Support rebalance and validate purchase splits

Add ParticipantShare type and client-side rebalance/validation helpers for purchase splits (rebalancePurchaseSplit, recalculatePercentages, calculateRemainingToAllocate, validatePurchaseDraft). Integrate rebalancing and validation into the miniapp ledger UI (auto-adjust shares, percentage<>amount syncing, remaining/error display, prefill participants on new purchase, disable save when invalid). On the backend, tighten input validation in finance-command-service for custom_amounts (require explicit shares and sum match) and make settlement-engine more lenient when reading legacy/malformed custom splits (ignore missing shares, accept explicit subset). Also add a test ensuring dashboard generation doesn't 500 on legacy malformed purchases.

packages/application/src/finance-command-service.ts

@@ -15,6 +15,8 @@ import type {
 import {
   BillingCycleId,
   BillingPeriod,
+  DomainError,
+  DOMAIN_ERROR_CODE,
   MemberId,
   Money,
   PurchaseEntryId,
@@ -867,6 +869,27 @@ export function createFinanceCommandService(
       )
       const currency = parseCurrency(currencyArg, settings.settlementCurrency)
       const amount = Money.fromMajor(amountArg, currency)
+
+      if (split?.mode === 'custom_amounts') {
+        if (split.participants.some((p) => p.shareAmountMajor === undefined)) {
+          throw new DomainError(
+            DOMAIN_ERROR_CODE.INVALID_SETTLEMENT_INPUT,
+            'Purchase custom split must include explicit share amounts for every participant'
+          )
+        }
+
+        const totalMinor = split.participants.reduce(
+          (sum, p) => sum + Money.fromMajor(p.shareAmountMajor!, currency).amountMinor,
+          0n
+        )
+        if (totalMinor !== amount.amountMinor) {
+          throw new DomainError(
+            DOMAIN_ERROR_CODE.INVALID_SETTLEMENT_INPUT,
+            'Purchase custom split must add up to the full amount'
+          )
+        }
+      }
+
       const updated = await repository.updateParsedPurchase({
         purchaseId,
         amountMinor: amount.amountMinor,