Let me work through this payroll case.

Inputs:
- gross_pay: "4999.99"
- payroll_month: "2026-02" → first-half row
- allowed_deduction: "355.71"
- contract gross_pay: "4999.99" — matches gross_pay, so no conflict (R9: matching contract values require no amendment).
- Authoritative case schedule supplied: first-half: rate 0.07, cap 5000.00, deduction 400.00, free 900.00, upper 3000.00, middle_rate 0.12, upper_rate 0.22.

Per R1, when a case schedule is supplied, its numeric values replace defaults. Payroll month 2026-02 → first-half row.

Step 1: Employee contribution (R3): rate 0.07 × min(gross 4999.99, cap 5000.00) = 0.07 × 4999.99 = 349.9993. Round half-up to two decimals: 350.00.

Wait — 349.9993 rounds to 350.00? Round to two decimals: 349.9993 → third decimal is 9, so 349.99 + ... let's compute: 349.9993 → two decimal places: look at digits after second decimal: 349.99|93 → the part beyond is 0.0093... Actually 349.9993 = 349.99 + 0.0093. Rounding to two decimals: 0.0093 ≥ 0.005, so rounds up to 350.00. Yes, 350.00.

Step 2: Allowed deduction check (R4): must not exceed deduction cap (400.00) or gross pay minus rounded contribution: 4999.99 − 350.00 = 4649.99. Deduction 355.71 ≤ 400.00 and ≤ 4649.99. OK.

Step 3: Taxable pay (R4): gross − contribution − deduction = 4999.99 − 350.00 − 355.71 = 4294.28.

Compute: 4999.99 − 350.00 = 4649.99; 4649.99 − 355.71 = 4294.28.

Step 4: Income tax (R5): free = 900.00, upper boundary = 3000.00.
- Portion up to 900: untaxed.
- Portion 900 to 3000: 2100.00 × 0.12 = 252.00.
- Portion above 3000: 4294.28 − 3000.00 = 1294.28 × 0.22 = 284.7416.

Total = 252.00 + 284.7416 = 536.7416 → round half-up → 536.74.

Step 5: Net pay (R6): 4999.99 − 350.00 − 355.71 − 536.74 = ?

4999.99 − 350.00 = 4649.99; − 355.71 = 4294.28; − 536.74 = 3757.54.

Check: 4294.28 − 536.74 = 3757.54. Yes.

Fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "4999.99"
- employee_contribution: "350.00"
- allowed_deduction: "355.71"
- taxable_pay: "4294.28"
- income_tax: "536.74"
- net_pay: "3757.54"
- clauses: R1, R2, R3, R4, R5, R6. Contract matches gross pay, so no amendment needed — no R9 citation needed.

Citation requirements: calculated answers cite R1 through R6; R9 only when amendment needed. So clauses: ["R1","R2","R3","R4","R5","R6"].

Optionally include explanation. Keep it brief.

JSON without markdown fences, one object.

Let me work through this payroll calculation.

Input:
- gross_pay: 4999.99
- payroll_month: 2026-02
- allowed_deduction: 355.71
- contract gross_pay: 4999.99 (matches, so no conflict)
- Case reference schedule supplied: first-half: rate 0.07, cap 5000.00, deduction 400.00, free 900.00, upper 3000.00, middle_rate 0.12, upper_rate 0.22

Payroll month 2026-02 → first-half row. Use the case schedule's first-half values (per R1, case schedule replaces defaults).

Step 1: Employee contribution (R3): rate 0.07 × min(4999.99, 5000.00) = 0.07 × 4999.99 = 349.9993 → round to 350.00.

Wait: 0.07 × 4999.99 = 349.9993. Round half-up to two decimals: 350.00. Hmm, 349.9993 → 350.00. Yes.

Step 2: Allowed deduction check (R4): deduction cap = 400.00. Gross pay minus contribution = 4999.99 − 350.00 = 4649.99. Allowed deduction 355.71 ≤ 400.00 and ≤ 4649.99. Valid. Use 355.71.

Step 3: Taxable pay (R4): 4999.99 − 350.00 − 355.71 = 4294.28.

Step 4: Income tax (R5): first-half schedule: free = 900.00, upper = 3000.00, middle_rate = 0.12, upper_rate = 0.22.

Taxable pay = 4294.28.
- Portion up to 900.00: untaxed.
- Portion 900.00 to 3000.00: 2100.00 × 0.12 = 252.00.
- Portion above 3000.00: 4294.28 − 3000.00 = 1294.28 × 0.22 = 284.7416.

Total = 252.00 + 284.7416 = 536.7416 → round to 536.74.

Step 5: Net pay (R6): 4999.99 − 350.00 − 355.71 − 536.74 = ?

4999.99 − 350.00 = 4649.99
4649.99 − 355.71 = 4294.28
4294.28 − 536.74 = 3757.54.

Net pay = 3757.54.

Let me double check the contribution: 0.07 × 4999.99 = 349.9993. Round half-up: 349.9993 → third decimal is 9, so round up second decimal: 349.99 + 0.01 = 350.00. Yes, 350.00.

Taxable pay: 4294.28.

Tax: middle band: 3000.00 − 900.00 = 2100.00 × 0.12 = 252.00. Upper band: 4294.28 − 3000.00 = 1294.28 × 0.22 = 284.7416. Sum = 536.7416 → 536.74.

Net: 3757.54.

Contract gross matches payroll gross (4999.99 = 4999.99), so no amendment needed, no R9 citation.

Clauses: R1 (row selection, case schedule), R2 (rounding), R3 (contribution), R4 (deduction/taxable), R5 (tax), R6 (net pay/answer).

Output JSON:
{
  "decision": "calculate",
  "currency": "LCR",
  "gross_pay": "4999.99",
  "employee_contribution": "350.00",
  "allowed_deduction": "355.71",
  "taxable_pay": "4294.28",
  "income_tax": "536.74",
  "net_pay": "3757.54",
  "clauses": ["R1", "R2", "R3", "R4", "R5", "R6"]
}

Maybe include an explanation. Optional. I'll include a brief explanation.

Let me process this payroll record.

Inputs:
- gross_pay: "4999.99"
- payroll_month: "2026-02"
- allowed_deduction: "355.71"
- contract gross_pay: "4999.99" (matches, so no conflict)
- Case reference schedule: first-half: rate 0.07, cap 5000.00, deduction 400.00, free 900.00, upper 3000.00, middle_rate 0.12, upper_rate 0.22

Payroll month 2026-02 is in first-half. The case schedule exists, so its values replace defaults.

Steps:
1. Employee contribution = rate 0.07 × min(4999.99, 5000.00) = 0.07 × 4999.99 = 349.9993 → round to 350.00 (round-half-up at two decimals: 349.9993 → 350.00? Wait, 349.9993 rounds to 350.00? Let's compute: 349.9993, rounding to two decimals: the third decimal is 9, so 349.99 + 0.01 = 350.00. Actually 349.9993 → two decimals: look at 349.9993; the digits are 349.99|93, the part after two decimals is 0.0093 which is ≥ 0.005, so round up: 350.00. Yes, 350.00.

2. Allowed deduction check: cap 400.00; gross pay minus rounded contribution = 4999.99 − 350.00 = 4649.99. Deduction 355.71 ≤ 400.00 and ≤ 4649.99. OK.

3. Taxable pay = 4999.99 − 350.00 − 355.71 = 4294.28.

4. Income tax:
- Tax-free: 900.00
- Upper bracket begins: 3000.00
- Middle rate: 0.12 on portion from 900.00 to 3000.00 = 2100.00 × 0.12 = 252.00
- Upper rate: 0.22 on portion above 3000.00 = 4294.28 − 3000.00 = 1294.28 × 0.22 = 284.7416
- Total = 252.00 + 284.7416 = 536.7416 → round to 536.74.

5. Net pay = 4999.99 − 350.00 − 355.71 − 536.74 = 3757.54.

Check: 4999.99 − 350.00 = 4649.99; 4649.99 − 355.71 = 4294.28; 4294.28 − 536.74 = 3757.54.

Contract matches gross pay, so no amendment needed; cite R1–R6.

Output JSON:
{
  "decision": "calculate",
  "currency": "LCR",
  "gross_pay": "4999.99",
  "employee_contribution": "350.00",
  "allowed_deduction": "355.71",
  "taxable_pay": "4294.28",
  "income_tax": "536.74",
  "net_pay": "3757.54",
  "clauses": ["R1", "R2", "R3", "R4", "R5", "R6"]
}