feat: sprints with burndown and carry-over

Plan sprints with dates and a goal, run one at a time per project, and
put tickets in them from the ticket page. The Sprints tab follows the one
under way with its progress and a burndown in tickets or points against
the ideal line. Closing a sprint sends what was left to the next one or
back to the backlog; the board can be filtered by sprint.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

libs/api/tracker/application/src/lib/analytics/analytics.ts

@@ -5,6 +5,8 @@ import {
   ProjectAnalyticsReadModel,
   ReleaseBurnupReadModel,
   ReleaseReadModel,
+  SprintBurndownReadModel,
+  SprintReadModel,
   StatusCategory,
   UserRefReadModel,
 } from '@task-stream/api/tracker/domain';
@@ -313,3 +315,85 @@ export function computeReleaseBurnup(
     done,
   };
 }
+
+export interface SprintBurndownInput {
+  sprint: SprintReadModel;
+  issues: IssueReadModel[];
+  timeline: IssueTimelineEntry[];
+  now: Date;
+}
+
+/**
+ * Per day of the sprint (start to end date, UTC): tickets in it, how many
+ * are still open and their points, and the ideal line. Points are today's
+ * estimates (their history is not kept). Days after today, or after the
+ * sprint closed, are null.
+ */
+export function computeSprintBurndown(
+  input: SprintBurndownInput,
+): SprintBurndownReadModel {
+  const { sprint } = input;
+  const steps = stepsByIssue(input.issues, input.timeline);
+  const points = new Map(input.issues.map((i) => [i.id, i.storyPoints ?? 0]));
+  const membership = new Map<
+    string,
+    { at: number; sprintId: string | null }[]
+  >();
+  for (const entry of input.timeline) {
+    if (entry.kind !== 'sprint') continue;
+    const list = membership.get(entry.issueId) ?? [];
+    list.push({ at: Date.parse(entry.at), sprintId: entry.sprintId ?? null });
+    membership.set(entry.issueId, list);
+  }
+  for (const list of membership.values()) list.sort((a, b) => a.at - b.at);
+
+  const start = Date.parse(`${sprint.startDate}T00:00:00Z`);
+  const end = Date.parse(`${sprint.endDate}T00:00:00Z`);
+  const last = Math.min(
+    sprint.closedAt ? Date.parse(sprint.closedAt) : input.now.getTime(),
+    end + DAY - 1,
+  );
+  const dayEnds = days(start, end + DAY - 1);
+  const scope: (number | null)[] = [];
+  const remaining: (number | null)[] = [];
+  const remainingPoints: (number | null)[] = [];
+  for (const time of dayEnds) {
+    // The day under way counts up to now; the ones to come are unknown.
+    const at = Math.min(time, last);
+    if (time - DAY >= last) {
+      scope.push(null);
+      remaining.push(null);
+      remainingPoints.push(null);
+      continue;
+    }
+    let inScope = 0;
+    let open = 0;
+    let openPoints = 0;
+    for (const [issueId, list] of membership) {
+      const current = list.filter((m) => m.at <= at).at(-1);
+      if (current?.sprintId !== sprint.id) continue;
+      const step = stepAt(steps.get(issueId) ?? [], at);
+      if (!step || step.category === StatusCategory.CANCELLED) continue;
+      inScope++;
+      if (step.category !== StatusCategory.DONE) {
+        open++;
+        openPoints += points.get(issueId) ?? 0;
+      }
+    }
+    scope.push(inScope);
+    remaining.push(open);
+    remainingPoints.push(openPoints);
+  }
+  const first = remaining[0] ?? 0;
+  const span = Math.max(dayEnds.length - 1, 1);
+  return {
+    sprintId: sprint.id,
+    dates: dayEnds.map(dayOf),
+    scope,
+    remaining,
+    remainingPoints,
+    ideal: dayEnds.map(
+      (_, i) => Math.round((first * (span - i) * 100) / span) / 100,
+    ),
+  };
+}