We need to process payroll for 2026-06, which is first-half. The authoritative case reference schedule for first-half: rate 0.06, cap 5000.00, deduction 400.00, free 900.00, upper 3600.00, middle_rate 0.12, upper_rate 0.24.

Per R1, when a case schedule is supplied, its numeric values replace defaults. So use first-half row.

Gross pay: 4093.39
Employee contribution: rate 0.06 × min(4093.39, 5000.00) = 0.06 × 4093.39 = 245.6034 → round half up to 245.60.

Allowed deduction: 247.81. Check cap: 400.00 — OK. Check gross pay minus rounded contribution: 4093.39 − 245.60 = 3847.79. 247.81 ≤ 3847.79 — OK.

Taxable pay: 4093.39 − 245.60 − 247.81 = 3600. - let's compute: 4093.39 − 245.60 = 3847.79; 3847.79 − 247.81 = 3599.98.

Income tax: taxable pay 3599.98.
- Up to free 900.00: untaxed.
- 900.00 to 3600.00: middle rate 0.12. Portion: 3600.00 − 900.00 = 2700.00 → but taxable is 3599.98, so portion above 900 up to 3600 = 3599.98 − 900.00 = 2699.98 → tax = 2699.98 × 0.12 = 323.9976.
- Above 3600: 0 (3599.98 < 3600).

Total tax = 323.9976 → round half up to 324.00.

Wait: 2699.98 × 0.12 = 323.9976. Round to two decimals: 324.00? 323.9976 → third decimal is 7, round half up: 323.9976 → 324.00? Let's check: 323.9976 rounded to two decimals: look at third decimal digit 7 ≥ 5, so round up second decimal: 323.99 + 0.01 = 324.00. Yes, 324.00.

Net pay: 4093.39 − 245.60 − 247.81 − 324.00 = 4093.39 − 245.60 = 3847.79; 3847.79 − 247.81 = 3599.98; 3599.98 − 324.00 = 3275.98.

Fields: decision "calculate", currency "LCR", gross_pay "4093.39", employee_contribution "245.60", allowed_deduction "247.81", taxable_pay "3599.98", income_tax "324.00", net_pay "3275.98".

Clauses: R1 (schedule selection), R2 (rounding), R3 (contribution), R4 (deduction/taxable), R5 (tax), R6 (net pay/answer). No amendment needed.

JSON only, no markdown fences.

We need to process payroll for gross_pay 4093.39, payroll_month 2026-06, allowed_deduction 247.81.

The case supplies an authoritative reference schedule. Per R1, when supplied, its numeric values replace defaults. The payroll month 2026-06 is in first half, so use the first-half row: rate 0.06, cap 5000.00, deduction 400.00, free 900.00, upper 3600.00, middle_rate 0.12, upper_rate 0.24.

Employee contribution: rate * min(gross, cap) = 0.06 * min(4093.39, 5000.00) = 0.06 * 4093.39 = 245.6034 → round to 245.60.

Allowed deduction: 247.81. Check cap: deduction cap 400.00 — 247.81 ≤ 400.00 OK. Check gross minus contribution: 4093.39 - 245.60 = 3847.79. 247.81 ≤ 3847.79 OK.

Taxable pay: gross - contribution - deduction = 4093.39 - 245.60 - 247.81 = 3599.98.

Income tax: brackets: free 900.00, upper boundary 3600.00.
- Portion up to 900: untaxed.
- Portion above 900 up to 3600: 3600 - 900 = 2700 at 0.12 = 324.00.
- Taxable pay is 3599.98, which is below upper boundary 3600, so no upper-rate portion.

Total tax = 0.12 * (3599.98 - 900) = 0.12 * 2699.98 = 323.9976 → round half up = 324.00.

Wait: R2 says do not round intermediate bracket products separately before summing income tax. So compute 323.9976, round to 324.00.

Net pay: gross - contribution - deduction - tax = 4093.39 - 245.60 - 247.81 - 324.00 = 3275.98.

Check: 4093.39 - 245.60 = 3847.79; 3847.79 - 247.81 = 3599.98; 3599.98 - 324.00 = 3275.98.

Return JSON with decision calculate, currency LCR, gross_pay "4093.39", employee_contribution "245.60", allowed_deduction "247.81", taxable_pay "3599.98", income_tax "324.00", net_pay "3275.98", clauses: R1 (schedule selection), R2 (rounding), R3, R4, R5, R6.

Citations: R1, R2, R3, R4, R5, R6.

We need to process payroll for 2026-06, which is first-half. The case provides an authoritative reference schedule, which replaces defaults.

First-half schedule from case:
- rate: 0.06
- cap: 5000.00
- deduction: 400.00
- free: 900.00
- upper: 3600.00
- middle_rate: 0.12
- upper_rate: 0.24

Inputs:
- gross_pay: 4093.39
- payroll_month: 2026-06
- allowed_deduction: 247.81

Step 1: Employee contribution = rate * min(gross, cap) = 0.06 * min(4093.39, 5000.00) = 0.06 * 4093.39 = 245.6034 → round half up to 245.60.

Step 2: Allowed deduction check: must not exceed deduction cap (400.00) or gross minus rounded contribution = 4093.39 - 245.60 = 3847.79. 247.81 ≤ 400.00 and ≤ 3847.79. OK.

Step 3: Taxable pay = gross - contribution - allowed deduction = 4093.39 - 245.60 - 247.81 = 3599.98.

Let me compute: 4093.39 - 245.60 = 3847.79. 3847.79 - 247.81 = 3599.98. Yes.

Step 4: Income tax:
- Tax-free: 900.00
- Upper bracket begins at 3600.00
- Middle rate 0.12 applies to portion above 900 up to 3600: 3600 - 900 = 2700. Taxable pay is 3599.98, which is below 3600. So middle portion = 3599.98 - 900 = 2699.98. Tax = 0.12 * 2699.98 = 323.9976.
- Upper portion: 0 (taxable below upper boundary).

Total tax = 323.9976 → round half up to 324.00? 323.9976 rounds to 324.00 (since 323.9976 → third decimal is 7, so 324.00). Wait: 323.9976 to two decimals: 323.9976 → look at 323.99|76 → the fractional part beyond two decimals is 0.0076 ≥ 0.005, so rounds to 324.00. Yes, income_tax = 324.00.

Step 5: Net pay = gross - contribution - deduction - tax = 4093.39 - 245.60 - 247.81 - 324.00 = ?

4093.39 - 245.60 = 3847.79. 3847.79 - 247.81 = 3599.98. 3599.98 - 324.00 = 3275.98.

Net pay = 3275.98.

Check: taxable 3599.98, tax 324.00, net = 3275.98.

All good. Decision: calculate.

Citations: R1 (schedule selection), R2 (rounding), R3 (contribution), R4 (deduction/taxable), R5 (tax), R6 (net pay/answer format). No amendment needed.

Output JSON with fields: decision, currency, gross_pay, employee_contribution, allowed_deduction, taxable_pay, income_tax, net_pay, clauses. Optional explanation.