feat: Wave 1 complete — state machine, Paseo hub, collision detection, PTY search

- Task state machine: TIMED_OUT state, retriable steps, timeout detection
- Paseo hub: paseo-client.ts (HTTP+CLI), PaseoBackend (AgentBackend), 14 tests
- Collision detection: collision-detector.ts, conflict-index.ts, ws-frames type
- PTY search: ring buffer, search route, capture-pane fallback

apps/booterm/src/pty/registry.ts

@@ -33,6 +33,7 @@ export function register(
 
 export function unregister(paneId: string): void {
   sessions.delete(paneId);
+  ringBuffers.delete(paneId);
 }
 
 export function list(): SessionMeta[] {
@@ -42,3 +43,120 @@ export function list(): SessionMeta[] {
 export function get(paneId: string): SessionMeta | undefined {
   return sessions.get(paneId);
 }
+
+// ── Ring buffer for PTY output search ──────────────────────────────────────
+
+export interface SearchMatch {
+  line: number;
+  content: string;
+  contextBefore: string[];
+  contextAfter: string[];
+}
+
+const ringBuffers = new Map<string, string[]>();
+
+/**
+ * Append raw PTY data to the ring buffer for a given pane.
+ * Splits incoming data on newlines and pushes each line into the buffer,
+ * trimming to `maxLines` (default 5000) from the tail.
+ */
+export function appendOutput(
+  paneId: string,
+  data: string,
+  maxLines: number = 5000,
+): void {
+  let buf = ringBuffers.get(paneId);
+  if (!buf) {
+    buf = [];
+    ringBuffers.set(paneId, buf);
+  }
+
+  // Split on newlines — each chunk may contain multiple complete lines and
+  // potentially a trailing partial line (which we store as-is; the next chunk
+  // will either complete it or be another partial).
+  const lines = data.split('\n');
+
+  // The first element of `lines` may be a continuation of the last partial
+  // line from the previous append. If the buffer is non-empty and the last
+  // stored entry is a partial (no trailing newline previously), glue them.
+  // We detect "partial" by checking whether `data` ended with '\n' — if it
+  // did, the last element after split is '' (empty) which we drop.
+  const endedWithNewline = data.endsWith('\n');
+  if (endedWithNewline) {
+    // The final empty-string element is discarded.
+    lines.pop();
+  }
+
+  if (buf.length > 0 && lines.length > 0) {
+    // Concatenate the last partial line in the buffer with the first split
+    // segment. This avoids splitting ANSI sequences or text across chunks.
+    buf[buf.length - 1] = (buf[buf.length - 1] ?? '') + (lines[0] ?? '');
+    lines.shift();
+  }
+
+  for (const line of lines) {
+    buf.push(line);
+  }
+
+  // Trim from head if over maxLines
+  if (buf.length > maxLines) {
+    buf = buf.slice(buf.length - maxLines);
+    ringBuffers.set(paneId, buf);
+  }
+}
+
+/**
+ * Search the ring buffer for a pane using a regex pattern.
+ * Returns matches with optional context lines before and after each match.
+ */
+export function searchRingBuffer(
+  paneId: string,
+  pattern: string,
+  opts?: { limit?: number; context?: number },
+): SearchMatch[] {
+  const buf = ringBuffers.get(paneId);
+  if (!buf || buf.length === 0) return [];
+
+  const limit = opts?.limit ?? 50;
+  const context = opts?.context ?? 0;
+
+  let re: RegExp;
+  try {
+    re = new RegExp(pattern, 'u');
+  } catch {
+    return []; // invalid regex — caller should validate, but be defensive
+  }
+
+  const results: SearchMatch[] = [];
+
+  for (let i = 0; i < buf.length; i++) {
+    if (results.length >= limit) break;
+    if (re.test(buf[i]!)) {
+      const contextBefore: string[] = [];
+      const contextAfter: string[] = [];
+      for (let c = 1; c <= context; c++) {
+        const ci = i - c;
+        if (ci >= 0) contextBefore.unshift(buf[ci]!);
+      }
+      for (let c = 1; c <= context; c++) {
+        const ci = i + c;
+        if (ci < buf.length) contextAfter.push(buf[ci]!);
+      }
+      results.push({
+        line: i + 1, // 1-based line number for display
+        content: buf[i]!,
+        contextBefore,
+        contextAfter,
+      });
+    }
+  }
+
+  return results;
+}
+
+/**
+ * Remove the ring buffer for a pane. Called on session kill / pane close.
+ */
+export function clearBuffer(paneId: string): void {
+  ringBuffers.delete(paneId);
+}