Interpreting Certificates

Interpreting Certificates

Quick-Scan Infobox

Aspect	Details
Target user	Engineers and educators interpreting routing decisions
Core goal	Map certificate fields to actionable interpretation
Time to first insight	5 minutes: read, compare to one run
Known limitation	Ranges are typical, not absolute; tune to your data

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Key Signals and How to Read Them

• Utility (scalar): 0.5–0.9 typical. Lower values can indicate tight constraints or a novel/off‑manifold prompt. Compare relative changes across runs.
• Boundary gap (preference separation): >0.15 clear preference; <0.05 ambiguous. See Math-Boundary-Gap-and-Entropy.
• Entropy (decision spread): lower → concentrated preference; higher → diffuse confidence. Interpret alongside gap.
• Shadow prices (constraint sensitivity): near 0 → not limiting; >0.5 → limiting utility. Focus remediation where largest.
• Feasibility and slack: negative slack pinpoints the violated/active constraint; investigate policy or bounds first.
• Drift (stability): small negative drift across iterations indicates stable improvement; large magnitude or positive values suggest instability.

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A Compact Flow

graph TD
  A[Certificate] --> B{Gap > 0.15?}
  B -- Yes --> C[Stable choice]
  B -- No --> D[Ambiguous]
  A --> E{Max shadow > 0.5?}
  E -- Yes --> F[Constraint-limited]
  E -- No --> G[Capacity available]
  A --> H{Utility < 0.6?}
  H -- Yes --> I[Recalibrate / Review data]
  H -- No --> J[Proceed]

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Caption: Decision aid for reading certificates. Alt text: Graph branching on gap, shadow prices, utility.

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Typical Actions by Signal

• High shadow price on one constraint (>0.5): review that bound; consider relaxing or revising policy.
• Multiple high shadow prices: multiple bottlenecks; adjust one at a time and track utility.
• Ambiguous boundary (gap <0.05): collect additional data near decision boundary or adjust temperature.
• Low utility despite feasibility: revisit metric calibration and prompt family; examine off‑manifold indicators.
• Increasing drift across trials: reduce trust region, check seeds, or pause batch changes.

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Where the Math Lives

• Boundary/entropy: see Math-Boundary-Gap-and-Entropy
• Constraint duals/shadow prices: see Math-Constraints-Duality-and-Shadow-Prices
• SPD metric and geometry: see Math-SPD-Metrics-and-Riemannian-Geometry
• Coherence and density: see Math-Kernel-Density-and-Coherence

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Practical Checklist

• Read gap + entropy first: confident vs ambiguous.
• Scan shadow prices: identify top constraint pressures.
• Confirm feasibility + slack: any violations?
• Track utility and drift across runs: trending in the right direction?
• Write down a single action: change one variable at a time.