feat(documents): add timeline helpers (boundary + gap-fill) (#385)

Pure utilities backing the TimelineDensityFilter component:
- monthBoundaryFrom/To convert YYYY-MM into LocalDate strings the existing
  /api/documents/search accepts (first/last day of the month).
- buildMonthSequence enumerates months between minDate and maxDate, crossing
  year boundaries.
- fillDensityGaps merges sparse backend buckets with the full month sequence,
  producing zero-count entries for months that the API omitted.

14 unit tests cover leap years, year boundaries, null inputs, and out-of-order
buckets.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/src/lib/document/timeline.spec.ts

@@ -0,0 +1,108 @@
+import { describe, it, expect } from 'vitest';
+import {
+	monthBoundaryFrom,
+	monthBoundaryTo,
+	buildMonthSequence,
+	fillDensityGaps
+} from './timeline';
+
+describe('monthBoundaryFrom', () => {
+	it('returns the first day of the given month', () => {
+		expect(monthBoundaryFrom('1915-08')).toBe('1915-08-01');
+	});
+
+	it('handles January', () => {
+		expect(monthBoundaryFrom('1920-01')).toBe('1920-01-01');
+	});
+});
+
+describe('monthBoundaryTo', () => {
+	it('returns the last day of a 31-day month', () => {
+		expect(monthBoundaryTo('1915-08')).toBe('1915-08-31');
+	});
+
+	it('returns the last day of a 30-day month', () => {
+		expect(monthBoundaryTo('1915-04')).toBe('1915-04-30');
+	});
+
+	it('returns 28 for February in a non-leap year', () => {
+		expect(monthBoundaryTo('1915-02')).toBe('1915-02-28');
+	});
+
+	it('returns 29 for February in a leap year', () => {
+		expect(monthBoundaryTo('1916-02')).toBe('1916-02-29');
+	});
+});
+
+describe('buildMonthSequence', () => {
+	it('returns a single month when min and max are in the same month', () => {
+		expect(buildMonthSequence('1915-08-03', '1915-08-22')).toEqual(['1915-08']);
+	});
+
+	it('returns months from minDate through maxDate inclusive', () => {
+		expect(buildMonthSequence('1915-08-03', '1915-11-15')).toEqual([
+			'1915-08',
+			'1915-09',
+			'1915-10',
+			'1915-11'
+		]);
+	});
+
+	it('crosses year boundaries correctly', () => {
+		expect(buildMonthSequence('1915-11-30', '1916-02-01')).toEqual([
+			'1915-11',
+			'1915-12',
+			'1916-01',
+			'1916-02'
+		]);
+	});
+
+	it('returns empty array when minDate or maxDate is null', () => {
+		expect(buildMonthSequence(null, '1915-08-01')).toEqual([]);
+		expect(buildMonthSequence('1915-08-01', null)).toEqual([]);
+		expect(buildMonthSequence(null, null)).toEqual([]);
+	});
+});
+
+describe('fillDensityGaps', () => {
+	it('returns empty array when minDate or maxDate is null', () => {
+		expect(fillDensityGaps([], null, null)).toEqual([]);
+	});
+
+	it('preserves existing buckets and adds zero-count buckets for missing months', () => {
+		const buckets = [
+			{ month: '1915-08', count: 5 },
+			{ month: '1915-11', count: 2 }
+		];
+
+		const result = fillDensityGaps(buckets, '1915-08-03', '1915-11-30');
+
+		expect(result).toEqual([
+			{ month: '1915-08', count: 5 },
+			{ month: '1915-09', count: 0 },
+			{ month: '1915-10', count: 0 },
+			{ month: '1915-11', count: 2 }
+		]);
+	});
+
+	it('returns all-zero sequence when buckets array is empty', () => {
+		const result = fillDensityGaps([], '1915-08-03', '1915-10-15');
+
+		expect(result).toEqual([
+			{ month: '1915-08', count: 0 },
+			{ month: '1915-09', count: 0 },
+			{ month: '1915-10', count: 0 }
+		]);
+	});
+
+	it('keeps results sorted chronologically even when buckets arrive out of order', () => {
+		const buckets = [
+			{ month: '1915-10', count: 3 },
+			{ month: '1915-08', count: 1 }
+		];
+
+		const result = fillDensityGaps(buckets, '1915-08-01', '1915-10-31');
+
+		expect(result.map((b) => b.month)).toEqual(['1915-08', '1915-09', '1915-10']);
+	});
+});

frontend/src/lib/document/timeline.ts

@@ -0,0 +1,47 @@
+import type { components } from '$lib/generated/api';
+
+type MonthBucket = components['schemas']['MonthBucket'];
+
+export function monthBoundaryFrom(yearMonth: string): string {
+	return `${yearMonth}-01`;
+}
+
+export function monthBoundaryTo(yearMonth: string): string {
+	const [year, month] = yearMonth.split('-').map(Number);
+	const lastDay = new Date(Date.UTC(year, month, 0)).getUTCDate();
+	return `${yearMonth}-${String(lastDay).padStart(2, '0')}`;
+}
+
+export function buildMonthSequence(minDate: string | null, maxDate: string | null): string[] {
+	if (!minDate || !maxDate) return [];
+
+	const [minY, minM] = minDate.split('-').map(Number);
+	const [maxY, maxM] = maxDate.split('-').map(Number);
+
+	const sequence: string[] = [];
+	let year = minY;
+	let month = minM;
+
+	while (year < maxY || (year === maxY && month <= maxM)) {
+		sequence.push(`${year}-${String(month).padStart(2, '0')}`);
+		month += 1;
+		if (month > 12) {
+			month = 1;
+			year += 1;
+		}
+	}
+
+	return sequence;
+}
+
+export function fillDensityGaps(
+	buckets: MonthBucket[],
+	minDate: string | null,
+	maxDate: string | null
+): MonthBucket[] {
+	const sequence = buildMonthSequence(minDate, maxDate);
+	if (sequence.length === 0) return [];
+
+	const counts = new Map(buckets.map((b) => [b.month, b.count]));
+	return sequence.map((month) => ({ month, count: counts.get(month) ?? 0 }));
+}