenario
Dimensional constraints collapse computational causal pathways.

CW Output

{
  "regime": "R2-R4",
  "causal_magnitude": 0.88,
  "causal_direction": "R4→R2",
  "causal_curvature": 0.55,
  "discontinuity_depth": 0.33,
  "propagation_rate": 0.29,
  "stability_envelope": 0.73
}

5. Drift‑Sensitive Discontinuity Cases#

Case 9 — Drift‑Amplified Causal Discontinuity (R3 → R4)#

Scenario
Physical drift amplifies causal curvature, forming a drift‑sensitive discontinuity.

CW Output

{
  "regime": "R3-R4",
  "causal_magnitude": 0.91,
  "causal_direction": "R3→R4",
  "causal_curvature": 0.71,
  "discontinuity_depth": 0.52,
  "propagation_rate": 0.44,
  "stability_envelope": 0.82
}

Case 10 — Stability‑Coherence Causal Ridge (R2 ↔ R3)#

Scenario
Computational stability reduces coherence while physical stability increases coherence sensitivity, forming a causal ridge.

CW Output

{
  "regime": "R2-R3",
  "causal_magnitude": 0.86,
  "causal_direction": "R2↔R3",
  "causal_curvature": 0.62,
  "discontinuity_depth": 0.49,
  "propagation_rate": 0.48,
  "stability_envelope": 0.77
}

6. Canonical CW Discontinuity Snippet#

{
  "regime": "R1-R4",
  "causal_magnitude": 0.83,
  "causal_direction": "R1↔R4",
  "causal_curvature": 0.52,
  "discontinuity_depth": 0.22,
  "propagation_rate": 0.33,
  "stability_envelope": 0.69
}

Status#

• Version: 1.0
• Status: canon‑stable
• Category: rtt‑causality
• Module Path: /docs/rtt/Cross_Domain_Causality_Weaver/