proffesor-for-testing__agentic-qe/docs/implementation/specs/SPEC-030-A-lambda-calculation.md

SPEC-030-A: Quality Lambda Calculation

Field	Value
Specification ID	SPEC-030-A
Parent ADR	ADR-030
Version	1.0
Status	Accepted
Last Updated	2026-01-10
Author	Architecture Team

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Overview

This specification defines the Quality Lambda calculation algorithm, which determines the "minimum cut" coherence signal across multiple quality dimensions.

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Quality Lambda Structure

export interface QualityLambda {
  /** Current lambda value (0-100 scale) */
  lambda: number;

  /** Previous lambda value for delta calculation */
  lambdaPrev: number;

  /** Number of quality dimensions at boundary (unstable) */
  boundaryEdges: number;

  /** Concentration of instability (Q15: 0-32767) */
  boundaryConcentrationQ15: number;

  /** Number of quality partitions (fragmented quality) */
  partitionCount: number;

  /** Control flags */
  flags: number;
}

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Lambda Calculation Algorithm

export function calculateQualityLambda(metrics: QualityMetrics): QualityLambda {
  // Normalize each metric to 0-1 scale
  const normalized = {
    coverage: metrics.lineCoverage / 100,
    passRate: metrics.testPassRate / 100,
    security: 1 - Math.min(metrics.criticalVulns / 5, 1),
    performance: Math.min(metrics.p95Latency / metrics.targetLatency, 1),
    maintainability: metrics.maintainabilityIndex / 100,
    reliability: 1 - (metrics.flakyTestRatio || 0),
  };

  // Find minimum "cut" - the weakest quality dimension
  const values = Object.values(normalized);
  const lambda = Math.min(...values) * 100;

  // Count boundary edges (dimensions near threshold)
  const threshold = 0.7;
  const boundaryEdges = values.filter(
    v => v < threshold + 0.1 && v >= threshold - 0.1
  ).length;

  // Calculate concentration (Q15 fixed-point)
  const belowThreshold = values.filter(v => v < threshold);
  const concentrationQ15 = belowThreshold.length > 0
    ? Math.round((belowThreshold.reduce((a, b) => a + b, 0) / belowThreshold.length) * 32767)
    : 32767;

  // Count quality partitions (clusters of related issues)
  const partitionCount = countQualityPartitions(metrics);

  return {
    lambda,
    lambdaPrev: metrics.previousLambda || lambda,
    boundaryEdges,
    boundaryConcentrationQ15: concentrationQ15,
    partitionCount,
    flags: 0,
  };
}

function countQualityPartitions(metrics: QualityMetrics): number {
  // Group related quality issues into partitions
  let partitions = 0;

  if (metrics.lineCoverage < 70 || metrics.branchCoverage < 60) partitions++;
  if (metrics.criticalVulns > 0 || metrics.highVulns > 2) partitions++;
  if (metrics.testPassRate < 95 || metrics.flakyTestRatio > 0.05) partitions++;
  if (metrics.maintainabilityIndex < 60) partitions++;

  return partitions;
}

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Quality Dimensions

Dimension	Source	Normalization
Coverage	Line coverage %	value / 100
Pass Rate	Test pass rate %	value / 100
Security	Critical vulns	1 - min(vulns/5, 1)
Performance	P95 latency	min(actual/target, 1)
Maintainability	Maintainability index	value / 100
Reliability	Flaky test ratio	1 - ratio

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Validation Rules

Rule ID	Description	Severity
SPEC-030-A-001	Lambda must be 0-100 scale	Error
SPEC-030-A-002	At least 4 quality dimensions required	Warning
SPEC-030-A-003	BoundaryConcentrationQ15 must be 0-32767	Error

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Changelog

Version	Date	Author	Changes
1.0	2026-01-10	Architecture Team	Initial specification

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References

• Parent ADR
• ruvector-mincut-gated-transformer