H-5641: Add Distribution.Lognormal(mu, sigma) support

Uses standard mathematical parameterization where mu and sigma are the
mean and standard deviation of the underlying normal distribution ln(X).

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

Author: kube

libs/@hashintel/petrinaut/src/lsp/lib/generate-virtual-files.ts

@@ -32,6 +32,7 @@ export function generateVirtualFiles(sdcpn: SDCPN): Map<string, VirtualFile> {
       `declare namespace Distribution {`,
       `  function Gaussian(mean: number, deviation: number): Distribution;`,
       `  function Uniform(min: number, max: number): Distribution;`,
+      `  function Lognormal(mu: number, sigma: number): Distribution;`,
       `}`,
     ].join("\n"),
   });

libs/@hashintel/petrinaut/src/simulation/simulator/distribution.ts

@@ -19,6 +19,11 @@ export type RuntimeDistribution =
       deviation: number;
     })
   | (DistributionBase & { type: "uniform"; min: number; max: number })
+  | (DistributionBase & {
+      type: "lognormal";
+      mu: number;
+      sigma: number;
+    })
   | (DistributionBase & {
       type: "mapped";
       inner: RuntimeDistribution;
@@ -55,6 +60,9 @@ export const distributionRuntimeCode = `
     },
     Uniform: function(min, max) {
       return __addMap({ __brand: "distribution", type: "uniform", min: min, max: max });
+    },
+    Lognormal: function(mu, sigma) {
+      return __addMap({ __brand: "distribution", type: "lognormal", mu: mu, sigma: sigma });
     }
   };
 `;
@@ -93,6 +101,15 @@ export function sampleDistribution(
       nextRng = newRng;
       break;
     }
+    case "lognormal": {
+      // Lognormal(μ, σ): if X ~ Normal(μ, σ), then e^X ~ Lognormal(μ, σ)
+      const [u1, rng1] = nextRandom(rngState);
+      const [u2, rng2] = nextRandom(rng1);
+      const z = Math.sqrt(-2 * Math.log(u1)) * Math.cos(2 * Math.PI * u2);
+      value = Math.exp(distribution.mu + z * distribution.sigma);
+      nextRng = rng2;
+      break;
+    }
     case "mapped": {
       const [innerValue, newRng] = sampleDistribution(
         distribution.inner,