diff --git a/web/src/matcher.test.ts b/web/src/matcher.test.ts
new file mode 100644
index 0000000..094c089
--- /dev/null
+++ b/web/src/matcher.test.ts
@@ -0,0 +1,201 @@
+import { describe, expect, it } from "vitest";
+
+import {
+  matchAndRank,
+  type CommandCandidate,
+  type DirectoryCandidate,
+  type MatchCandidate,
+  type MatchResult,
+  type SessionCandidate,
+} from "./matcher.js";
+
+function session(
+  name: string,
+  directory?: string,
+  command?: string,
+  tool?: string,
+): SessionCandidate {
+  return { kind: "session", fields: { name, directory, command, tool } };
+}
+
+function command(label: string): CommandCandidate {
+  return { kind: "command", fields: { label } };
+}
+
+function directory(path: string): DirectoryCandidate {
+  return { kind: "directory", fields: { path } };
+}
+
+function label(result: MatchResult): string {
+  switch (result.candidate.kind) {
+    case "session":
+      return `session:${result.candidate.fields.name}`;
+    case "command":
+      return `command:${result.candidate.fields.label}`;
+    case "directory":
+      return `directory:${result.candidate.fields.path}`;
+  }
+}
+
+function positions(result: MatchResult): number[] {
+  return result.ranges.flatMap(([start, end]) =>
+    Array.from({ length: end - start }, (_, offset) => start + offset),
+  );
+}
+
+function expectResults(
+  query: string,
+  candidates: MatchCandidate[],
+  expected: Array<[label: string, score: number, field?: string, positions?: number[]]>,
+): void {
+  const results = matchAndRank(query, candidates);
+
+  expect(results.map((result) => [label(result), result.score])).toEqual(
+    expected.map(([candidateLabel, score]) => [candidateLabel, score]),
+  );
+  expect(results.map((result) => result.field)).toEqual(
+    expected.map(([, , field]) => field),
+  );
+  expect(results.map(positions)).toEqual(expected.map(([, , , matched]) => matched ?? []));
+}
+
+describe("matchAndRank fixtures", () => {
+  it("F1: an empty query keeps input order", () => {
+    expectResults(
+      "",
+      [
+        session("kill", "~/dev/api", "bash"),
+        session("killer-app", "~/dev/killer-app", "claude --resume", "claude"),
+        command("Kill selected session"),
+      ],
+      [
+        ["session:kill", 0],
+        ["session:killer-app", 0],
+        ["command:Kill selected session", 0],
+      ],
+    );
+  });
+
+  it("F2: an exact session name beats a prefix and kind breaks a tie", () => {
+    expectResults(
+      "kill",
+      [
+        session("kill", "~/dev/api", "bash"),
+        session("killer-app", "~/dev/killer-app", "claude --resume", "claude"),
+        command("Kill selected session"),
+      ],
+      [
+        ["session:kill", 178, "name", [0, 1, 2, 3]],
+        ["session:killer-app", 146, "name", [0, 1, 2, 3]],
+        ["command:Kill selected session", 146, "label", [0, 1, 2, 3]],
+      ],
+    );
+  });
+
+  it("F3: path segment boundaries beat mid-segment matches", () => {
+    expectResults(
+      "foo",
+      [directory("~/dev/foobar"), directory("~/src/myfoo"), directory("~/foo")],
+      [
+        ["directory:~/foo", 78, "path", [2, 3, 4]],
+        ["directory:~/dev/foobar", 74, "path", [6, 7, 8]],
+        ["directory:~/src/myfoo", 56, "path", [8, 9, 10]],
+      ],
+    );
+  });
+
+  it("F4: a query matching nothing returns no candidates", () => {
+    expectResults("zzz", [session("kill", "~/dev/api", "bash"), command("Kill selected session")], []);
+  });
+
+  it("F5: the highest-scoring embedding can differ from the greedy embedding", () => {
+    expectResults(
+      "mtu",
+      [session("maestro-tui"), session("maestro-daemon"), session("mtui-scratch")],
+      [
+        ["session:mtui-scratch", 122, "name", [0, 1, 2]],
+        ["session:maestro-tui", 91, "name", [0, 8, 9]],
+      ],
+    );
+  });
+
+  it("F6: a name beats a weighted directory match", () => {
+    expectResults(
+      "api",
+      [session("api", "~/dev/web", "bash"), session("worker", "~/dev/api", "bash")],
+      [
+        ["session:api", 154, "name", [0, 1, 2]],
+        ["session:worker", 50, "directory", [6, 7, 8]],
+      ],
+    );
+  });
+
+  it("F7: matching is case-insensitive and field length breaks a tie", () => {
+    expectResults(
+      "api",
+      [session("API-Gateway"), session("apiary")],
+      [
+        ["session:apiary", 122, "name", [0, 1, 2]],
+        ["session:API-Gateway", 122, "name", [0, 1, 2]],
+      ],
+    );
+  });
+
+  it("F8: the exact tool field beats the command field", () => {
+    expectResults(
+      "claude",
+      [session("nameless", "~/dev/x", "claude --resume", "claude"), session("clay", "~/dev/y", "bash")],
+      [["session:nameless", 186, "tool", [0, 1, 2, 3, 4, 5]]],
+    );
+  });
+
+  it("F9: a separator earns a word-boundary bonus", () => {
+    expectResults(
+      "ws",
+      [session("websearch"), session("web-search")],
+      [
+        ["session:web-search", 71, "name", [0, 4]],
+        ["session:websearch", 56, "name", [0, 3]],
+      ],
+    );
+  });
+
+  it("F10: command labels rank by boundary and initial gap", () => {
+    expectResults(
+      "se",
+      [command("Kill selected session"), command("Create a session"), command("Show help")],
+      [
+        ["command:Show help", 53, "label", [0, 6]],
+        ["command:Kill selected session", 51, "label", [5, 6]],
+        ["command:Create a session", 47, "label", [9, 10]],
+      ],
+    );
+  });
+
+  it("F11: directory matches separate on their initial gap", () => {
+    expectResults(
+      "dev",
+      [
+        session("api", "~/dev/api", "bash"),
+        session("notes", "~/documents/dev-notes", "nvim"),
+        session("scratch", "~/srv/devops", "bash"),
+      ],
+      [
+        ["session:api", 54, "directory", [2, 3, 4]],
+        ["session:scratch", 50, "directory", [6, 7, 8]],
+        ["session:notes", 44, "directory", [12, 13, 14]],
+      ],
+    );
+  });
+
+  it("F12: an exact field beats a prefix", () => {
+    expectResults(
+      "quit",
+      [command("Quit Maestro"), command("Quit")],
+      [
+        ["command:Quit", 178, "label", [0, 1, 2, 3]],
+        ["command:Quit Maestro", 146, "label", [0, 1, 2, 3]],
+      ],
+    );
+  });
+});
diff --git a/web/src/matcher.ts b/web/src/matcher.ts
new file mode 100644
index 0000000..00adb5c
--- /dev/null
+++ b/web/src/matcher.ts
@@ -0,0 +1,224 @@
+export type CandidateKind = "session" | "command" | "directory";
+
+export interface SessionCandidate {
+  kind: "session";
+  fields: {
+    name: string;
+    directory?: string;
+    command?: string;
+    tool?: string;
+  };
+}
+
+export interface CommandCandidate {
+  kind: "command";
+  fields: { label: string };
+}
+
+export interface DirectoryCandidate {
+  kind: "directory";
+  fields: { path: string };
+}
+
+export type MatchCandidate = SessionCandidate | CommandCandidate | DirectoryCandidate;
+export type MatchFieldName = "name" | "directory" | "command" | "tool" | "label" | "path";
+export type MatchRange = readonly [start: number, end: number];
+
+export interface MatchResult<C extends MatchCandidate = MatchCandidate> {
+  candidate: C;
+  score: number;
+  field: MatchFieldName | undefined;
+  ranges: MatchRange[];
+}
+
+interface Field {
+  name: MatchFieldName;
+  text: string;
+  weight: number;
+}
+
+interface Embedding {
+  score: number;
+  positions: number[];
+}
+
+interface RankedResult<C extends MatchCandidate> extends MatchResult<C> {
+  matchedText: string;
+  inputIndex: number;
+}
+
+const KIND_ORDER: Record<CandidateKind, number> = {
+  session: 0,
+  command: 1,
+  directory: 2,
+};
+
+function fields(candidate: MatchCandidate): Field[] {
+  switch (candidate.kind) {
+    case "session": {
+      const values: Array<[MatchFieldName, string | undefined, number]> = [
+        ["name", candidate.fields.name, 0],
+        ["directory", candidate.fields.directory, -24],
+        ["command", candidate.fields.command, -32],
+        ["tool", candidate.fields.tool, -40],
+      ];
+      return values.flatMap(([name, text, weight]) =>
+        text === undefined ? [] : [{ name, text, weight }],
+      );
+    }
+    case "command":
+      return [{ name: "label", text: candidate.fields.label, weight: 0 }];
+    case "directory":
+      return [{ name: "path", text: candidate.fields.path, weight: 0 }];
+  }
+}
+
+function normalizeQuery(query: string): string {
+  return query.toLowerCase().replace(/\s/g, "");
+}
+
+function boundaryBonus(text: string, position: number): number {
+  if (position === 0) return 18;
+
+  const previous = text[position - 1];
+  if ("/\\-_ .:".includes(previous)) return 16;
+
+  const current = text[position];
+  const isUppercase = current !== current.toLowerCase() && current === current.toUpperCase();
+  const previousIsLowercase =
+    previous !== previous.toUpperCase() && previous === previous.toLowerCase();
+  if (isUppercase && previousIsLowercase) return 12;
+
+  const isDigit = current >= "0" && current <= "9";
+  const previousIsDigit = previous >= "0" && previous <= "9";
+  if (isDigit && !previousIsDigit) return 12;
+
+  return 0;
+}
+
+function contribution(text: string, position: number, previousPosition: number): number {
+  const gap = position - previousPosition - 1;
+  return 16 + boundaryBonus(text, position) + (gap === 0 ? 8 : -Math.min(gap, 12));
+}
+
+function isBetterEmbedding(candidate: Embedding, incumbent: Embedding | undefined): boolean {
+  if (!incumbent || candidate.score !== incumbent.score) {
+    return !incumbent || candidate.score > incumbent.score;
+  }
+  for (let index = 0; index < candidate.positions.length; index++) {
+    if (candidate.positions[index] !== incumbent.positions[index]) {
+      return candidate.positions[index] < incumbent.positions[index];
+    }
+  }
+  return false;
+}
+
+function bestEmbedding(query: string, text: string): Embedding | undefined {
+  const lowerText = text.toLowerCase();
+  let previousStates = new Map<number, Embedding>();
+
+  for (let queryIndex = 0; queryIndex < query.length; queryIndex++) {
+    const states = new Map<number, Embedding>();
+    for (let position = 0; position < lowerText.length; position++) {
+      if (lowerText[position] !== query[queryIndex]) continue;
+
+      if (queryIndex === 0) {
+        states.set(position, {
+          score: contribution(text, position, -1),
+          positions: [position],
+        });
+        continue;
+      }
+
+      for (const [previousPosition, previous] of previousStates) {
+        if (previousPosition >= position) continue;
+        const candidate = {
+          score: previous.score + contribution(text, position, previousPosition),
+          positions: [...previous.positions, position],
+        };
+        if (isBetterEmbedding(candidate, states.get(position))) states.set(position, candidate);
+      }
+    }
+    if (states.size === 0) return undefined;
+    previousStates = states;
+  }
+
+  let best: Embedding | undefined;
+  for (const embedding of previousStates.values()) {
+    if (isBetterEmbedding(embedding, best)) best = embedding;
+  }
+  return best;
+}
+
+function toRanges(positions: number[]): MatchRange[] {
+  const ranges: MatchRange[] = [];
+  for (const position of positions) {
+    const previous = ranges[ranges.length - 1];
+    if (previous && previous[1] === position) {
+      ranges[ranges.length - 1] = [previous[0], position + 1];
+    } else {
+      ranges.push([position, position + 1]);
+    }
+  }
+  return ranges;
+}
+
+function compareByCodePoint(left: string, right: string): number {
+  const leftPoints = Array.from(left, (character) => character.codePointAt(0)!);
+  const rightPoints = Array.from(right, (character) => character.codePointAt(0)!);
+  const length = Math.min(leftPoints.length, rightPoints.length);
+  for (let index = 0; index < length; index++) {
+    if (leftPoints[index] !== rightPoints[index]) return leftPoints[index] - rightPoints[index];
+  }
+  return leftPoints.length - rightPoints.length;
+}
+
+export function matchAndRank<C extends MatchCandidate>(
+  query: string,
+  candidates: readonly C[],
+): MatchResult<C>[] {
+  const normalizedQuery = normalizeQuery(query);
+  if (normalizedQuery === "") {
+    return candidates.map((candidate) => ({ candidate, score: 0, field: undefined, ranges: [] }));
+  }
+
+  const results: RankedResult<C>[] = [];
+  candidates.forEach((candidate, inputIndex) => {
+    let best:
+      | { field: Field; score: number; positions: number[] }
+      | undefined;
+
+    for (const field of fields(candidate)) {
+      const embedding = bestEmbedding(normalizedQuery, field.text);
+      if (!embedding) continue;
+
+      const compactText = field.text.toLowerCase().replace(/\s/g, "");
+      const adjustment =
+        compactText === normalizedQuery ? 64 : compactText.startsWith(normalizedQuery) ? 32 : 0;
+      const score = embedding.score + adjustment + field.weight;
+      if (!best || score > best.score) best = { field, score, positions: embedding.positions };
+    }
+
+    if (best) {
+      results.push({
+        candidate,
+        score: best.score,
+        field: best.field.name,
+        ranges: toRanges(best.positions),
+        matchedText: best.field.text,
+        inputIndex,
+      });
+    }
+  });
+
+  results.sort(
+    (left, right) =>
+      right.score - left.score ||
+      KIND_ORDER[left.candidate.kind] - KIND_ORDER[right.candidate.kind] ||
+      left.matchedText.length - right.matchedText.length ||
+      compareByCodePoint(left.matchedText, right.matchedText) ||
+      left.inputIndex - right.inputIndex,
+  );
+
+  return results.map(({ candidate, score, field, ranges }) => ({ candidate, score, field, ranges }));
+}