feat: add start_time/end_time to session files for correlation

Add session boundary timestamps to enable correlating context entries
to sessions by time overlap:

- Manual saves (ctx session save): Include start_time and end_time in
  YYYY-MM-DD-HHMM format, using CTX_SESSION_START env var if available
- Auto-saves (SessionEnd hook): Extract start_time from transcript's
  first entry timestamp, add end_time as current time

These timestamps match the format used by ctx add, enabling agents to
determine which session added a learning/decision/task by checking if
its timestamp falls within the session's time bounds.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

Author: josealekhine

.context/TASKS.md

@@ -134,8 +134,8 @@
 - [x] Add timestamp to formatTask() in add.go — currently tasks have no timestamp, add `#added:YYYY-MM-DD-HHMM` or similar
 - [x] Increase timestamp precision in formatLearning() — change from YYYY-MM-DD to YYYY-MM-DD-HHMM
 - [x] Increase timestamp precision in formatDecision() — change from YYYY-MM-DD to YYYY-MM-DD-HHMM
-- [ ] Add start_time field to session summary files — record when session began
-- [ ] Add last_update_time field to session summary files — update on each ctx add call during session
+- [x] Add start_time field to session summary files — record when session began
+- [-] Add last_update_time field to session summary files — skipped: end_time provides session bounds; tracking live updates requires state persistence
 - [ ] Document timestamp correlation approach in AGENT_PLAYBOOK.md — explain how to correlate entries to sessions by time overlap
 
 ### Phase 13: Rich Context Entries `#priority:medium` `#area:cli`

internal/claude/tpl/auto-save-session.sh

@@ -37,6 +37,24 @@ FILENAME="$SESSIONS_DIR/${TIMESTAMP}-session-${REASON}.jsonl"
 # Copy the transcript
 cp "$TRANSCRIPT_PATH" "$FILENAME"
 
+# Extract session start time from transcript (first entry timestamp) if possible
+START_TIME=""
+if [ -f "$TRANSCRIPT_PATH" ]; then
+    # Try to get timestamp from first line of transcript
+    FIRST_TS=$(head -1 "$TRANSCRIPT_PATH" | jq -r '.timestamp // empty' 2>/dev/null)
+    if [ -n "$FIRST_TS" ]; then
+        # Convert to YYYY-MM-DD-HHMM format
+        START_TIME=$(date -d "$FIRST_TS" +%Y-%m-%d-%H%M 2>/dev/null || echo "")
+    fi
+fi
+
+# Fall back to current time if we couldn't extract start time
+if [ -z "$START_TIME" ]; then
+    START_TIME=$(date +%Y-%m-%d-%H%M)
+fi
+
+END_TIME=$(date +%Y-%m-%d-%H%M)
+
 # Also create a human-readable summary
 SUMMARY_FILE="$SESSIONS_DIR/${TIMESTAMP}-session-${REASON}-summary.md"
 cat > "$SUMMARY_FILE" << EOF
@@ -46,6 +64,8 @@ cat > "$SUMMARY_FILE" << EOF
 **Reason**: $REASON
 **Session ID**: $SESSION_ID
 **Transcript**: ${TIMESTAMP}-session-${REASON}.jsonl
+**start_time**: $START_TIME
+**end_time**: $END_TIME
 
 This session was auto-saved by the SessionEnd hook.
 To analyze the full transcript, read the .jsonl file.

internal/cli/session.go

@@ -680,11 +680,22 @@ func sanitizeFilename(s string) string {
 func buildSessionContent(topic, sessionType string, timestamp time.Time) (string, error) {
 	var sb strings.Builder
 
-	// Header
+	// Header with timestamp fields for session correlation
 	sb.WriteString(fmt.Sprintf("# Session: %s\n\n", topic))
 	sb.WriteString(fmt.Sprintf("**Date**: %s\n", timestamp.Format("2006-01-02")))
 	sb.WriteString(fmt.Sprintf("**Time**: %s\n", timestamp.Format("15:04:05")))
 	sb.WriteString(fmt.Sprintf("**Type**: %s\n", sessionType))
+
+	// Session correlation timestamps (YYYY-MM-DD-HHMM format matches ctx add timestamps)
+	// start_time: When session began (use CTX_SESSION_START env var if available, else save time)
+	startTime := timestamp
+	if envStart := os.Getenv("CTX_SESSION_START"); envStart != "" {
+		if parsed, err := time.Parse("2006-01-02-1504", envStart); err == nil {
+			startTime = parsed
+		}
+	}
+	sb.WriteString(fmt.Sprintf("**start_time**: %s\n", startTime.Format("2006-01-02-1504")))
+	sb.WriteString(fmt.Sprintf("**end_time**: %s\n", timestamp.Format("2006-01-02-1504")))
 	sb.WriteString("\n---\n\n")
 
 	// Summary section (placeholder for the user to fill in)