feat(backend): offer the candidate teeth for an unspecified quadrant

A tooth the resolver refuses to guess at is currently a dead end: the sheet
says the quadrant was missing and the clinician has to leave and find the
tooth on the chart. But the readings are enumerable — "دو" is one of four
teeth, "دو بالا" one of two — so unresolved items now carry them.

Narrowed by whatever was actually said, so this stays a choice offered to
the clinician rather than a guess made for them. Only tooth_missing_quadrant
carries candidates; a wrong position or a deciduous tooth has nothing to
choose between.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

backend/src/modules/voice/tooth-intent.resolver.ts

@@ -1,6 +1,15 @@
-import { isFdiTooth, normalizeFdiCode, toFdi } from '../../common/fdi';
+import {
+  isFdiTooth,
+  normalizeFdiCode,
+  toFdi,
+  type Arch,
+  type PatientSide,
+} from '../../common/fdi';
 import type { ToothIntent, UnresolvedItem } from './voice.types';
 
+const ARCHES: readonly Arch[] = ['upper', 'lower'];
+const SIDES: readonly PatientSide[] = ['patient_right', 'patient_left'];
+
 export type ToothResolution = {
   /** Unique FDI codes, sorted (matching normalizeTeeth's ordering). */
   teeth: string[];
@@ -68,6 +77,32 @@ function unresolvedReason(intent: ToothIntent): UnresolvedItem['reason'] {
   return 'malformed';
 }
 
+/**
+ * The teeth still consistent with what *was* heard.
+ *
+ * Narrowed by whatever the clinician did say, so "دو" offers four and "دو بالا" offers
+ * two. This is not a guess — it is the full set of readings, handed to the clinician to
+ * choose from rather than picked on their behalf.
+ */
+function quadrantCandidates(intent: ToothIntent): string[] {
+  if (intent.kind !== 'positional') return [];
+  const arches =
+    intent.arch === 'upper' || intent.arch === 'lower' ? [intent.arch] : ARCHES;
+  const sides =
+    intent.side === 'patient_right' || intent.side === 'patient_left'
+      ? [intent.side]
+      : SIDES;
+
+  const codes: string[] = [];
+  for (const arch of arches) {
+    for (const side of sides) {
+      const fdi = toFdi(arch, side, intent.position);
+      if (fdi) codes.push(fdi);
+    }
+  }
+  return codes.sort();
+}
+
 function spokenOf(intent: ToothIntent): string {
   const spoken = (intent as { spoken?: unknown })?.spoken;
   return typeof spoken === 'string' && spoken.trim() ? spoken.trim() : '';
@@ -101,14 +136,22 @@ export function resolveToothIntents(
     }
     const reason = unresolvedReason(intent);
     const spoken = spokenOf(intent);
+    const candidates =
+      reason === 'tooth_missing_quadrant' ? quadrantCandidates(intent) : [];
     // Only dedupe items we can actually tell apart. Without `spoken`, two distinct lost
-    // references would collapse into one blank review row and a tooth would vanish.
+    // references would collapse into one blank review row and a tooth would vanish. The
+    // candidates are part of the identity: the same word with a different arch heard
+    // offers a different choice.
     if (spoken) {
-      const key = `${spoken}::${reason}`;
+      const key = `${spoken}::${reason}::${candidates.join(',')}`;
       if (seenUnresolved.has(key)) continue;
       seenUnresolved.add(key);
     }
-    unresolved.push({ spoken, reason });
+    unresolved.push(
+      candidates.length > 0
+        ? { spoken, reason, candidates }
+        : { spoken, reason },
+    );
   }
 
   return { teeth: [...teeth].sort(), unresolved };