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🧪 MSM Analyzer — Worked Examples

📘 Example 1 — Network System Entering Drift#

Input Vector#

{
  S: 0.58,
  D: 0.72,
  A: 0.41,
  N: 0.63,
  T: 0.47
}

Invariant Evaluation#

  • Signal–Narrative Coherence: 0.22
  • Distribution–Attention Fit: 0.18
  • Temporal–Signal Stability: 0.31
  • Attention–Narrative Feedback: 0.27

Moderate strain across multiple invariants indicates early instability.

Basin Classification#

  • Closest basin: Network
  • Gate conditions: Satisfied
  • Distance: 0.19

The system remains in the Network basin but is under pressure.

Mode Determination#

  • Drift magnitude: 0.14 (meso drift)
  • Dominant invariant: Temporal–Signal Stability
  • Mode: Tension

The system is beginning to destabilize but has not yet entered full drift.

Drift Detection#

  • Δ from previous vector: moderate
  • Category: meso drift

Transition Detection#

  • Previous: Network / Stable
  • Current: Network / Tension
  • Trigger: cadence acceleration
  • Severity: 0.42

The system is shifting toward Drift mode.

📙 Example 2 — Fragment System Collapsing into Cascade#

Input Vector#

{
  S: 0.29,
  D: 0.34,
  A: 0.88,
  N: 0.21,
  T: 0.91
}

Invariant Evaluation#

  • Signal–Narrative Coherence: 0.71
  • Distribution–Attention Fit: 0.83
  • Temporal–Signal Stability: 0.92
  • Attention–Narrative Feedback: 0.79

Multiple invariants are near or above collapse thresholds.

Basin Classification#

  • Closest basin: Cascade
  • Gate conditions: Satisfied
  • Distance: 0.11

The system has entered the Cascade attractor.

Mode Determination#

  • Drift magnitude: 0.37 (macro drift)
  • Dominant invariant: Temporal–Signal Stability
  • Mode: Cascade

The system is in a high‑energy, unstable state.

Drift Detection#

  • Δ from previous vector: large
  • Category: macro drift

Transition Detection#

  • Previous: Fragment / Drift
  • Current: Cascade / Cascade
  • Trigger: attention spike + cadence acceleration
  • Severity: 0.87

This is a high‑severity structural transition.

📗 Example 3 — Collapse Moving into Reconstruction#

Input Vector#

{
  S: 0.44,
  D: 0.39,
  A: 0.27,
  N: 0.36,
  T: 0.33
}

Invariant Evaluation#

  • Signal–Narrative Coherence: 0.41
  • Distribution–Attention Fit: 0.19
  • Temporal–Signal Stability: 0.22
  • Attention–Narrative Feedback: 0.28

Strain is decreasing across all invariants.

Basin Classification#

  • Closest basin: Reconstruction
  • Gate conditions: Satisfied
  • Distance: 0.17

The system is stabilizing and rebuilding.

Mode Determination#

  • Drift magnitude: 0.09 (micro drift)
  • Dominant invariant: Signal–Narrative Coherence
  • Mode: Reconstruction

The system is recovering from collapse.

Drift Detection#

  • Δ from previous vector: small
  • Category: micro drift

Transition Detection#

  • Previous: Collapse / Collapse
  • Current: Reconstruction / Reconstruction
  • Trigger: signal recovery + narrative stabilization
  • Severity: 0.33

A positive‑direction transition.

📕 Example 4 — Stagnation with Minimal Drift#

Input Vector#

{
  S: 0.31,
  D: 0.28,
  A: 0.12,
  N: 0.29,
  T: 0.14
}

Invariant Evaluation#

  • Signal–Narrative Coherence: 0.38
  • Distribution–Attention Fit: 0.09
  • Temporal–Signal Stability: 0.12
  • Attention–Narrative Feedback: 0.17

Low strain but also low energy.

Basin Classification#

  • Closest basin: Stagnation
  • Gate conditions: Satisfied
  • Distance: 0.13

Mode Determination#

  • Drift magnitude: 0.03 (micro drift)
  • Mode: Stable

The system is quiet, low‑energy, and structurally inert.

Drift Detection#

  • Category: micro drift

Transition Detection#

  • No transition detected
  • Trigger: none
  • Severity: 0.00

The system remains in Stagnation.

📓 Example 5 — Broadcast System Under Early Pressure#

Input Vector#

{
  S: 0.82,
  D: 0.91,
  A: 0.22,
  N: 0.87,
  T: 0.29
}

Invariant Evaluation#

  • Signal–Narrative Coherence: 0.08
  • Distribution–Attention Fit: 0.11
  • Temporal–Signal Stability: 0.14
  • Attention–Narrative Feedback: 0.09

Very low strain; system is stable.

Basin Classification#

  • Closest basin: Broadcast
  • Gate conditions: Satisfied
  • Distance: 0.07

Mode Determination#

  • Drift magnitude: 0.05
  • Mode: Stable

Drift Detection#

  • Category: micro drift

Transition Detection#

  • No transition
  • System remains stable

These examples give us a complete set of reference patterns for how the MSM Analyzer behaves across different structural conditions.

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