How do you apply a single payment across multiple invoices with partial amounts and deductions?

Allocate the receipt across the specified invoices per the remittance, fully clearing those paid in full, partially applying where only part is paid (leaving residuals), and opening deduction cases for withheld amounts. The sum of applied amounts, residuals, and deductions must equal the payment received, keeping the ledger balanced.

Payment 9,300 covers:
  Inv A 5,000 (full), Inv B 3,000 (full),
  Inv C 2,000 paid 1,300 (residual 700 = logged deduction).
  Applied 9,300 = 5,000 + 3,000 + 1,300.