diff --git a/package-lock.json b/package-lock.json
index 53718fd..1bfc68c 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -28,6 +28,9 @@
         "supabase": "^2.24.3",
         "typescript": "^5.8.3",
         "zod": "^3.24.3"
+      },
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       }
     },
     "node_modules/@babel/code-frame": {
@@ -63,6 +66,397 @@
         "tslib": "^2.4.0"
       }
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+        "ia32"
+      ],
+      "dev": true,
+      "license": "MIT",
+      "optional": true,
+      "os": [
+        "win32"
+      ],
+      "engines": {
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+    },
+    "node_modules/@esbuild/win32-x64": {
+      "version": "0.21.5",
+      "resolved": "https://registry.npmjs.org/@esbuild/win32-x64/-/win32-x64-0.21.5.tgz",
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+      "cpu": [
+        "x64"
+      ],
+      "dev": true,
+      "license": "MIT",
+      "optional": true,
+      "os": [
+        "win32"
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+      "engines": {
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     "node_modules/@img/colour": {
       "version": "1.0.0",
       "resolved": "https://registry.npmjs.org/@img/colour/-/colour-1.0.0.tgz",
@@ -541,6 +935,13 @@
         "node": ">=18.0.0"
       }
     },
+    "node_modules/@jridgewell/sourcemap-codec": {
+      "version": "1.5.5",
+      "resolved": "https://registry.npmjs.org/@jridgewell/sourcemap-codec/-/sourcemap-codec-1.5.5.tgz",
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+      "license": "MIT"
+    },
     "node_modules/@mapbox/fusspot": {
       "version": "0.4.0",
       "resolved": "https://registry.npmjs.org/@mapbox/fusspot/-/fusspot-0.4.0.tgz",
@@ -792,15 +1193,365 @@
         "node": ">= 10"
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+      "resolved": "https://registry.npmjs.org/@rollup/rollup-android-arm-eabi/-/rollup-android-arm-eabi-4.62.2.tgz",
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+      "dev": true,
       "license": "MIT",
-      "engines": {
-        "node": ">=10"
-      },
-      "funding": {
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+      "os": [
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+      "license": "MIT",
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+        "url": "https://github.com/vitejs/vite?sponsor=1"
+      },
+      "optionalDependencies": {
+        "fsevents": "~2.3.3"
+      },
+      "peerDependencies": {
+        "@types/node": "^18.0.0 || >=20.0.0",
+        "less": "*",
+        "lightningcss": "^1.21.0",
+        "sass": "*",
+        "sass-embedded": "*",
+        "stylus": "*",
+        "sugarss": "*",
+        "terser": "^5.4.0"
+      },
+      "peerDependenciesMeta": {
+        "@types/node": {
+          "optional": true
+        },
+        "less": {
+          "optional": true
+        },
+        "lightningcss": {
+          "optional": true
+        },
+        "sass": {
+          "optional": true
+        },
+        "sass-embedded": {
+          "optional": true
+        },
+        "stylus": {
+          "optional": true
+        },
+        "sugarss": {
+          "optional": true
+        },
+        "terser": {
+          "optional": true
+        }
+      }
+    },
+    "node_modules/vite-node": {
+      "version": "2.1.9",
+      "resolved": "https://registry.npmjs.org/vite-node/-/vite-node-2.1.9.tgz",
+      "integrity": "sha512-AM9aQ/IPrW/6ENLQg3AGY4K1N2TGZdR5e4gu/MmmR2xR3Ll1+dib+nook92g4TV3PXVyeyxdWwtaCAiUL0hMxA==",
+      "dev": true,
+      "license": "MIT",
+      "dependencies": {
+        "cac": "^6.7.14",
+        "debug": "^4.3.7",
+        "es-module-lexer": "^1.5.4",
+        "pathe": "^1.1.2",
+        "vite": "^5.0.0"
+      },
+      "bin": {
+        "vite-node": "vite-node.mjs"
+      },
+      "engines": {
+        "node": "^18.0.0 || >=20.0.0"
+      },
+      "funding": {
+        "url": "https://opencollective.com/vitest"
+      }
+    },
+    "node_modules/vite/node_modules/postcss": {
+      "version": "8.5.16",
+      "resolved": "https://registry.npmjs.org/postcss/-/postcss-8.5.16.tgz",
+      "integrity": "sha512-vuwillviilfKZsg0VGj5R/YwwcHx4SLsIOI/7K6mQkWx+l5cUHTjj5g0AasTBcyXsbfTgrwsUNmVUb5xVwyPwg==",
+      "dev": true,
+      "funding": [
+        {
+          "type": "opencollective",
+          "url": "https://opencollective.com/postcss/"
+        },
+        {
+          "type": "tidelift",
+          "url": "https://tidelift.com/funding/github/npm/postcss"
+        },
+        {
+          "type": "github",
+          "url": "https://github.com/sponsors/ai"
+        }
+      ],
+      "license": "MIT",
+      "dependencies": {
+        "nanoid": "^3.3.12",
+        "picocolors": "^1.1.1",
+        "source-map-js": "^1.2.1"
+      },
+      "engines": {
+        "node": "^10 || ^12 || >=14"
+      }
+    },
+    "node_modules/vitest": {
+      "version": "2.1.9",
+      "resolved": "https://registry.npmjs.org/vitest/-/vitest-2.1.9.tgz",
+      "integrity": "sha512-MSmPM9REYqDGBI8439mA4mWhV5sKmDlBKWIYbA3lRb2PTHACE0mgKwA8yQ2xq9vxDTuk4iPrECBAEW2aoFXY0Q==",
+      "dev": true,
+      "license": "MIT",
+      "dependencies": {
+        "@vitest/expect": "2.1.9",
+        "@vitest/mocker": "2.1.9",
+        "@vitest/pretty-format": "^2.1.9",
+        "@vitest/runner": "2.1.9",
+        "@vitest/snapshot": "2.1.9",
+        "@vitest/spy": "2.1.9",
+        "@vitest/utils": "2.1.9",
+        "chai": "^5.1.2",
+        "debug": "^4.3.7",
+        "expect-type": "^1.1.0",
+        "magic-string": "^0.30.12",
+        "pathe": "^1.1.2",
+        "std-env": "^3.8.0",
+        "tinybench": "^2.9.0",
+        "tinyexec": "^0.3.1",
+        "tinypool": "^1.0.1",
+        "tinyrainbow": "^1.2.0",
+        "vite": "^5.0.0",
+        "vite-node": "2.1.9",
+        "why-is-node-running": "^2.3.0"
+      },
+      "bin": {
+        "vitest": "vitest.mjs"
+      },
+      "engines": {
+        "node": "^18.0.0 || >=20.0.0"
+      },
+      "funding": {
+        "url": "https://opencollective.com/vitest"
+      },
+      "peerDependencies": {
+        "@edge-runtime/vm": "*",
+        "@types/node": "^18.0.0 || >=20.0.0",
+        "@vitest/browser": "2.1.9",
+        "@vitest/ui": "2.1.9",
+        "happy-dom": "*",
+        "jsdom": "*"
+      },
+      "peerDependenciesMeta": {
+        "@edge-runtime/vm": {
+          "optional": true
+        },
+        "@types/node": {
+          "optional": true
+        },
+        "@vitest/browser": {
+          "optional": true
+        },
+        "@vitest/ui": {
+          "optional": true
+        },
+        "happy-dom": {
+          "optional": true
+        },
+        "jsdom": {
+          "optional": true
+        }
+      }
+    },
     "node_modules/vt-pbf": {
       "version": "3.1.3",
       "resolved": "https://registry.npmjs.org/vt-pbf/-/vt-pbf-3.1.3.tgz",
@@ -3250,6 +4581,23 @@
         "webidl-conversions": "^3.0.0"
       }
     },
+    "node_modules/why-is-node-running": {
+      "version": "2.3.0",
+      "resolved": "https://registry.npmjs.org/why-is-node-running/-/why-is-node-running-2.3.0.tgz",
+      "integrity": "sha512-hUrmaWBdVDcxvYqnyh09zunKzROWjbZTiNy8dBEjkS7ehEDQibXJ7XvlmtbwuTclUiIyN+CyXQD4Vmko8fNm8w==",
+      "dev": true,
+      "license": "MIT",
+      "dependencies": {
+        "siginfo": "^2.0.0",
+        "stackback": "0.0.2"
+      },
+      "bin": {
+        "why-is-node-running": "cli.js"
+      },
+      "engines": {
+        "node": ">=8"
+      }
+    },
     "node_modules/wrappy": {
       "version": "1.0.2",
       "resolved": "https://registry.npmjs.org/wrappy/-/wrappy-1.0.2.tgz",
diff --git a/package.json b/package.json
index ee99e16..64f7d2b 100644
--- a/package.json
+++ b/package.json
@@ -7,7 +7,9 @@
     "dev": "next dev",
     "build": "next build",
     "start": "next start",
-    "lint": "next lint"
+    "lint": "next lint",
+    "test": "vitest run",
+    "test:watch": "vitest"
   },
   "keywords": [
     "tasks",
@@ -18,9 +20,9 @@
   "author": "",
   "license": "ISC",
   "dependencies": {
+    "@mapbox/mapbox-gl-geocoder": "^5.0.3",
     "@stripe/react-stripe-js": "^3.7.0",
     "@stripe/stripe-js": "^7.3.1",
-    "@mapbox/mapbox-gl-geocoder": "^5.0.3",
     "@supabase/auth-helpers-nextjs": "^0.10.0",
     "@supabase/ssr": "^0.6.1",
     "@supabase/supabase-js": "^2.49.4",
@@ -37,5 +39,8 @@
     "supabase": "^2.24.3",
     "typescript": "^5.8.3",
     "zod": "^3.24.3"
+  },
+  "devDependencies": {
+    "vitest": "^2.1.9"
   }
 }
diff --git a/src/app/RaceTrack.tsx b/src/app/RaceTrack.tsx
index 51cb5ac..cce2ea2 100644
--- a/src/app/RaceTrack.tsx
+++ b/src/app/RaceTrack.tsx
@@ -10,26 +10,31 @@ type TaskType = {
 
 type RaceTrackVisualizationProps = {
   tasks?: TaskType[];
+  /** Car position 0–100. When provided, the demo animation is disabled. */
+  carPosition?: number;
   className?: string;
 };
 
 const RaceTrackVisualization: React.FC<RaceTrackVisualizationProps> = ({
   tasks = [],
+  carPosition: carPositionProp,
   className = "",
 }) => {
-  const [carPosition, setCarPosition] = useState(10);
+  // Real data drives the car when either tasks or an explicit position is given.
+  const isDriven = tasks.length > 0 || carPositionProp !== undefined;
+  const [demoPosition, setDemoPosition] = useState(10);
 
-  // Demo animation for the placeholder
+  // Demo animation only runs for the empty/placeholder state.
   useEffect(() => {
+    if (isDriven) return;
     const interval = setInterval(() => {
-      setCarPosition((prev) => {
-        if (prev >= 85) return 10;
-        return prev + 5;
-      });
+      setDemoPosition((prev) => (prev >= 85 ? 10 : prev + 5));
     }, 1000);
 
     return () => clearInterval(interval);
-  }, []);
+  }, [isDriven]);
+
+  const carPosition = isDriven ? (carPositionProp ?? 10) : demoPosition;
 
   // Default placeholder tasks if none provided
   const demoTasks =
diff --git a/src/app/dashboard/page.tsx b/src/app/dashboard/page.tsx
index 2eb8140..ff6da31 100644
--- a/src/app/dashboard/page.tsx
+++ b/src/app/dashboard/page.tsx
@@ -36,6 +36,8 @@ import {
 } from '../../lib/api/supabase';
 import { getUserPublicTasks } from '../../lib/api/publicTasks';
 import Board from '../../components/ui/Board';
+import RaceTrackVisualization from '../RaceTrack';
+import { computeRaceTasks, computeCarPosition } from '../../lib/raceProgress';
 import Button, { ButtonSize } from '../../components/ui/Button';
 import CreateTaskModal from '../../components/task/CreateTaskModal';
 import CreatePublicTaskModal from '../../components/task/CreatePublicTaskModal';
@@ -520,6 +522,13 @@ const DashboardPage: React.FC = () => {
                   </div>
 
                   <div className={styles.sidebar}>
+                    <Board title="Your Lap">
+                      <RaceTrackVisualization
+                        tasks={computeRaceTasks(myTasks)}
+                        carPosition={computeCarPosition(myTasks)}
+                      />
+                    </Board>
+
                     <Board title="Leaderboard" className={styles.leaderboard}>
                       {leaderboard.map((entry, index) => (
                         <div key={entry.id} className={styles.leaderboardEntry}>
diff --git a/src/app/leaderboard/Leaderboard.module.css b/src/app/leaderboard/Leaderboard.module.css
index 5e61840..3b73bb1 100644
--- a/src/app/leaderboard/Leaderboard.module.css
+++ b/src/app/leaderboard/Leaderboard.module.css
@@ -454,4 +454,34 @@
     align-items: flex-start;
     gap: 0.5rem;
   }
-} 
\ No newline at end of file
+} 
+/* Scope toggle (Everyone / Friends only) */
+.scopeToggle {
+  display: inline-flex;
+  gap: 0.25rem;
+  margin-top: 1rem;
+  background: var(--background-alt, #f1f3f5);
+  padding: 0.25rem;
+  border-radius: 999px;
+}
+
+.scopeButton {
+  border: none;
+  background: transparent;
+  padding: 0.4rem 1rem;
+  border-radius: 999px;
+  font-size: 0.85rem;
+  font-weight: 500;
+  color: var(--text-secondary, #666);
+  cursor: pointer;
+  transition: background 0.15s ease, color 0.15s ease;
+}
+
+.scopeButton:hover {
+  color: var(--text, #222);
+}
+
+.scopeActive {
+  background: var(--primary, #4f46e5);
+  color: #fff;
+}
diff --git a/src/app/leaderboard/page.tsx b/src/app/leaderboard/page.tsx
index 9e56b86..7ea2a97 100644
--- a/src/app/leaderboard/page.tsx
+++ b/src/app/leaderboard/page.tsx
@@ -13,6 +13,12 @@ import styles from './Leaderboard.module.css';
 
 // Leaderboard types
 const LEADERBOARD_TYPES = [
+  {
+    id: 'champions',
+    name: 'Champions',
+    description: 'Ranked by the composite score: throughput × quality × on-time',
+    icon: '👑',
+  },
   {
     id: 'tasks-completed',
     name: 'Tasks Completed',
@@ -47,24 +53,33 @@ const LeaderboardPage: React.FC = () => {
   const [entries, setEntries] = useState<LeaderboardEntry[]>([]);
   const [isLoading, setIsLoading] = useState(true);
   const [error, setError] = useState<string | null>(null);
+  const [friendsOnly, setFriendsOnly] = useState(false);
 
   useEffect(() => {
     if (user) {
       fetchLeaderboardData(activeLeaderboard);
     }
-  }, [user, activeLeaderboard]);
+  }, [user, activeLeaderboard, friendsOnly]);
 
   const fetchLeaderboardData = async (leaderboardType: string) => {
     setIsLoading(true);
     setError(null);
-    
+
     try {
       const leaderboardData = await getLeaderboard();
-      
+
       // Sort the leaderboard based on the type
       let sortedData = [...leaderboardData];
-      
+
+      // Friends-only toggle keeps the current user plus accepted friends.
+      if (friendsOnly) {
+        sortedData = sortedData.filter(entry => entry.isFriend);
+      }
+
       switch (leaderboardType) {
+        case 'champions':
+          sortedData.sort((a, b) => (b.compositeScore || 0) - (a.compositeScore || 0));
+          break;
         case 'tasks-completed':
           sortedData.sort((a, b) => b.tasksCompleted - a.tasksCompleted);
           break;
@@ -135,6 +150,20 @@ const LeaderboardPage: React.FC = () => {
           <div className={styles.header}>
             <h1 className={styles.title}>Leaderboards</h1>
             <p className={styles.subtitle}>See who's leading in different categories</p>
+            <div className={styles.scopeToggle}>
+              <button
+                className={`${styles.scopeButton} ${!friendsOnly ? styles.scopeActive : ''}`}
+                onClick={() => setFriendsOnly(false)}
+              >
+                Everyone
+              </button>
+              <button
+                className={`${styles.scopeButton} ${friendsOnly ? styles.scopeActive : ''}`}
+                onClick={() => setFriendsOnly(true)}
+              >
+                Friends only
+              </button>
+            </div>
           </div>
 
           {error && (
@@ -188,12 +217,14 @@ const LeaderboardPage: React.FC = () => {
                   <div className={styles.rankColumn}>Rank</div>
                   <div className={styles.userColumn}>User</div>
                   <div className={styles.statsColumn}>
+                    {activeLeaderboard === 'champions' && 'Score'}
                     {activeLeaderboard === 'tasks-completed' && 'Tasks Completed'}
                     {activeLeaderboard === 'quality-rating' && 'Avg. Quality'}
                     {activeLeaderboard === 'speed-demons' && 'Avg. Time'}
                     {activeLeaderboard === 'consistency' && 'Tasks Overdue'}
                   </div>
                   <div className={styles.extendedStatsColumn}>
+                    {activeLeaderboard === 'champions' && 'Breakdown'}
                     {activeLeaderboard === 'tasks-completed' && 'Additional Stats'}
                     {activeLeaderboard === 'quality-rating' && 'Rating Breakdown'}
                     {activeLeaderboard === 'speed-demons' && 'Performance'}
@@ -240,12 +271,29 @@ const LeaderboardPage: React.FC = () => {
                       </div>
                     </div>
                     <div className={styles.statsColumn}>
+                      {activeLeaderboard === 'champions' && <span className={styles.statValue}>{(entry.compositeScore || 0).toFixed(1)}</span>}
                       {activeLeaderboard === 'tasks-completed' && <span className={styles.statValue}>{entry.tasksCompleted}</span>}
                       {activeLeaderboard === 'quality-rating' && <span className={styles.statValue}>{formatRating(entry.avgQualityRating)}</span>}
                       {activeLeaderboard === 'speed-demons' && <span className={styles.statValue}>{formatTime(entry.avgCompletionTime)}</span>}
                       {activeLeaderboard === 'consistency' && <span className={styles.statValue}>{entry.tasksOverdue}</span>}
                     </div>
                     <div className={styles.extendedStatsColumn}>
+                      {activeLeaderboard === 'champions' && (
+                        <>
+                          <div className={styles.miniStat}>
+                            <span className={styles.miniStatLabel}>Tasks</span>
+                            <span className={styles.miniStatValue}>{entry.tasksCompleted}</span>
+                          </div>
+                          <div className={styles.miniStat}>
+                            <span className={styles.miniStatLabel}>Quality</span>
+                            <span className={styles.miniStatValue}>{formatRating(entry.avgQualityRating)}</span>
+                          </div>
+                          <div className={styles.miniStat}>
+                            <span className={styles.miniStatLabel}>5★ Tasks</span>
+                            <span className={styles.miniStatValue}>{entry.perfectTasks || 0}</span>
+                          </div>
+                        </>
+                      )}
                       {activeLeaderboard === 'tasks-completed' && (
                         <>
                           <div className={styles.miniStat}>
diff --git a/src/app/task/TasksPage.module.css b/src/app/task/TasksPage.module.css
index 6ea939d..bbf2b93 100644
--- a/src/app/task/TasksPage.module.css
+++ b/src/app/task/TasksPage.module.css
@@ -477,4 +477,38 @@
     font-size: 0.75rem;
     padding: 0.4rem 0.8rem;
   }
-} 
\ No newline at end of file
+} 
+/* Search + priority filter row (spec US-5) */
+.searchRow {
+  display: flex;
+  gap: 0.75rem;
+  margin-bottom: 1rem;
+  flex-wrap: wrap;
+}
+
+.searchInput {
+  flex: 1 1 240px;
+  min-width: 0;
+  padding: 0.6rem 0.9rem;
+  border: 1px solid var(--border, #d0d5dd);
+  border-radius: 8px;
+  font-size: 0.95rem;
+  background: var(--background, #fff);
+  color: var(--text, #1a1a1a);
+}
+
+.searchInput:focus {
+  outline: none;
+  border-color: var(--primary, #4f46e5);
+  box-shadow: 0 0 0 3px rgba(79, 70, 229, 0.15);
+}
+
+.prioritySelect {
+  padding: 0.6rem 0.9rem;
+  border: 1px solid var(--border, #d0d5dd);
+  border-radius: 8px;
+  font-size: 0.95rem;
+  background: var(--background, #fff);
+  color: var(--text, #1a1a1a);
+  cursor: pointer;
+}
diff --git a/src/app/task/page.tsx b/src/app/task/page.tsx
index 78ed617..585c640 100644
--- a/src/app/task/page.tsx
+++ b/src/app/task/page.tsx
@@ -3,11 +3,12 @@
 import React, { useState, useEffect } from 'react';
 import { useRouter } from 'next/navigation';
 import AppLayout from '../../components/layout/AppLayout';
-import { Task, TaskStatus } from '../../types';
+import { Task, TaskStatus, TaskPriority } from '../../types';
 import ProtectedRoute from '../../components/layout/ProtectedRoute';
 import { useAuth } from '../../context/AuthContext';
 import Button from '../../components/ui/Button';
 import { getUserTasks, getUserAssignedTasks } from '../../lib/api/supabase';
+import { filterTasks } from '../../lib/taskFilters';
 import styles from './TasksPage.module.css';
 
 const TasksPage: React.FC = () => {
@@ -20,6 +21,12 @@ const TasksPage: React.FC = () => {
   const [activeFilter, setActiveFilter] = useState<string>('all');
   const [activeTab, setActiveTab] = useState<string>('active');
   const [viewMode, setViewMode] = useState<string>('my-tasks');
+  const [searchQuery, setSearchQuery] = useState<string>('');
+  const [priorityFilter, setPriorityFilter] = useState<'all' | TaskPriority>('all');
+
+  // Apply free-text search + priority before any status grouping (spec US-5).
+  const searchedTasks = filterTasks(tasks, { search: searchQuery, priority: priorityFilter });
+  const searchedFriendTasks = filterTasks(friendTasks, { search: searchQuery, priority: priorityFilter });
 
   useEffect(() => {
     if (user) {
@@ -52,63 +59,63 @@ const TasksPage: React.FC = () => {
   };
 
   const getFilteredTasks = () => {
-    // Just filter by status if not showing 'all'
-    let filteredTasks = tasks;
-    
+    // Status is applied on top of the search + priority filtered list.
+    let filteredTasks = searchedTasks;
+
     if (activeFilter !== 'all') {
       if (activeFilter === 'active') {
-        filteredTasks = tasks.filter(task => 
-          task.status === TaskStatus.PENDING || 
+        filteredTasks = searchedTasks.filter(task =>
+          task.status === TaskStatus.PENDING ||
           task.status === TaskStatus.IN_PROGRESS
         );
       } else {
-        filteredTasks = tasks.filter(task => task.status === activeFilter);
+        filteredTasks = searchedTasks.filter(task => task.status === activeFilter);
       }
     }
-    
+
     return filteredTasks;
   };
 
   const getTasks = (status: TaskStatus | 'active' | 'all'): Task[] => {
     if (status === 'all') {
-      return tasks;
+      return searchedTasks;
     } else if (status === 'active') {
-      return tasks.filter(task => 
-        task.status === TaskStatus.PENDING || 
+      return searchedTasks.filter(task =>
+        task.status === TaskStatus.PENDING ||
         task.status === TaskStatus.IN_PROGRESS
       );
     } else {
-      return tasks.filter(task => task.status === status);
+      return searchedTasks.filter(task => task.status === status);
     }
   };
 
   const getFilteredFriendTasks = () => {
-    let filteredTasks = friendTasks;
-    
+    let filteredTasks = searchedFriendTasks;
+
     if (activeFilter !== 'all') {
       if (activeFilter === 'active') {
-        filteredTasks = friendTasks.filter(task => 
-          task.status === TaskStatus.PENDING || 
+        filteredTasks = searchedFriendTasks.filter(task =>
+          task.status === TaskStatus.PENDING ||
           task.status === TaskStatus.IN_PROGRESS
         );
       } else {
-        filteredTasks = friendTasks.filter(task => task.status === activeFilter);
+        filteredTasks = searchedFriendTasks.filter(task => task.status === activeFilter);
       }
     }
-    
+
     return filteredTasks;
   };
 
   const getFriendTasks = (status: TaskStatus | 'active' | 'all'): Task[] => {
     if (status === 'all') {
-      return friendTasks;
+      return searchedFriendTasks;
     } else if (status === 'active') {
-      return friendTasks.filter(task => 
-        task.status === TaskStatus.PENDING || 
+      return searchedFriendTasks.filter(task =>
+        task.status === TaskStatus.PENDING ||
         task.status === TaskStatus.IN_PROGRESS
       );
     } else {
-      return friendTasks.filter(task => task.status === status);
+      return searchedFriendTasks.filter(task => task.status === status);
     }
   };
 
@@ -244,7 +251,7 @@ const TasksPage: React.FC = () => {
             <h2 className={styles.sectionTitle}>Overdue</h2>
             <div className={styles.taskCards}>
               {getTasks(TaskStatus.OVERDUE).map(renderTaskCard)}
-              {tasks
+              {searchedTasks
                 .filter(task => 
                   new Date(task.dueDate) < new Date() && 
                   task.status !== TaskStatus.COMPLETED &&
@@ -252,7 +259,7 @@ const TasksPage: React.FC = () => {
                 )
                 .map(renderTaskCard)}
               {getTasks(TaskStatus.OVERDUE).length === 0 && 
-               tasks.filter(task => 
+               searchedTasks.filter(task => 
                  new Date(task.dueDate) < new Date() && 
                  task.status !== TaskStatus.COMPLETED &&
                  task.status !== TaskStatus.GRADED
@@ -323,15 +330,15 @@ const TasksPage: React.FC = () => {
             <h2 className={styles.sectionTitle}>Overdue</h2>
             <div className={styles.taskCards}>
               {getFriendTasks(TaskStatus.OVERDUE).map(renderTaskCard)}
-              {friendTasks
-                .filter(task => 
-                  new Date(task.dueDate) < new Date() && 
+              {searchedFriendTasks
+                .filter(task =>
+                  new Date(task.dueDate) < new Date() &&
                   task.status !== TaskStatus.COMPLETED &&
                   task.status !== TaskStatus.GRADED
                 )
                 .map(renderTaskCard)}
-              {getFriendTasks(TaskStatus.OVERDUE).length === 0 && 
-               friendTasks.filter(task => 
+              {getFriendTasks(TaskStatus.OVERDUE).length === 0 &&
+               searchedFriendTasks.filter(task =>
                  new Date(task.dueDate) < new Date() && 
                  task.status !== TaskStatus.COMPLETED &&
                  task.status !== TaskStatus.GRADED
@@ -419,6 +426,27 @@ const TasksPage: React.FC = () => {
             </div>
           </div>
           
+          <div className={styles.searchRow}>
+            <input
+              type="search"
+              className={styles.searchInput}
+              placeholder="Search tasks by title or description..."
+              value={searchQuery}
+              onChange={(e) => setSearchQuery(e.target.value)}
+            />
+            <select
+              className={styles.prioritySelect}
+              value={priorityFilter}
+              onChange={(e) => setPriorityFilter(e.target.value as 'all' | TaskPriority)}
+            >
+              <option value="all">All priorities</option>
+              <option value={TaskPriority.URGENT}>Urgent</option>
+              <option value={TaskPriority.HIGH}>High</option>
+              <option value={TaskPriority.MEDIUM}>Medium</option>
+              <option value={TaskPriority.LOW}>Low</option>
+            </select>
+          </div>
+
           <div className={styles.filtersContainer}>
             <div className={styles.filters}>
               <button 
diff --git a/src/lib/__tests__/raceProgress.test.ts b/src/lib/__tests__/raceProgress.test.ts
new file mode 100644
index 0000000..720fc07
--- /dev/null
+++ b/src/lib/__tests__/raceProgress.test.ts
@@ -0,0 +1,74 @@
+import { describe, it, expect } from 'vitest';
+import { computeRaceTasks, computeCarPosition } from '../raceProgress';
+import { Task, TaskStatus, TaskPriority } from '../../types';
+
+function task(overrides: Partial<Task> = {}): Task {
+  return {
+    id: Math.random().toString(36).slice(2),
+    title: 'Task',
+    description: '',
+    createdAt: new Date('2026-07-01'),
+    dueDate: new Date('2026-07-10'),
+    assignerId: 'alice',
+    assigneeId: 'bob',
+    status: TaskStatus.PENDING,
+    priority: TaskPriority.MEDIUM,
+    ...overrides,
+  };
+}
+
+describe('computeRaceTasks', () => {
+  it('returns an empty lap for no tasks', () => {
+    expect(computeRaceTasks([])).toEqual([]);
+  });
+
+  it('centers a single task', () => {
+    const [point] = computeRaceTasks([task()]);
+    expect(point.position).toBe(50);
+  });
+
+  it('spaces multiple tasks across the track and orders by due date', () => {
+    const points = computeRaceTasks([
+      task({ id: 'b', dueDate: new Date('2026-07-20') }),
+      task({ id: 'a', dueDate: new Date('2026-07-05') }),
+    ]);
+    expect(points.map((p) => p.id)).toEqual(['a', 'b']);
+    expect(points[0].position).toBe(15);
+    expect(points[1].position).toBe(85);
+  });
+
+  it('marks completed and graded tasks as completed', () => {
+    const points = computeRaceTasks([
+      task({ id: 'x', status: TaskStatus.GRADED }),
+      task({ id: 'y', status: TaskStatus.PENDING }),
+    ]);
+    expect(points.find((p) => p.id === 'x')!.completed).toBe(true);
+    expect(points.find((p) => p.id === 'y')!.completed).toBe(false);
+  });
+
+  it('caps the lap at max checkpoints', () => {
+    const many = Array.from({ length: 10 }, (_, i) => task({ id: String(i) }));
+    expect(computeRaceTasks(many, 6)).toHaveLength(6);
+  });
+});
+
+describe('computeCarPosition', () => {
+  it('sits at the start with no tasks', () => {
+    expect(computeCarPosition([])).toBe(10);
+  });
+
+  it('advances with completion ratio', () => {
+    const tasks = [
+      task({ status: TaskStatus.COMPLETED }),
+      task({ status: TaskStatus.GRADED }),
+      task({ status: TaskStatus.PENDING }),
+      task({ status: TaskStatus.IN_PROGRESS }),
+    ];
+    // 2/4 done -> 10 + 0.5*80 = 50
+    expect(computeCarPosition(tasks)).toBe(50);
+  });
+
+  it('reaches the finish when all done', () => {
+    expect(computeCarPosition([task({ status: TaskStatus.COMPLETED })])).toBe(90);
+  });
+});
diff --git a/src/lib/__tests__/scoring.test.ts b/src/lib/__tests__/scoring.test.ts
new file mode 100644
index 0000000..68efe1f
--- /dev/null
+++ b/src/lib/__tests__/scoring.test.ts
@@ -0,0 +1,118 @@
+import { describe, it, expect } from 'vitest';
+import {
+  computeUserMetrics,
+  computeCompositeScore,
+  isCompleted,
+  isPerfect,
+  isOnTime,
+  decayFactor,
+  PERFECT_BONUS,
+  NEUTRAL_QUALITY,
+  ScoringTask,
+} from '../scoring';
+
+const NOW = new Date('2026-07-07T12:00:00Z');
+
+function task(overrides: Partial<ScoringTask> = {}): ScoringTask {
+  return {
+    status: 'COMPLETED',
+    dueDate: '2026-07-05T12:00:00Z',
+    completedAt: '2026-07-04T12:00:00Z',
+    ...overrides,
+  };
+}
+
+describe('isCompleted', () => {
+  it('counts COMPLETED and GRADED as done', () => {
+    expect(isCompleted('COMPLETED')).toBe(true);
+    expect(isCompleted('GRADED')).toBe(true);
+  });
+  it('does not count in-flight statuses', () => {
+    expect(isCompleted('PENDING')).toBe(false);
+    expect(isCompleted('IN_PROGRESS')).toBe(false);
+    expect(isCompleted('OVERDUE')).toBe(false);
+  });
+});
+
+describe('isPerfect', () => {
+  it('requires 5 on all four axes', () => {
+    expect(
+      isPerfect(task({ qualityRating: 5, timelinessRating: 5, effortRating: 5, accuracyRating: 5 })),
+    ).toBe(true);
+    expect(
+      isPerfect(task({ qualityRating: 5, timelinessRating: 4, effortRating: 5, accuracyRating: 5 })),
+    ).toBe(false);
+  });
+});
+
+describe('isOnTime', () => {
+  it('uses dates when available', () => {
+    expect(isOnTime(task({ completedAt: '2026-07-04', dueDate: '2026-07-05' }))).toBe(true);
+    expect(isOnTime(task({ completedAt: '2026-07-06', dueDate: '2026-07-05' }))).toBe(false);
+  });
+  it('falls back to timeliness grade', () => {
+    expect(isOnTime(task({ completedAt: null, dueDate: null, timelinessRating: 4 }))).toBe(true);
+    expect(isOnTime(task({ completedAt: null, dueDate: null, timelinessRating: 2 }))).toBe(false);
+  });
+});
+
+describe('decayFactor', () => {
+  it('is full within the grace window', () => {
+    const recent = new Date(NOW.getTime() - 3 * 24 * 3600 * 1000);
+    expect(decayFactor(recent, NOW)).toBe(1);
+  });
+  it('halves after one half-life past grace', () => {
+    const stale = new Date(NOW.getTime() - (7 + 14) * 24 * 3600 * 1000);
+    expect(decayFactor(stale, NOW)).toBeCloseTo(0.5, 5);
+  });
+  it('is 1 when there is no activity date', () => {
+    expect(decayFactor(null, NOW)).toBe(1);
+  });
+});
+
+describe('computeCompositeScore', () => {
+  it('multiplies completed × quality × on-time and adds perfect bonus', () => {
+    const score = computeCompositeScore({
+      tasksCompleted: 4,
+      avgQualityRating: 4,
+      onTimeRate: 0.5,
+      perfectTasks: 1,
+    });
+    // 4 * 4 * 0.5 + 2*1 = 10
+    expect(score).toBe(8 + PERFECT_BONUS);
+  });
+  it('uses a neutral quality factor before any grades exist', () => {
+    const score = computeCompositeScore({
+      tasksCompleted: 3,
+      avgQualityRating: undefined,
+      onTimeRate: 1,
+      perfectTasks: 0,
+    });
+    expect(score).toBe(3 * NEUTRAL_QUALITY * 1);
+  });
+});
+
+describe('computeUserMetrics', () => {
+  it('rolls up ratings and keeps graded tasks in the completed count', () => {
+    const tasks: ScoringTask[] = [
+      task({ status: 'GRADED', qualityRating: 5, timelinessRating: 5, effortRating: 5, accuracyRating: 5, actualTimeMinutes: 30 }),
+      task({ status: 'COMPLETED', qualityRating: 3, actualTimeMinutes: 90, completedAt: '2026-07-06', dueDate: '2026-07-05' }),
+      task({ status: 'PENDING', completedAt: null, dueDate: '2026-07-01' }), // overdue
+    ];
+    const m = computeUserMetrics(tasks, NOW);
+    expect(m.tasksCompleted).toBe(2);
+    expect(m.perfectTasks).toBe(1);
+    expect(m.tasksOnTime).toBe(1); // second one is late
+    expect(m.tasksOverdue).toBe(1);
+    expect(m.fastestCompletionTime).toBe(30);
+    expect(m.avgQualityRating).toBe(4); // (5+3)/2
+    expect(m.compositeScore).toBeGreaterThan(0);
+  });
+
+  it('returns a zero score for a user with no completed tasks', () => {
+    const m = computeUserMetrics([task({ status: 'PENDING', completedAt: null, dueDate: '2026-08-01' })], NOW);
+    expect(m.tasksCompleted).toBe(0);
+    expect(m.compositeScore).toBe(0);
+    expect(m.onTimeRate).toBe(0);
+  });
+});
diff --git a/src/lib/__tests__/taskFilters.test.ts b/src/lib/__tests__/taskFilters.test.ts
new file mode 100644
index 0000000..bd4db3a
--- /dev/null
+++ b/src/lib/__tests__/taskFilters.test.ts
@@ -0,0 +1,75 @@
+import { describe, it, expect } from 'vitest';
+import { filterTasks, isOverdue } from '../taskFilters';
+import { Task, TaskStatus, TaskPriority } from '../../types';
+
+const NOW = new Date('2026-07-07T12:00:00Z');
+
+function task(overrides: Partial<Task> = {}): Task {
+  return {
+    id: Math.random().toString(36).slice(2),
+    title: 'Write the report',
+    description: 'Quarterly numbers',
+    createdAt: new Date('2026-07-01'),
+    dueDate: new Date('2026-07-10'),
+    assignerId: 'alice',
+    assigneeId: 'bob',
+    status: TaskStatus.PENDING,
+    priority: TaskPriority.MEDIUM,
+    ...overrides,
+  };
+}
+
+describe('isOverdue', () => {
+  it('is true when past due and not done', () => {
+    expect(isOverdue(task({ dueDate: new Date('2026-07-01'), status: TaskStatus.PENDING }), NOW)).toBe(true);
+  });
+  it('is false when completed or graded even if past due', () => {
+    expect(isOverdue(task({ dueDate: new Date('2026-07-01'), status: TaskStatus.COMPLETED }), NOW)).toBe(false);
+    expect(isOverdue(task({ dueDate: new Date('2026-07-01'), status: TaskStatus.GRADED }), NOW)).toBe(false);
+  });
+});
+
+describe('filterTasks', () => {
+  const tasks = [
+    task({ title: 'Buy milk', status: TaskStatus.PENDING, priority: TaskPriority.LOW, assigneeId: 'bob' }),
+    task({ title: 'Ship release', status: TaskStatus.IN_PROGRESS, priority: TaskPriority.URGENT, assigneeId: 'bob' }),
+    task({ title: 'Review PR', status: TaskStatus.COMPLETED, priority: TaskPriority.HIGH, assigneeId: 'carol' }),
+    task({ title: 'Old chore', status: TaskStatus.PENDING, priority: TaskPriority.MEDIUM, dueDate: new Date('2026-07-01'), assigneeId: 'bob' }),
+  ];
+
+  it('returns everything with no options', () => {
+    expect(filterTasks(tasks)).toHaveLength(4);
+  });
+
+  it('search matches title case-insensitively', () => {
+    expect(filterTasks(tasks, { search: 'ship' }).map((t) => t.title)).toEqual(['Ship release']);
+  });
+
+  it('search matches description too', () => {
+    expect(filterTasks(tasks, { search: 'quarterly' })).toHaveLength(4);
+  });
+
+  it('status "active" keeps pending and in-progress', () => {
+    expect(filterTasks(tasks, { status: 'active' })).toHaveLength(3);
+  });
+
+  it('status "overdue" is computed', () => {
+    const overdue = filterTasks(tasks, { status: 'overdue', now: NOW });
+    expect(overdue.map((t) => t.title)).toEqual(['Old chore']);
+  });
+
+  it('priority filter narrows results', () => {
+    expect(filterTasks(tasks, { priority: TaskPriority.URGENT })).toHaveLength(1);
+  });
+
+  it('combines filters with AND', () => {
+    const res = filterTasks(tasks, { status: 'active', assigneeId: 'bob', priority: TaskPriority.LOW });
+    expect(res.map((t) => t.title)).toEqual(['Buy milk']);
+  });
+
+  it('dueWithinDays keeps only near-term tasks', () => {
+    const res = filterTasks(tasks, { dueWithinDays: 1, now: NOW });
+    // Only the overdue "Old chore" (2026-07-01) is within/under the +1 day cutoff
+    expect(res.map((t) => t.title)).toEqual(['Old chore']);
+  });
+});
diff --git a/src/lib/analytics.ts b/src/lib/analytics.ts
new file mode 100644
index 0000000..57075e8
--- /dev/null
+++ b/src/lib/analytics.ts
@@ -0,0 +1,57 @@
+/**
+ * Loop instrumentation (feature spec §6).
+ *
+ * Every state transition in the assign → start → submit → grade loop emits an
+ * event stamped with whether it was peer (assigner ≠ assignee) or self. That
+ * makes the north-star "weekly graded peer tasks" and the peer:self ratio
+ * queryable from day one. Events go to the existing user_logs sink via addLog
+ * and, when available, to Vercel Analytics custom events.
+ */
+import { addLog } from './logging';
+import { LogCategory } from '../../confy/types';
+
+export type TaskEventType = 'assign' | 'start' | 'submit' | 'grade';
+
+export interface TaskEventPayload {
+  taskId: string;
+  assignerId?: string | null;
+  assigneeId?: string | null;
+  actorId?: string | null;
+  extra?: Record<string, string | number | boolean>;
+}
+
+/** Peer = one person handed the task to another; self = solo task. */
+export function relationOf(assignerId?: string | null, assigneeId?: string | null): 'peer' | 'self' | 'unknown' {
+  if (!assignerId || !assigneeId) return 'unknown';
+  return assignerId === assigneeId ? 'self' : 'peer';
+}
+
+export async function trackTaskEvent(type: TaskEventType, payload: TaskEventPayload): Promise<void> {
+  const relation = relationOf(payload.assignerId, payload.assigneeId);
+  const isPeer = relation === 'peer';
+
+  const details: Record<string, any> = {
+    event: `task_${type}`,
+    taskId: payload.taskId,
+    relation,
+    isPeer,
+    ...payload.extra,
+  };
+
+  // Fire-and-forget to Vercel Analytics if we're in the browser.
+  try {
+    if (typeof window !== 'undefined') {
+      const { track } = await import('@vercel/analytics');
+      track(`task_${type}`, { relation, isPeer });
+    }
+  } catch {
+    // Analytics is best-effort; never block the loop on it.
+  }
+
+  await addLog({
+    userId: payload.actorId ?? undefined,
+    category: LogCategory.TASK,
+    action: `task_${type}`,
+    details,
+  });
+}
diff --git a/src/lib/api/supabase.ts b/src/lib/api/supabase.ts
index 8047ea9..abd836e 100644
--- a/src/lib/api/supabase.ts
+++ b/src/lib/api/supabase.ts
@@ -1,5 +1,7 @@
 import { createClient } from '@supabase/supabase-js';
 import { Task, TaskStatus, TaskPriority, User, Friendship, FriendshipStatus, LeaderboardEntry, TaskAttachment, SubmissionType } from '../../types';
+import { computeUserMetrics, ScoringTask } from '../scoring';
+import { trackTaskEvent } from '../analytics';
 
 // Logger utility for consistent logging
 const logger = {
@@ -843,6 +845,15 @@ export const createTask = async (task: Omit<Task, 'id' | 'createdAt'>): Promise<
   // Type assert the data to our expected structure
   const data = rawData as unknown as InsertedTaskData;
 
+  // Instrument the assignment (spec §6): peer vs self is the key signal.
+  trackTaskEvent('assign', {
+    taskId: data.id,
+    assignerId: task.assignerId,
+    assigneeId: task.assigneeId,
+    actorId: task.assignerId,
+    extra: { priority: task.priority, isInvitation: !!task.isInvitation },
+  });
+
   // Send email notification if task is assigned to someone other than the creator AND assigneeId exists
   if (task.assigneeId && task.assignerId !== task.assigneeId) {
     try {
@@ -1001,6 +1012,21 @@ export const updateTaskStatus = async (
   
   const transformedTask = transformTaskFromDb(data);
 
+  // Instrument loop transitions (spec §6). Actor is the assignee for
+  // start/submit and the assigner for grade.
+  const eventType =
+    status === TaskStatus.IN_PROGRESS ? 'start' :
+    status === TaskStatus.COMPLETED ? 'submit' :
+    status === TaskStatus.GRADED ? 'grade' : null;
+  if (eventType) {
+    trackTaskEvent(eventType, {
+      taskId: transformedTask.id,
+      assignerId: transformedTask.assignerId,
+      assigneeId: transformedTask.assigneeId,
+      actorId: eventType === 'grade' ? transformedTask.assignerId : transformedTask.assigneeId,
+    });
+  }
+
   // Send notifications based on the type of update
   try {
     // Check if this is a task completion (status changed to COMPLETED) or has grading
@@ -1230,6 +1256,8 @@ export const getLeaderboard = async (): Promise<LeaderboardEntry[]> => {
     effort_rating: number | null;
     accuracy_rating: number | null;
     due_date: string;
+    completed_at: string | null;
+    submission_date: string | null;
   }
   
   // First get accepted friendships to mark friends on leaderboard
@@ -1263,91 +1291,60 @@ export const getLeaderboard = async (): Promise<LeaderboardEntry[]> => {
   // Get tasks for calculations
   const { data: tasks, error: tasksError } = await supabase
     .from('tasks')
-    .select('id, status, assignee_id, actual_time_minutes, quality_rating, timeliness_rating, effort_rating, accuracy_rating, due_date')
+    .select('id, status, assignee_id, actual_time_minutes, quality_rating, timeliness_rating, effort_rating, accuracy_rating, due_date, completed_at, submission_date')
     .returns<TaskRecord[]>();
-    
+
   if (tasksError || !tasks) {
     console.error('Error fetching tasks for leaderboard:', tasksError);
     return [];
   }
-  
-  // Calculate leaderboard data manually
+
+  const now = new Date();
+
+  // Build the composite-score leaderboard (spec §3.3). Metrics + score come
+  // from lib/scoring so the formula is shared and unit-tested.
   const leaderboardData: LeaderboardEntry[] = users.map(user => {
-    // Get tasks assigned to this user
-    const userTasks = tasks.filter(task => task.assignee_id === user.id);
-    
-    // Calculate metrics
-    const tasksCompleted = userTasks.filter(task => task.status === 'COMPLETED').length;
-    
-    const completedTasksWithTime = userTasks.filter(
-      task => task.status === 'COMPLETED' && task.actual_time_minutes !== null
-    );
-    
-    const avgCompletionTime = completedTasksWithTime.length 
-      ? completedTasksWithTime.reduce((sum, task) => sum + (task.actual_time_minutes || 0), 0) / completedTasksWithTime.length
-      : undefined;
-    
-    const completedTasksWithRating = userTasks.filter(
-      task => task.status === 'COMPLETED' && task.quality_rating !== null
-    );
-    
-    const avgQualityRating = completedTasksWithRating.length
-      ? completedTasksWithRating.reduce((sum, task) => sum + (task.quality_rating || 0), 0) / completedTasksWithRating.length
-      : undefined;
-      
-    const completedTasksWithTimelinessRating = userTasks.filter(
-      task => task.status === 'COMPLETED' && task.timeliness_rating !== null
-    );
-    
-    const avgTimelinessRating = completedTasksWithTimelinessRating.length
-      ? completedTasksWithTimelinessRating.reduce((sum, task) => sum + (task.timeliness_rating || 0), 0) / completedTasksWithTimelinessRating.length
-      : undefined;
-      
-    const completedTasksWithEffortRating = userTasks.filter(
-      task => task.status === 'COMPLETED' && task.effort_rating !== null
-    );
-    
-    const avgEffortRating = completedTasksWithEffortRating.length
-      ? completedTasksWithEffortRating.reduce((sum, task) => sum + (task.effort_rating || 0), 0) / completedTasksWithEffortRating.length
-      : undefined;
-      
-    const completedTasksWithAccuracyRating = userTasks.filter(
-      task => task.status === 'COMPLETED' && task.accuracy_rating !== null
-    );
-    
-    const avgAccuracyRating = completedTasksWithAccuracyRating.length
-      ? completedTasksWithAccuracyRating.reduce((sum, task) => sum + (task.accuracy_rating || 0), 0) / completedTasksWithAccuracyRating.length
-      : undefined;
-    
-    const tasksOverdue = userTasks.filter(task => 
-      task.status === 'OVERDUE' || 
-      (task.status !== 'COMPLETED' && new Date(task.due_date) < new Date())
-    ).length;
-    
+    const userTasks: ScoringTask[] = tasks
+      .filter(task => task.assignee_id === user.id)
+      .map(task => ({
+        status: task.status,
+        qualityRating: task.quality_rating,
+        timelinessRating: task.timeliness_rating,
+        effortRating: task.effort_rating,
+        accuracyRating: task.accuracy_rating,
+        actualTimeMinutes: task.actual_time_minutes,
+        dueDate: task.due_date,
+        completedAt: task.completed_at,
+        submissionDate: task.submission_date,
+      }));
+
+    const m = computeUserMetrics(userTasks, now);
+
     return {
       id: user.id,
       name: user.name,
       avatarUrl: user.avatar_url,
-      tasksCompleted,
-      avgCompletionTime,
-      avgQualityRating,
-      avgTimelinessRating,
-      avgEffortRating,
-      avgAccuracyRating,
-      tasksOverdue,
+      tasksCompleted: m.tasksCompleted,
+      avgCompletionTime: m.avgCompletionTime,
+      avgQualityRating: m.avgQualityRating,
+      avgTimelinessRating: m.avgTimelinessRating,
+      avgEffortRating: m.avgEffortRating,
+      avgAccuracyRating: m.avgAccuracyRating,
+      tasksOverdue: m.tasksOverdue,
+      perfectTasks: m.perfectTasks,
+      tasksOnTime: m.tasksOnTime,
+      fastestCompletionTime: m.fastestCompletionTime,
+      compositeScore: m.compositeScore,
       isFriend: friendIds.includes(user.id) || user.id === session.user.id
     };
   });
-  
-  // Sort leaderboard by tasks completed and quality rating
+
+  // Rank by composite score (quality-weighted), then completed volume.
   return leaderboardData.sort((a, b) => {
-    if (a.tasksCompleted !== b.tasksCompleted) {
-      return b.tasksCompleted - a.tasksCompleted;
-    }
-    
-    const aRating = a.avgQualityRating || 0;
-    const bRating = b.avgQualityRating || 0;
-    return bRating - aRating;
+    const aScore = a.compositeScore || 0;
+    const bScore = b.compositeScore || 0;
+    if (aScore !== bScore) return bScore - aScore;
+    return b.tasksCompleted - a.tasksCompleted;
   });
 };
 
diff --git a/src/lib/raceProgress.ts b/src/lib/raceProgress.ts
new file mode 100644
index 0000000..2d8fed4
--- /dev/null
+++ b/src/lib/raceProgress.ts
@@ -0,0 +1,58 @@
+/**
+ * Race-track progress (feature spec §2.4 US-8 / §3.3).
+ *
+ * Turns a user's tasks into checkpoint flags along the track and a car
+ * position that advances as tasks complete. Pure so the RaceTrack component
+ * can render real data and the mapping stays unit-testable. The name TaskLapp
+ * is "task lap" — completing tasks runs laps.
+ */
+import { Task, TaskStatus } from '../types';
+
+export interface RaceTaskPoint {
+  id: string;
+  title: string;
+  completed: boolean;
+  /** Position along the track, 0–100. */
+  position: number;
+}
+
+const TRACK_START = 15;
+const TRACK_END = 85;
+
+function isDone(task: Task): boolean {
+  return task.status === TaskStatus.COMPLETED || task.status === TaskStatus.GRADED;
+}
+
+/**
+ * Pick the tasks that make up the current lap and space them along the track.
+ * Prefers the soonest-due tasks; completed ones stay on the board so the lap
+ * reads as progress. Returns at most `max` checkpoints.
+ */
+export function computeRaceTasks(tasks: Task[], max = 6): RaceTaskPoint[] {
+  const sorted = [...tasks].sort(
+    (a, b) => new Date(a.dueDate).getTime() - new Date(b.dueDate).getTime(),
+  );
+  const lap = sorted.slice(0, max);
+  const span = TRACK_END - TRACK_START;
+
+  return lap.map((task, index) => ({
+    id: task.id,
+    title: task.title,
+    completed: isDone(task),
+    position:
+      lap.length === 1
+        ? (TRACK_START + TRACK_END) / 2
+        : Math.round(TRACK_START + (span * index) / (lap.length - 1)),
+  }));
+}
+
+/**
+ * Car position, 10–90, from the completion ratio of the current lap.
+ * Empty lap keeps the car at the start line.
+ */
+export function computeCarPosition(tasks: Task[]): number {
+  if (tasks.length === 0) return 10;
+  const done = tasks.filter(isDone).length;
+  const ratio = done / tasks.length;
+  return Math.round(10 + ratio * 80);
+}
diff --git a/src/lib/scoring.ts b/src/lib/scoring.ts
new file mode 100644
index 0000000..f3a92bf
--- /dev/null
+++ b/src/lib/scoring.ts
@@ -0,0 +1,183 @@
+/**
+ * Leaderboard scoring.
+ *
+ * Implements the composite score from the TaskLapp feature spec §3.3:
+ *
+ *   score = completed_tasks × avg_quality × on_time_rate
+ *           + PERFECT_BONUS per perfect (5/5 on all axes) task,
+ *           with a time decay so stale accounts fall off the board.
+ *
+ * All functions here are pure so they can be unit-tested without a database.
+ * `getLeaderboard()` in `lib/api/supabase.ts` feeds normalized rows into
+ * `computeUserMetrics` and reads `compositeScore` back for ranking.
+ */
+
+/** Minimal shape a task needs to be scored. Field names mirror the DB rows. */
+export interface ScoringTask {
+  status: string;
+  qualityRating?: number | null;
+  timelinessRating?: number | null;
+  effortRating?: number | null;
+  accuracyRating?: number | null;
+  actualTimeMinutes?: number | null;
+  dueDate?: string | Date | null;
+  completedAt?: string | Date | null;
+  submissionDate?: string | Date | null;
+}
+
+export interface UserMetrics {
+  tasksCompleted: number;
+  avgCompletionTime?: number;
+  avgQualityRating?: number;
+  avgTimelinessRating?: number;
+  avgEffortRating?: number;
+  avgAccuracyRating?: number;
+  tasksOverdue: number;
+  perfectTasks: number;
+  tasksOnTime: number;
+  fastestCompletionTime?: number;
+  onTimeRate: number;
+  compositeScore: number;
+}
+
+/** Bonus points added per perfect (5/5 on all four axes) task. */
+export const PERFECT_BONUS = 2;
+/**
+ * Quality multiplier used before a user has any graded work. Kept at 1.0 so
+ * ungraded completions count for something without out-ranking graded work.
+ */
+export const NEUTRAL_QUALITY = 1.0;
+/** Days of inactivity before decay starts biting. */
+export const DECAY_GRACE_DAYS = 7;
+/** Half-life (in days) of the staleness decay past the grace window. */
+export const DECAY_HALFLIFE_DAYS = 14;
+
+const MS_PER_DAY = 24 * 60 * 60 * 1000;
+
+function toDate(value?: string | Date | null): Date | null {
+  if (!value) return null;
+  const d = value instanceof Date ? value : new Date(value);
+  return isNaN(d.getTime()) ? null : d;
+}
+
+function avg(values: number[]): number | undefined {
+  if (values.length === 0) return undefined;
+  return values.reduce((sum, v) => sum + v, 0) / values.length;
+}
+
+/** A COMPLETED task and a GRADED task are both "done" — grading must not drop the count. */
+export function isCompleted(status: string): boolean {
+  return status === 'COMPLETED' || status === 'GRADED';
+}
+
+/** True when all four grading axes are a perfect 5. */
+export function isPerfect(task: ScoringTask): boolean {
+  return (
+    task.qualityRating === 5 &&
+    task.timelinessRating === 5 &&
+    task.effortRating === 5 &&
+    task.accuracyRating === 5
+  );
+}
+
+/**
+ * Decide whether a completed task landed on time. Prefer real dates
+ * (completion vs due). Fall back to the timeliness grade (>=3 = on time),
+ * then to a benefit-of-the-doubt "yes" when nothing is known.
+ */
+export function isOnTime(task: ScoringTask): boolean {
+  const due = toDate(task.dueDate);
+  const done = toDate(task.completedAt) ?? toDate(task.submissionDate);
+  if (due && done) return done.getTime() <= due.getTime();
+  if (task.timelinessRating != null) return task.timelinessRating >= 3;
+  return true;
+}
+
+/**
+ * Time-decay multiplier in (0, 1]. Full credit within the grace window,
+ * then halves every DECAY_HALFLIFE_DAYS of further inactivity.
+ */
+export function decayFactor(lastActivity: Date | null, now: Date): number {
+  if (!lastActivity) return 1;
+  const daysStale = (now.getTime() - lastActivity.getTime()) / MS_PER_DAY;
+  const over = daysStale - DECAY_GRACE_DAYS;
+  if (over <= 0) return 1;
+  return Math.pow(0.5, over / DECAY_HALFLIFE_DAYS);
+}
+
+/**
+ * Raw composite score from a set of metrics. Kept separate from
+ * `computeUserMetrics` so the formula can be tested and tuned in isolation.
+ */
+export function computeCompositeScore(
+  m: Pick<UserMetrics, 'tasksCompleted' | 'avgQualityRating' | 'onTimeRate' | 'perfectTasks'>,
+  decay = 1,
+): number {
+  const quality = m.avgQualityRating && m.avgQualityRating > 0 ? m.avgQualityRating : NEUTRAL_QUALITY;
+  const base = m.tasksCompleted * quality * m.onTimeRate + PERFECT_BONUS * m.perfectTasks;
+  return Math.round(base * decay * 100) / 100;
+}
+
+/**
+ * Roll a user's assignee tasks up into leaderboard metrics + composite score.
+ * `now` is injectable so tests are deterministic and the decay is reproducible.
+ */
+export function computeUserMetrics(tasks: ScoringTask[], now: Date = new Date()): UserMetrics {
+  const completed = tasks.filter((t) => isCompleted(t.status));
+
+  const completionTimes = completed
+    .map((t) => t.actualTimeMinutes)
+    .filter((v): v is number => v != null);
+
+  const qualityRatings = completed
+    .map((t) => t.qualityRating)
+    .filter((v): v is number => v != null);
+  const timelinessRatings = completed
+    .map((t) => t.timelinessRating)
+    .filter((v): v is number => v != null);
+  const effortRatings = completed
+    .map((t) => t.effortRating)
+    .filter((v): v is number => v != null);
+  const accuracyRatings = completed
+    .map((t) => t.accuracyRating)
+    .filter((v): v is number => v != null);
+
+  const perfectTasks = completed.filter(isPerfect).length;
+  const tasksOnTime = completed.filter(isOnTime).length;
+
+  const tasksOverdue = tasks.filter((t) => {
+    if (t.status === 'OVERDUE') return true;
+    if (isCompleted(t.status)) return false;
+    const due = toDate(t.dueDate);
+    return due != null && due.getTime() < now.getTime();
+  }).length;
+
+  const lastActivity = completed
+    .map((t) => toDate(t.completedAt) ?? toDate(t.submissionDate))
+    .filter((d): d is Date => d != null)
+    .sort((a, b) => b.getTime() - a.getTime())[0] ?? null;
+
+  const tasksCompleted = completed.length;
+  const onTimeRate = tasksCompleted > 0 ? tasksOnTime / tasksCompleted : 0;
+  const avgQualityRating = avg(qualityRatings);
+
+  const compositeScore = computeCompositeScore(
+    { tasksCompleted, avgQualityRating, onTimeRate, perfectTasks },
+    decayFactor(lastActivity, now),
+  );
+
+  return {
+    tasksCompleted,
+    avgCompletionTime: avg(completionTimes),
+    avgQualityRating,
+    avgTimelinessRating: avg(timelinessRatings),
+    avgEffortRating: avg(effortRatings),
+    avgAccuracyRating: avg(accuracyRatings),
+    tasksOverdue,
+    perfectTasks,
+    tasksOnTime,
+    fastestCompletionTime: completionTimes.length ? Math.min(...completionTimes) : undefined,
+    onTimeRate,
+    compositeScore,
+  };
+}
diff --git a/src/lib/taskFilters.ts b/src/lib/taskFilters.ts
new file mode 100644
index 0000000..0457883
--- /dev/null
+++ b/src/lib/taskFilters.ts
@@ -0,0 +1,80 @@
+/**
+ * Pure task filtering + search (feature spec §2.3 US-5).
+ *
+ * Filters combine with AND. Free-text search matches title and description
+ * case-insensitively. Overdue is computed (past due, not COMPLETED/GRADED).
+ * Kept dependency-free so the tasks page can filter client-side and so the
+ * behavior is unit-testable.
+ */
+import { Task, TaskStatus, TaskPriority } from '../types';
+
+export type StatusFilter = 'all' | 'active' | TaskStatus;
+export type PriorityFilter = 'all' | TaskPriority;
+
+export interface TaskFilterOptions {
+  /** Case-insensitive substring match over title + description. */
+  search?: string;
+  /** 'all', 'active' (PENDING|IN_PROGRESS), 'overdue', or a concrete status. */
+  status?: StatusFilter | 'overdue';
+  priority?: PriorityFilter;
+  assigneeId?: string;
+  assignerId?: string;
+  /** Only tasks due within this many days from `now` (future window). */
+  dueWithinDays?: number;
+  now?: Date;
+}
+
+/** A task is overdue when it is past due and not yet completed or graded. */
+export function isOverdue(task: Task, now: Date = new Date()): boolean {
+  return (
+    new Date(task.dueDate).getTime() < now.getTime() &&
+    task.status !== TaskStatus.COMPLETED &&
+    task.status !== TaskStatus.GRADED
+  );
+}
+
+function isActive(task: Task): boolean {
+  return task.status === TaskStatus.PENDING || task.status === TaskStatus.IN_PROGRESS;
+}
+
+function matchesSearch(task: Task, term: string): boolean {
+  const q = term.trim().toLowerCase();
+  if (!q) return true;
+  return (
+    task.title.toLowerCase().includes(q) ||
+    (task.description ?? '').toLowerCase().includes(q)
+  );
+}
+
+export function filterTasks(tasks: Task[], options: TaskFilterOptions = {}): Task[] {
+  const now = options.now ?? new Date();
+  const { search, status, priority, assigneeId, assignerId, dueWithinDays } = options;
+
+  return tasks.filter((task) => {
+    if (search && !matchesSearch(task, search)) return false;
+
+    if (status && status !== 'all') {
+      if (status === 'active' && !isActive(task)) return false;
+      if (status === 'overdue' && !isOverdue(task, now)) return false;
+      if (
+        status !== 'active' &&
+        status !== 'overdue' &&
+        task.status !== status
+      ) {
+        return false;
+      }
+    }
+
+    if (priority && priority !== 'all' && task.priority !== priority) return false;
+    if (assigneeId && task.assigneeId !== assigneeId) return false;
+    if (assignerId && task.assignerId !== assignerId) return false;
+
+    if (dueWithinDays != null) {
+      const cutoff = now.getTime() + dueWithinDays * 24 * 60 * 60 * 1000;
+      const due = new Date(task.dueDate).getTime();
+      if (due > cutoff) return false;
+    }
+
+    return true;
+  });
+}
diff --git a/src/types/index.ts b/src/types/index.ts
index 8089583..8b2452c 100644
--- a/src/types/index.ts
+++ b/src/types/index.ts
@@ -99,6 +99,7 @@ export interface LeaderboardEntry {
   perfectTasks?: number; // Number of tasks with perfect (5/5) ratings
   fastestCompletionTime?: number; // Fastest task completion time in minutes
   tasksOnTime?: number; // Number of tasks completed on time
+  compositeScore?: number; // Composite ranking score (spec §3.3)
 }
 
 export enum TaskStatus {
diff --git a/vitest.config.ts b/vitest.config.ts
new file mode 100644
index 0000000..3bfba84
--- /dev/null
+++ b/vitest.config.ts
@@ -0,0 +1,9 @@
+import { defineConfig } from 'vitest/config';
+
+export default defineConfig({
+  test: {
+    // Only run our unit tests for pure logic; exclude e2e/browser concerns.
+    include: ['src/**/__tests__/**/*.test.ts'],
+    environment: 'node',
+  },
+});