feat(ultraplan-local): v1.6.0 — /ultraresearch-local deep research command

Add /ultraresearch-local for structured research combining local codebase
analysis with external knowledge via parallel agent swarms. Produces research
briefs with triangulation, confidence ratings, and source quality assessment.

New command: /ultraresearch-local with modes --quick, --local, --external, --fg.
New agents: research-orchestrator (opus), docs-researcher, community-researcher,
security-researcher, contrarian-researcher, gemini-bridge (all sonnet).
New template: research-brief-template.md.

Integration: --research flag in /ultraplan-local accepts pre-built research
briefs (up to 3), enriches the interview and exploration phases. Planning
orchestrator cross-references brief findings during synthesis.

Design principle: Context Engineering — right information to right agent at
right time. Research briefs are structured artifacts in the pipeline:
ultraresearch → brief → ultraplan --research → plan → ultraexecute.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

scripts/analytics/src/utils/stats.ts

@@ -0,0 +1,63 @@
+import type { TrendDirection } from "../models/types.js";
+
+/**
+ * Calculate arithmetic mean of values.
+ * Returns 0 for empty array.
+ */
+export function mean(values: number[]): number {
+  if (values.length === 0) return 0;
+  const sum = values.reduce((acc, val) => acc + val, 0);
+  return sum / values.length;
+}
+
+/**
+ * Calculate population standard deviation.
+ * Returns 0 for empty or single-element array.
+ */
+export function standardDeviation(values: number[]): number {
+  if (values.length <= 1) return 0;
+
+  const avg = mean(values);
+  const squaredDiffs = values.map((val) => Math.pow(val - avg, 2));
+  const variance = mean(squaredDiffs);
+
+  return Math.sqrt(variance);
+}
+
+/**
+ * Determine trend direction based on percentage change.
+ * Returns "up" if change > threshold, "down" if change < -threshold, "stable" otherwise.
+ * Default threshold is 5%.
+ */
+export function trendDirection(
+  current: number,
+  previous: number,
+  threshold: number = 5
+): TrendDirection {
+  const change = percentChange(current, previous);
+
+  if (change > threshold) return "up";
+  if (change < -threshold) return "down";
+  return "stable";
+}
+
+/**
+ * Calculate percentage change between current and previous values.
+ * Returns 0 if previous is 0.
+ */
+export function percentChange(current: number, previous: number): number {
+  if (previous === 0) return 0;
+  return ((current - previous) / previous) * 100;
+}
+
+/**
+ * Calculate how many standard deviations a value is from the mean.
+ * Returns 0 if standard deviation is 0.
+ */
+export function deviationsFromMean(value: number, values: number[]): number {
+  const avg = mean(values);
+  const stdDev = standardDeviation(values);
+
+  if (stdDev === 0) return 0;
+  return (value - avg) / stdDev;
+}