Let me work through this payroll calculation.

Input:
- gross_pay: 3999.99
- payroll_month: 2026-09
- allowed_deduction: 391.99
- contract gross_pay: 3999.99 (matches, no conflict)

Case reference schedule (authoritative, replaces defaults):
- second-half (2026-07 through 2026-12): rate 0.07, cap 4000.00, deduction 400.00, free 1200.00, upper 3000.00, middle_rate 0.14, upper_rate 0.22

Steps:
1. Employee contribution (R3): rate × min(gross, cap) = 0.07 × min(3999.99, 4000.00) = 0.07 × 3999.99 = 279.9993 → round half up to 280.00.

Wait, 0.07 × 3999.99 = 279.9993. Rounded to two decimals: 280.00 (since 279.9993 → 280.00? Let's check: 279.9993 rounded to 2 decimals: third decimal is 9, so 279.99 + 0.01 = 280.00. Actually 279.9993: two decimal places look at 279.99|93 → the digits after are 93, which is ≥ 50? Rounding to two decimals: 279.9993 → look at third decimal digit which is 9 → round up → 280.00. Yes, 280.00.

2. Allowed deduction check (R4): must not exceed deduction cap (400.00) or gross pay minus rounded contribution (3999.99 − 280.00 = 3719.99). 391.99 ≤ 400.00 and ≤ 3719.99. OK.

3. Taxable pay (R4): gross − contribution − deduction = 3999.99 − 280.00 − 391.99 = 3328.00.

4. Income tax (R5), second-half row: free = 1200.00, upper = 3000.00, middle_rate = 0.14, upper_rate = 0.22.
- Taxable up to 1200: 0 tax.
- 1200 to 3000: 1800 × 0.14 = 252.00.
- Above 3000: 3328.00 − 3000.00 = 328.00 × 0.22 = 72.16.
Total tax = 252.00 + 72.16 = 324.16.

5. Net pay (R6): 3999.99 − 280.00 − 391.99 − 324.16 = 3003.84.

Let me verify: 3999.99 − 280.00 = 3719.99; 3719.99 − 391.99 = 3328.00; 3328.00 − 324.16 = 3003.84.

Contract gross pay matches payroll gross pay (3999.99 = 3999.99), so no amendment needed; R9 not cited.

Answer fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "3999.99"
- employee_contribution: "280.00"
- allowed_deduction: "391.99"
- taxable_pay: "3328.00"
- income_tax: "324.16"
- net_pay: "3003.84"
- clauses: ["R1", "R2", "R3", "R4", "R5", "R6"]

The schedule is authoritative per R1, so citing R1 covers the schedule selection. Output JSON without markdown fences.

Let me process this payroll record.

Inputs:
- gross_pay: "3999.99"
- payroll_month: "2026-09"
- allowed_deduction: "391.99"
- contract gross_pay: "3999.99" (matches, so no conflict)

Reference schedule (authoritative case schedule overrides defaults):
- Payroll month 2026-09 is in second-half (2026-07 through 2026-12).
- Second-half row: rate = 0.07, cap = 4000.00, deduction cap = 400.00, free = 1200.00, upper = 3000.00, middle_rate = 0.14, upper_rate = 0.22

Steps:

1. Employee contribution (R3): rate × min(gross, cap) = 0.07 × min(3999.99, 4000.00) = 0.07 × 3999.99 = 279.9993 → round to 280.00 (round half up: 279.9993 → 280.00? Wait, 279.9993 rounds to 280.00 at two decimals: 279.9993 → the third decimal is 9, so 279.9993 ≈ 280.00. Actually 279.9993 to two decimals: 279.99|93 → the part after two decimals is 0.0093, which is ≥ 0.005, so rounds up to 280.00. Yes, 280.00.

2. Allowed deduction check (R4): allowed_deduction = 391.99. Cap = 400.00. Gross pay minus rounded contribution = 3999.99 − 280.00 = 3719.99. 391.99 ≤ 400.00 and ≤ 3719.99, so valid.

3. Taxable pay (R4): gross − contribution − deduction = 3999.99 − 280.00 − 391.99 = 3328.00.

Let me compute: 3999.99 − 280.00 = 3719.99. 3719.99 − 391.99 = 3328.00. Yes.

4. Income tax (R5): progressive brackets with free = 1200.00, upper boundary = 3000.00, middle rate = 0.14, upper rate = 0.22.
- First 1200.00: 0 tax.
- 1200.00 to 3000.00: 1800.00 × 0.14 = 252.00.
- Above 3000.00: 3328.00 − 3000.00 = 328.00 × 0.22 = 72.16.
- Total = 252.00 + 72.16 = 324.16.

5. Net pay (R6): gross − contribution − deduction − tax = 3999.99 − 280.00 − 391.99 − 324.16 = ?

3999.99 − 280.00 = 3719.99. 3719.99 − 391.99 = 3328.00. 3328.00 − 324.16 = 3003.84.

So:
- gross_pay: "3999.99"
- employee_contribution: "280.00"
- allowed_deduction: "391.99"
- taxable_pay: "3328.00"
- income_tax: "324.16"
- net_pay: "3003.84"
- currency: "LCR"
- decision: "calculate"

Clauses: R1 (row selection, schedule), R2 (rounding), R3 (contribution), R4 (deduction/taxable), R5 (tax), R6 (net pay/answer). Contract matches gross pay so no R9 needed.

Check contribution rounding: 0.07 × 3999.99 = 279.9993. Round half-up to two decimals: 280.00. Yes.

Check tax computation doesn't round intermediate products before summing: 252.00 and 72.16 are exact anyway.

Output JSON without markdown fences.

Let me work through this payroll case.

Inputs:
- gross_pay: "3999.99"
- payroll_month: "2026-09"
- allowed_deduction: "391.99"
- contract gross_pay: "3999.99" (matches, so no conflict)

Case reference schedule (authoritative):
- second-half (2026-07 through 2026-12): rate 0.07, cap 4000.00, deduction 400.00, free 1200.00, upper 3000.00, middle_rate 0.14, upper_rate 0.22

Step 1: Employee contribution (R3): rate × min(gross, cap) = 0.07 × min(3999.99, 4000.00) = 0.07 × 3999.99 = 279.9993 → round to 280.00.

Wait, 0.07 × 3999.99 = 279.9993. Round half up to two decimals: 280.00? 279.9993 → 280.00 when rounded to two decimals? 279.9993 rounds to 280.00 (since 279.9993 is closer to 280.00 than 279.99? Let's check: 279.9993 - 279.99 = 0.0093; 280.00 - 279.9993 = 0.0007. Yes, 280.00).

Actually wait: rounding 279.9993 to two decimal places: third decimal is 9, so we round up: 279.99 + 0.01 = 280.00. Yes, 280.00.

Step 2: Allowed deduction check (R4): must not exceed deduction cap (400.00) or gross pay minus rounded employee contribution = 3999.99 - 280.00 = 3719.99. Allowed deduction 391.99 ≤ 400.00 and ≤ 3719.99. OK.

Step 3: Taxable pay = gross - contribution - deduction = 3999.99 - 280.00 - 391.99 = 3328.00.

Step 4: Income tax (R5): brackets: free = 1200.00, upper begins at 3000.00, middle rate 0.14, upper rate 0.22.
- First 1200.00: 0 tax.
- Portion from 1200.00 to 3000.00: 1800.00 × 0.14 = 252.00.
- Portion above 3000.00: 3328.00 - 3000.00 = 328.00 × 0.22 = 72.16.
Total tax = 252.00 + 72.16 = 324.16.

Step 5: Net pay = 3999.99 - 280.00 - 391.99 - 324.16 = 3003.84.

Let me verify: 3999.99 - 280.00 = 3719.99. 3719.99 - 391.99 = 3328.00. 3328.00 - 324.16 = 3003.84. Yes.

Answer JSON:
{
  "decision": "calculate",
  "currency": "LCR",
  "gross_pay": "3999.99",
  "employee_contribution": "280.00",
  "allowed_deduction": "391.99",
  "taxable_pay": "3328.00",
  "income_tax": "324.16",
  "net_pay": "3003.84",
  "clauses": ["R1", "R2", "R3", "R4", "R5", "R6"]
}

Contract matches gross pay, so no R9 citation needed.

Should I include an explanation? Optional. I could include a brief explanation. The instructions say an optional explanation string is permitted. I'll include a brief one.

Note: the case schedule replaces defaults. The second-half row from the schedule: rate 0.07, cap 4000.00, deduction 400.00, free 1200.00, upper 3000.00, middle 0.14, upper_rate 0.22. I used that correctly.

Output one JSON object without Markdown fences.