feat(web): multiple-choice — explanation-Feld, Edit-Bug-Fix, State-Reset

- MultipleChoiceCardForm: optionales `explanation`-Feld (Erklärung wird
  nach Auswahl angezeigt); `field-optional`-Style ergänzt
- MultipleChoiceView: `explanation`-Prop; zeigt Erklärungsbox nach
  Auswahl (grün bei richtig, neutral bei falsch); `{#key card_id}`-Block
  erzwingt Remount bei Kartenwechsel — behebt State-Leak zwischen Karten
- edit/+page.svelte: MC-Edit-Bug behoben — Karten wurden fälschlich mit
  `{front, back}` gespeichert und haben `answer`/`distractor_pool`
  überschrieben; `MultipleChoiceCardForm` importiert und verdrahtet;
  `canSave` und `onSubmit` handhaben MC korrekt; lädt `answer` +
  `distractor_pool` beim Öffnen zurück in `mcOptions`-Array
- new/+page.svelte: `mcExplanation`-State an Form gebunden und beim
  Speichern als `fields.explanation` gesetzt
- study/+page.svelte: `explanation` aus Card-Fields extrahiert und
  an MultipleChoiceView durchgereicht
- scripts/migrate-factfulness-to-mc.ts: einmalige Migration — 13
  Factfulness-Quiz-Karten von `basic` (A/B/C in Freitext) auf
  `multiple-choice` mit strukturierten Feldern konvertiert; Deck auf
  `visibility=public` gesetzt

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

apps/web/src/lib/components/MultipleChoiceCardForm.svelte

@@ -5,10 +5,12 @@
 		front = $bindable(),
 		mcOptions = $bindable(),
 		mcCorrectIdx = $bindable(),
+		mcExplanation = $bindable(''),
 	}: {
 		front: string;
 		mcOptions: string[];
 		mcCorrectIdx: number;
+		mcExplanation: string;
 	} = $props();
 </script>
 
@@ -59,6 +61,17 @@
 	</div>
 </div>
 
+<div class="field">
+	<span class="field-label">Erklärung <span class="field-optional">(optional)</span></span>
+	<span class="field-hint">Wird nach der Auswahl angezeigt — erklärt warum die Antwort richtig ist.</span>
+	<textarea
+		bind:value={mcExplanation}
+		rows="3"
+		placeholder="z.B. Weil … / Hintergrund: …"
+		class="input"
+	></textarea>
+</div>
+
 <style>
 	.field {
 		display: flex;
@@ -73,6 +86,11 @@
 		letter-spacing: 0.01em;
 	}
 
+	.field-optional {
+		font-weight: 400;
+		color: hsl(var(--color-muted-foreground));
+	}
+
 	.field-hint {
 		font-size: 0.75rem;
 		color: hsl(var(--color-muted-foreground));

apps/web/src/lib/components/MultipleChoiceView.svelte

@@ -7,6 +7,7 @@
 		promptHtml,
 		answer,
 		distractorPool,
+		explanation,
 		deckId,
 		cardId,
 		ongrade,
@@ -14,6 +15,7 @@
 		promptHtml: string;
 		answer: string;
 		distractorPool?: string;
+		explanation?: string;
 		deckId: string;
 		cardId: string;
 		ongrade: (r: Rating) => void;
@@ -146,6 +148,13 @@
 			{/each}
 		</div>
 
+		{#if selected !== null && explanation}
+			<div class="explanation" class:explanation-correct={correct} class:explanation-wrong={!correct}>
+				<span class="explanation-label">{correct ? '✓' : 'ℹ'}</span>
+				<p class="explanation-text">{explanation}</p>
+			</div>
+		{/if}
+
 		{#if selected !== null}
 			<button class="confirm-btn" onclick={confirm}>
 				{correct ? 'Weiter' : 'Verstanden'} <kbd>Space</kbd>
@@ -295,6 +304,38 @@
 	.option-correct .option-icon { color: hsl(var(--color-success)); }
 	.option-wrong .option-icon { color: hsl(var(--color-error)); }
 
+	.explanation {
+		display: flex;
+		gap: 0.5rem;
+		padding: 0.625rem 0.75rem;
+		border-radius: 0.5rem;
+		border: 1px solid hsl(var(--color-border));
+		background: hsl(var(--color-surface));
+	}
+	.explanation-correct {
+		background: hsl(var(--color-success) / 0.08);
+		border-color: hsl(var(--color-success) / 0.4);
+	}
+	.explanation-wrong {
+		background: hsl(var(--color-muted) / 0.5);
+	}
+	.explanation-label {
+		flex-shrink: 0;
+		font-size: 0.75rem;
+		font-weight: 600;
+		color: hsl(var(--color-muted-foreground));
+		padding-top: 0.125rem;
+	}
+	.explanation-correct .explanation-label {
+		color: hsl(var(--color-success));
+	}
+	.explanation-text {
+		margin: 0;
+		font-size: 0.875rem;
+		line-height: 1.5;
+		color: hsl(var(--color-foreground));
+	}
+
 	.confirm-btn {
 		align-self: center;
 		display: inline-flex;

apps/web/src/routes/cards/[id]/edit/+page.svelte

@@ -16,6 +16,7 @@
 	import { toasts } from '$lib/stores/toasts.svelte.ts';
 	import { t } from '$lib/i18n/index.svelte.ts';
 	import ImageOcclusionEditor from '$lib/components/ImageOcclusionEditor.svelte';
+	import MultipleChoiceCardForm from '$lib/components/MultipleChoiceCardForm.svelte';
 
 	let card = $state<Card | null>(null);
 	let cardType = $state<CardType>('basic');
@@ -25,6 +26,9 @@
 	let extra = $state('');
 	let imageRef = $state('');
 	let maskRegionsJson = $state('[]');
+	let mcOptions = $state(['', '', '', '']);
+	let mcCorrectIdx = $state(0);
+	let mcExplanation = $state('');
 	let loading = $state(true);
 	let saving = $state(false);
 	let error = $state<string | null>(null);
@@ -56,6 +60,14 @@
 			} else if (c.type === 'image-occlusion') {
 				imageRef = fields.image_ref ?? '';
 				maskRegionsJson = fields.mask_regions ?? '[]';
+			} else if (c.type === 'multiple-choice') {
+				front = fields.front ?? '';
+				const answer = fields.answer ?? '';
+				const pool = fields.distractor_pool ?? '';
+				const distractors = pool.split('\n').map((s) => s.trim()).filter((s) => s);
+				mcOptions = [answer, ...distractors, '', '', ''].slice(0, 4);
+				mcCorrectIdx = 0;
+				mcExplanation = fields.explanation ?? '';
 			} else {
 				front = fields.front ?? '';
 				back = fields.back ?? '';
@@ -71,11 +83,11 @@
 
 	const canSave = $derived.by(() => {
 		if (saving) return false;
-		if (cardType === 'cloze') {
-			return text.trim().length > 0 && clusterIds.length > 0;
-		}
-		if (cardType === 'image-occlusion') {
-			return imageRef.length > 0 && maskCount > 0;
+		if (cardType === 'cloze') return text.trim().length > 0 && clusterIds.length > 0;
+		if (cardType === 'image-occlusion') return imageRef.length > 0 && maskCount > 0;
+		if (cardType === 'multiple-choice') {
+			const filledCount = mcOptions.filter((o) => o.trim()).length;
+			return front.trim().length > 0 && mcOptions[mcCorrectIdx].trim().length > 0 && filledCount >= 2;
 		}
 		return front.trim().length > 0 && back.trim().length > 0;
 	});
@@ -92,6 +104,14 @@
 					: { text: text.trim() };
 			} else if (cardType === 'image-occlusion') {
 				fields = { image_ref: imageRef, mask_regions: maskRegionsJson };
+			} else if (cardType === 'multiple-choice') {
+				const distractors = mcOptions
+					.filter((_, i) => i !== mcCorrectIdx)
+					.filter((o) => o.trim())
+					.join('\n');
+				fields = { front: front.trim(), answer: mcOptions[mcCorrectIdx].trim() };
+				if (distractors) fields.distractor_pool = distractors;
+				if (mcExplanation.trim()) fields.explanation = mcExplanation.trim();
 			} else {
 				fields = { front: front.trim(), back: back.trim() };
 			}
@@ -142,6 +162,8 @@
 		<form class="mt-6 space-y-5" onsubmit={onSubmit}>
 			{#if cardType === 'image-occlusion'}
 				<ImageOcclusionEditor bind:imageRef bind:maskRegionsJson />
+			{:else if cardType === 'multiple-choice'}
+				<MultipleChoiceCardForm bind:front bind:mcOptions bind:mcCorrectIdx bind:mcExplanation />
 			{:else if cardType === 'cloze'}
 				<div>
 					<label class="block">

apps/web/src/routes/cards/new/+page.svelte

@@ -40,6 +40,7 @@
 	// Multiple-Choice builder state
 	let mcOptions = $state(['', '', '', '']);
 	let mcCorrectIdx = $state(0);
+	let mcExplanation = $state('');
 
 	const frontHtml = $derived(renderMarkdown(front));
 	const backHtml = $derived(renderMarkdown(back));
@@ -125,6 +126,7 @@
 					.join('\n');
 				fields = { front: front.trim(), answer: mcOptions[mcCorrectIdx].trim() };
 				if (distractors) fields.distractor_pool = distractors;
+				if (mcExplanation.trim()) fields.explanation = mcExplanation.trim();
 			} else if (cardType === 'audio-front') {
 				fields = { audio_ref: audioFileRef.trim(), back: back.trim() };
 			} else {
@@ -198,7 +200,7 @@
 					<ClozeCardForm bind:text bind:extra {clusterIds} />
 
 				{:else if cardType === 'multiple-choice'}
-					<MultipleChoiceCardForm bind:front bind:mcOptions bind:mcCorrectIdx />
+					<MultipleChoiceCardForm bind:front bind:mcOptions bind:mcCorrectIdx bind:mcExplanation />
 
 				{:else if cardType === 'typing'}
 					<div class="grid-2">

apps/web/src/routes/study/[deckId]/+page.svelte

@@ -105,6 +105,7 @@
 		return {
 			answer: fields.answer ?? '',
 			distractorPool: fields.distractor_pool || undefined,
+			explanation: fields.explanation || undefined,
 		};
 	});
 
@@ -256,14 +257,17 @@
 							{revealed}
 						/>
 					{:else if isMultipleChoice && multipleChoiceData}
+						{#key current?.card_id}
 						<MultipleChoiceView
 							promptHtml={promptHtml}
 							answer={multipleChoiceData.answer}
 							distractorPool={multipleChoiceData.distractorPool}
+							explanation={multipleChoiceData.explanation}
 							deckId={deckId}
 							cardId={current?.card_id ?? ''}
 							ongrade={grade}
 						/>
+						{/key}
 					{:else if isTyping && typingData}
 						<TypingView
 							promptHtml={promptHtml}