Causal Discontinuity Cases — RTT/1

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

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/

Updated Jul 20, 2026