Let me work through this payroll calculation.

Input:
- gross_pay: 8370.45
- payroll_month: 2026-05
- allowed_deduction: 370.62

Case reference schedule (authoritative, replaces defaults):
- first-half (2026-01 through 2026-06): rate 0.04, cap 5000.00, deduction 400.00, free 1000.00, upper 3600.00, middle_rate 0.10, upper_rate 0.24
- second-half: rate 0.04, cap 4000.00, deduction 400.00, free 1000.00, upper 3600.00, middle_rate 0.12, upper_rate 0.22

Payroll month 2026-05 → first-half row.

Step 1: Employee contribution (R3): rate 0.04 × min(8370.45, 5000.00) = 0.04 × 5000.00 = 200.00. Rounded: 200.00.

Step 2: Allowed deduction (R4): 370.62. Check cap: 400.00 — OK. Check gross pay minus contribution: 8370.45 − 200.00 = 8170.45 — 370.62 ≤ 8170.45 — OK.

Step 3: Taxable pay: 8370.45 − 200.00 − 370.62 = 7799.83.

Step 4: Income tax (R5), marginal:
- Tax-free: 1000.00 → 0 tax.
- Middle bracket: from 1000.00 to 3600.00 → 2600.00 × 0.10 = 260.00.
- Upper bracket: above 3600.00 → 7799.83 − 3600.00 = 4199.83 × 0.24 = 1007.9592.
- Total tax = 260.00 + 1007.9592 = 1267.9592 → round half-up to 1267.96.

Step 5: Net pay (R6): 8370.45 − 200.00 − 370.62 − 1267.96 = 6531.87.

Let me verify: 8370.45 − 200.00 = 8170.45. 8170.45 − 370.62 = 7799.83. 7799.83 − 1267.96 = 6531.87.

Check upper bracket calculation: 4199.83 × 0.24 = 1007.9592. Yes. 0.24 × 4199.83 = 1007.9592. Total 1267.9592 → 1267.96.

Net pay: 6531.87.

Fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "8370.45"
- employee_contribution: "200.00"
- allowed_deduction: "370.62"
- taxable_pay: "7799.83"
- income_tax: "1267.96"
- net_pay: "6531.87"
- clauses: R1 (row selection, schedule), R2 (rounding), R3 (contribution), R4 (deduction/taxable), R5 (tax), R6 (net pay/answer).

The schedule is authoritative per R1, so cite R1. No amendment needed.

Output JSON only, no markdown fences.

Let me process this payroll record.

Input:
- gross_pay: 8370.45
- payroll_month: 2026-05
- allowed_deduction: 370.62

Payroll month 2026-05 is in first-half (2026-01 through 2026-06). There's an authoritative case reference schedule provided, so I use its first-half row:
- rate: 0.04
- cap: 5000.00
- deduction cap: 400.00
- tax-free: 1000.00
- upper bracket begins: 3600.00
- middle rate: 0.10
- upper rate: 0.24

Step 1: Employee contribution (R3):
contribution = rate × min(gross_pay, cap) = 0.04 × min(8370.45, 5000.00) = 0.04 × 5000.00 = 200.00
Rounded: 200.00

Step 2: Allowed deduction check (R4):
allowed_deduction = 370.62
- Must not exceed deduction cap: 400.00. 370.62 ≤ 400.00 ✓
- Must not exceed gross pay minus rounded employee contribution: 8370.45 − 200.00 = 8170.45. 370.62 ≤ 8170.45 ✓

So allowed_deduction = 370.62.

Step 3: Taxable pay (R4):
taxable_pay = gross_pay − employee_contribution − allowed_deduction = 8370.45 − 200.00 − 370.62 = 7799.83

Step 4: Income tax (R5):
- Tax-free amount: 1000.00
- Upper bracket begins: 3600.00
- Middle rate: 0.10
- Upper rate: 0.24

Portion up to 1000.00: untaxed.
Portion from 1000.00 to 3600.00: (3600.00 − 1000.00) × 0.10 = 2600.00 × 0.10 = 260.00
Portion above 3600.00: (7799.83 − 3600.00) × 0.24 = 4199.83 × 0.24 = 1007.9592

Total tax = 260.00 + 1007.9592 = 1267.9592
Round half-up to two decimals: 1267.96

Step 5: Net pay (R6):
net_pay = gross_pay − employee_contribution − allowed_deduction − income_tax
= 8370.45 − 200.00 − 370.62 − 1267.96
= 8370.45 − 200.00 = 8170.45
8170.45 − 370.62 = 7799.83
7799.83 − 1267.96 = 6531.87

Let me double check: 7799.83 − 1267.96 = 6531.87. Yes.

Fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "8370.45"
- employee_contribution: "200.00"
- allowed_deduction: "370.62"
- taxable_pay: "7799.83"
- income_tax: "1267.96"
- net_pay: "6531.87"
- clauses: R1 (selecting row / schedule), R2 (rounding), R3 (contribution), R4 (deduction and taxable pay), R5 (income tax), R6 (net pay).

No amendment needed, no contract conflict (no contract_gross_pay present).

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

Output as JSON without markdown fences.

Let me work through this payroll calculation.

Input:
- gross_pay: 8370.45
- payroll_month: 2026-05
- allowed_deduction: 370.62

Payroll month 2026-05 is in first-half (2026-01 through 2026-06), so use the case schedule's first-half row:
- rate: 0.04
- cap: 5000.00
- deduction cap: 400.00
- free: 1000.00
- upper: 3600.00
- middle_rate: 0.10
- upper_rate: 0.24

Step 1: Employee contribution (R3)
Contribution = rate × min(gross_pay, cap) = 0.04 × min(8370.45, 5000.00) = 0.04 × 5000.00 = 200.00

Step 2: Allowed deduction check (R4)
allowed_deduction = 370.62
- Must not exceed deduction cap (400.00): 370.62 ≤ 400.00 ✓
- Must not exceed gross pay minus rounded contribution: 8370.45 − 200.00 = 8170.45. 370.62 ≤ 8170.45 ✓

Step 3: Taxable pay (R4)
taxable_pay = gross_pay − contribution − allowed_deduction = 8370.45 − 200.00 − 370.62 = 7799.83

Step 4: Income tax (R5)
- Tax-free amount: 1000.00
- Upper bracket begins: 3600.00
- Middle rate: 0.10
- Upper rate: 0.24

Portion 1: 0 to 1000.00 → 1000.00 untaxed, tax = 0
Portion 2: 1000.00 to 3600.00 → 2600.00 × 0.10 = 260.00
Portion 3: above 3600.00 → 7799.83 − 3600.00 = 4199.83 × 0.24 = 1007.9592

Total tax = 260.00 + 1007.9592 = 1267.9592 → round half-up to 1267.96

Step 5: Net pay (R6)
net_pay = gross_pay − contribution − allowed_deduction − tax
= 8370.45 − 200.00 − 370.62 − 1267.96
= 8370.45 − 200.00 = 8170.45
8170.45 − 370.62 = 7799.83
7799.83 − 1267.96 = 6531.87

Check: 7799.83 − 1267.96 = 6531.87. Yes.

Fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "8370.45"
- employee_contribution: "200.00"
- allowed_deduction: "370.62"
- taxable_pay: "7799.83"
- income_tax: "1267.96"
- net_pay: "6531.87"
- clauses: R1, R2, R3, R4, R5, R6

The case schedule exists, so I use its values (R1 says schedule replaces defaults). No amendment needed, no conflict.

Let me double-check the tax calculation:
7799.83 − 1000 = 6799.83 above free
Of that, up to 3600: 3600 − 1000 = 2600 at 0.10 = 260.00
Above 3600: 7799.83 − 3600 = 4199.83 at 0.24 = 1007.9592
Total: 1267.9592 → 1267.96 (round half up, but 0.0092 rounds down... 1267.9592 → third decimal is 9, so 1267.96). Correct.

Net pay: 6531.87.

Output JSON without markdown fences.