ci(benchmark): gate scenario speed relative to the runner

Before the protocol, time the frozen engine on the two-year scenario, best
of three, and fail any scenario whose mean planning time exceeds its
multiplier times that calibration. Multipliers come from development-machine
ratios with about 1.5x headroom until #286 tightens them. The 300-second
timeout stays only as a hang guard. The benchmark keeps running on push and
pull_request events because the push run gates image publication.

This replaces the absolute 300-second acceptance protocol named in #78.

Refs #285

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/app/benchmark/leave-planner-benchmark.ts

@@ -307,3 +307,40 @@ export function benchmarkReport(measurements: BenchmarkMeasurement[]): string {
 		? [BENCHMARK_REPORT_HEADER, benchmarkReportRows(measurements)].join('\n')
 		: BENCHMARK_REPORT_HEADER;
 }
+
+// Measured on the development machine (ratio to the frozen two-years run), tightened by #286.
+export const BENCHMARK_BUDGET_MULTIPLIERS: Record<string, number> = {
+	'representative year': 0.25,
+	'typed obligations': 3,
+	'chained earned entitlements': 0.05,
+	'deliberate conflict': 0.05,
+	'loaded year': 25,
+	'two years': 1,
+	'three years': 3.5,
+};
+
+/** One message per scenario whose mean planning time exceeds multiplier x calibration, or that has no multiplier. */
+export function budgetViolations(
+	measurements: BenchmarkMeasurement[],
+	calibrationMs: number,
+	multipliers: Record<string, number> = BENCHMARK_BUDGET_MULTIPLIERS,
+): string[] {
+	const byScenario = new Map<string, number[]>();
+	for (const { scenario, planningMs } of measurements)
+		byScenario.set(scenario, [...(byScenario.get(scenario) ?? []), planningMs]);
+	const violations: string[] = [];
+	for (const [scenario, times] of byScenario) {
+		const mean = times.reduce((sum, value) => sum + value, 0) / times.length;
+		const multiplier = multipliers[scenario];
+		if (multiplier === undefined) {
+			violations.push(`${scenario}: no budget multiplier defined`);
+			continue;
+		}
+		const budget = multiplier * calibrationMs;
+		if (mean > budget)
+			violations.push(
+				`${scenario}: measured ${mean.toFixed(1)} ms > budget ${budget.toFixed(1)} ms (multiplier ${multiplier} x calibration ${calibrationMs.toFixed(1)} ms)`,
+			);
+	}
+	return violations;
+}