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概要

Stability Basin Cartographer Examples — RTT/1

Example Dictionary for the Stability Basin Cartographer (SBC)#

These examples illustrate how the Stability Basin Cartographer (SBC) maps stability basins, computes basin gradients, identifies stability fields, detects collapse zones, and evaluates stability topology across R1–R4.

Each example demonstrates one or more SBC operators:

  • SBC‑Map
  • SBC‑Basin
  • SBC‑Gradient
  • SBC‑Field
  • SBC‑Collapse
  • SBC‑Stabilize

Examples are grouped by basin type.

1. Stability Basin Examples#

Example 1 — Conceptual Stability Basin (R1)#

Scenario
A conceptual model exhibits a stable region with low curvature and shallow collapse potential.

SBC Output

{
  "basin_type": "stability",
  "regime": "R1",
  "basin_magnitude": 0.41,
  "basin_direction": "conceptual",
  "basin_curvature": 0.22,
  "collapse_zone": 0.11,
  "stability_field": 0.63,
  "envelope_boundary": 0.44
}

Example 2 — Computational Stability Basin (R2)#

Scenario
A computational structure forms a stability basin with moderate curvature and medium collapse sensitivity.

SBC Output

{
  "basin_type": "stability",
  "regime": "R2",
  "basin_magnitude": 0.52,
  "basin_direction": "computational",
  "basin_curvature": 0.33,
  "collapse_zone": 0.27,
  "stability_field": 0.57,
  "envelope_boundary": 0.41
}

2. Gradient Basin Examples#

Example 3 — Gradient Basin Opposition (R1 ↔ R4)#

Scenario
Conceptual and dimensional gradients oppose each other, forming a gradient basin with high curvature.

SBC Output

{
  "basin_type": "gradient",
  "regime": "R1-R4",
  "basin_magnitude": 0.83,
  "basin_direction": "R1↔R4",
  "basin_curvature": 0.51,
  "collapse_zone": 0.22,
  "stability_field": 0.69,
  "envelope_boundary": 0.46
}

Example 4 — Gradient Inversion Basin (R2 ↔ R3)#

Scenario
Computational stability decreases while physical stability increases, forming a gradient inversion basin.

SBC Output

{
  "basin_type": "gradient",
  "regime": "R2-R3",
  "basin_magnitude": 0.79,
  "basin_direction": "R3→R2",
  "basin_curvature": 0.58,
  "collapse_zone": 0.31,
  "stability_field": 0.72,
  "envelope_boundary": 0.41
}

3. Boundary Basin Examples#

Example 5 — Abstraction‑Measurement Stability Basin (R1 ↔ R3)#

Scenario
Conceptual abstraction predicts behavior that contradicts physical measurement, forming a boundary stability basin.

SBC Output

{
  "basin_type": "boundary",
  "regime": "R1-R3",
  "basin_magnitude": 0.67,
  "basin_direction": "R1→R3",
  "basin_curvature": 0.33,
  "collapse_zone": 0.22,
  "stability_field": 0.55,
  "envelope_boundary": 0.38
}

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

Scenario
Aligned gradients across computational and dimensional regimes produce contradictory stability outcomes.

SBC Output

{
  "basin_type": "boundary",
  "regime": "R2-R4",
  "basin_magnitude": 0.88,
  "basin_direction": "R2↔R4",
  "basin_curvature": 0.47,
  "collapse_zone": 0.29,
  "stability_field": 0.66,
  "envelope_boundary": 0.58
}

4. Stability‑Field Examples#

Example 7 — Multi‑Regime Stability Field (R1 ↔ R2 ↔ R3)#

Scenario
A multi‑regime stability field binds conceptual, computational, and physical stability basins.

SBC Output

{
  "basin_type": "field",
  "regime": "R1-R2-R3",
  "basin_magnitude": 0.94,
  "basin_direction": "tensor",
  "basin_curvature": 0.63,
  "collapse_zone": 0.37,
  "stability_field": 0.78,
  "envelope_boundary": 0.57
}

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

Scenario
Dimensional constraints influence computational stability pathways.

SBC Output

{
  "basin_type": "field",
  "regime": "R2-R4",
  "basin_magnitude": 0.88,
  "basin_direction": "R4→R2",
  "basin_curvature": 0.55,
  "collapse_zone": 0.33,
  "stability_field": 0.73,
  "envelope_boundary": 0.63
}

5. Collapse‑Zone Examples#

Example 9 — Stability Collapse Basin (R3 → R4)#

Scenario
Physical stability collapses into dimensional instability, forming a collapse basin.

SBC Output

{
  "basin_type": "collapse",
  "regime": "R3-R4",
  "basin_magnitude": 0.91,
  "basin_direction": "R3→R4",
  "basin_curvature": 0.71,
  "collapse_zone": 0.52,
  "stability_field": 0.82,
  "envelope_boundary": 0.44
}

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

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

SBC Output

{
  "basin_type": "collapse",
  "regime": "R2-R3",
  "basin_magnitude": 0.86,
  "basin_direction": "R2↔R3",
  "basin_curvature": 0.62,
  "collapse_zone": 0.49,
  "stability_field": 0.77,
  "envelope_boundary": 0.48
}

6. Canonical SBC Output Snippet#

{
  "basin_type": "gradient",
  "regime": "R1-R4",
  "basin_magnitude": 0.83,
  "basin_direction": "R1↔R4",
  "basin_curvature": 0.51,
  "collapse_zone": 0.22,
  "stability_field": 0.69,
  "envelope_boundary": 0.46
}

Status#

  • Version: 1.0
  • Status: canon‑stable
  • Category: rtt‑stability
  • Module Path: /docs/rtt/Stability_Basin_Cartographer/

Updated

提供： Docsbook