fix(backend): read a tooth code whatever script its digits are in

The extraction model transcribes Persian speech, so it can hand back "۲۶"
in Persian digits or "2 6" from a digit-by-digit dictation. Both were
compared literally against /^[1-8][1-8]$/, missed, and fell through to the
positional branch with no quadrant — where the tooth was reported as "not
understood". The clinician loses a tooth and is told the words were the
problem.

normalizeFdiCode() now runs at both the branch choice and the final
validation, so the two cannot disagree. toLatinDigits moves out of
jalali.ts into common/digits.ts: it was exported but unused in production,
and a tooth module reaching into the calendar module would read as an
accident.

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

backend/src/common/fdi.ts

@@ -6,6 +6,8 @@
  * midline pairs (11–21, 41–31) are neighbours, exactly as the chart treats them.
  */
 
+import { toLatinDigits } from './digits';
+
 export type Arch = 'upper' | 'lower';
 
 /** Which side of the *patient*, not of the screen. Quadrant 1 is the patient's upper right. */
@@ -65,6 +67,19 @@ export function isFdiTooth(value: unknown): value is string {
   return typeof value === 'string' && FDI_TOOTH_IDS.has(value);
 }
 
+/**
+ * Clean up a tooth code the extraction model echoed back, before it is matched.
+ *
+ * The model is transcribing Persian speech, so it can hand back "۲۶" in Persian digits or
+ * "2 6" from a digit-by-digit dictation. Neither matches an FDI code literally, and a
+ * near-miss here does not fail loudly — the tooth quietly turns into "not understood".
+ * Returns '' for anything that is not a string.
+ */
+export function normalizeFdiCode(value: unknown): string {
+  if (typeof value !== 'string') return '';
+  return toLatinDigits(value).replace(/\s+/g, '');
+}
+
 function archOrder(tooth: string): readonly string[] | null {
   if ((FDI_UPPER_ARCH_ORDER as readonly string[]).includes(tooth))
     return FDI_UPPER_ARCH_ORDER;