Let me process this payroll record.

Input:
- gross_pay: "2978.74"
- payroll_month: "2026-07"
- allowed_deduction: "0.00"

Reference schedule (authoritative case schedule):
- second-half (2026-07 through 2026-12): rate 0.06, cap 4500.00, deduction 400.00, free 1200.00, upper 2800.00, middle_rate 0.14, upper_rate 0.20

Payroll month 2026-07 → second-half row.

Step 1: Employee contribution (R3):
- min(gross_pay, cap) = min(2978.74, 4500.00) = 2978.74
- contribution = 0.06 × 2978.74 = 178.7244 → round half up to 178.72

Wait: 2978.74 × 0.06 = 178.7244. Round to two decimals: 178.72 (since third decimal is 4, round down). Yes, 178.72.

Step 2: Allowed deduction check (R4):
- allowed_deduction = 0.00, which is ≤ 400.00 cap and ≤ gross_pay − contribution = 2978.74 − 178.72 = 2800.02. OK.

Step 3: Taxable pay (R4):
- taxable = gross − contribution − deduction = 2978.74 − 178.72 − 0.00 = 2800.02

Step 4: Income tax (R5), second-half row:
- tax-free amount: 1200.00
- upper bracket begins: 2800.00
- middle rate: 0.14
- upper rate: 0.20

Taxable pay = 2800.02
- Portion up to 1200.00: untaxed
- Portion 1200.00 to 2800.00: 1600.00 × 0.14 = 224.00
- Portion above 2800.00: 2800.02 − 2800.00 = 0.02 × 0.20 = 0.004

Total tax = 224.00 + 0.004 = 224.004 → round half up to 224.00

Wait, 224.004 rounds to 224.00 (third decimal is 4, rounds down). Yes.

Step 5: Net pay (R6):
- net = 2978.74 − 178.72 − 0.00 − 224.00 = 2576.02

Check: 2978.74 − 178.72 = 2800.02. 2800.02 − 224.00 = 2576.02. Yes.

Fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "2978.74"
- employee_contribution: "178.72"
- allowed_deduction: "0.00"
- taxable_pay: "2800.02"
- income_tax: "224.00"
- net_pay: "2576.02"
- clauses: R1, R2, R3, R4, R5, R6

Note: the case schedule replaces defaults — the schedule's second-half values differ from defaults (free 1200 vs 1100, upper 2800 vs 3300, middle 0.14 vs 0.12, upper_rate 0.20 vs 0.22). I used the schedule values correctly per R1.

Citations: R1 (row selection, schedule authority), R2 (rounding), R3 (contribution), R4 (deduction and taxable), R5 (tax), R6 (net pay/answer format).

No amendment present, no conflict.

Let me work through this payroll calculation.

Input:
- gross_pay: 2978.74
- payroll_month: 2026-07
- allowed_deduction: 0.00

The authoritative case reference schedule is supplied, so per R1, its values replace defaults. Payroll month 2026-07 falls in second-half (2026-07 through 2026-12).

Second-half row:
- rate: 0.06
- cap: 4500.00
- deduction cap: 400.00
- tax-free: 1200.00
- upper bracket begins: 2800.00
- middle rate: 0.14
- upper rate: 0.20

Step 1: Employee contribution (R3)
= rate × min(gross_pay, cap)
= 0.06 × min(2978.74, 4500.00)
= 0.06 × 2978.74
= 178.7244
Round to two decimals (round-half-up): 178.72

Step 2: Allowed deduction (R4)
allowed_deduction = 0.00. Check: must not exceed cap (400.00) or gross pay minus rounded contribution (2978.74 − 178.72 = 2800.02). 0.00 is fine.

Step 3: Taxable pay
= gross_pay − employee_contribution − allowed_deduction
= 2978.74 − 178.72 − 0.00
= 2800.02

Step 4: Income tax (R5)
Tax-free amount: 1200.00
Upper bracket begins: 2800.00

Portion up to 1200.00: untaxed.
Portion 1200.00 to 2800.00: 2800.00 − 1200.00 = 1600.00 at 0.14 = 224.00
Portion above 2800.00: 2800.02 − 2800.00 = 0.02 at 0.20 = 0.004

Total tax = 224.00 + 0.004 = 224.004
Round to two decimals: 224.00

Note R2: "Do not round intermediate bracket products separately before summing income tax." So sum first: 224.004 → 224.00.

Step 5: Net pay (R6)
= gross_pay − employee_contribution − allowed_deduction − income_tax
= 2978.74 − 178.72 − 0.00 − 224.00
= 1576.02

Let me verify: 2978.74 − 178.72 = 2800.02. 2800.02 − 224.00 = 2576.02. Wait, let me recompute.

2978.74 − 178.72 = 2800.02
2800.02 − 0.00 = 2800.02
2800.02 − 224.00 = 2576.02

So net pay = 2576.02.

Let me double-check the contribution: 0.06 × 2978.74 = 178.7244. Round half up at two decimals: 178.72 (since third decimal is 4, rounds down). Correct.

Taxable pay: 2978.74 − 178.72 = 2800.02. Correct.

Tax: bracket 1: 0 to 1200 → 0. Bracket 2: 1200 to 2800 → 1600 × 0.14 = 224.00. Bracket 3: above 2800 → 0.02 × 0.20 = 0.004. Total = 224.004 → 224.00.

Net pay: 2978.74 − 178.72 − 0.00 − 224.00 = 2576.02.

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

No amendment needed, no conflict.

Output JSON:
{
  "decision": "calculate",
  "currency": "LCR",
  "gross_pay": "2978.74",
  "employee_contribution": "178.72",
  "allowed_deduction": "0.00",
  "taxable_pay": "2800.02",
  "income_tax": "224.00",
  "net_pay": "2576.02",
  "clauses": ["R1", "R2", "R3", "R4", "R5", "R6"]
}

Optionally an explanation. I'll include a brief one.

We need to process payroll for 2026-07, gross pay 2978.74, allowed_deduction 0.00.

The authoritative case reference schedule is supplied. For 2026-07, we use second-half row: rate 0.06, cap 4500.00, deduction 400.00, free 1200.00, upper 2800.00, middle_rate 0.14, upper_rate 0.20.

Employee contribution: rate * min(gross, cap) = 0.06 * 2978.74 = 178.7244 → round to 178.72 (round half up: 178.7244 → 178.72).

Allowed deduction: 0.00, must not exceed cap 400.00 or gross minus contribution = 2978.74 - 178.72 = 2800.02. 0.00 is fine.

Taxable pay = 2978.74 - 178.72 - 0.00 = 2800.02.

Income tax: tax-free amount 1200.00; upper bracket begins at 2800.00.

Portion up to 1200: untaxed.
Portion 1200.01? Actually portion above 1200 up to 2800: (2800 - 1200) = 1600 at 14% = 224.00.
Portion above 2800: 2800.02 - 2800 = 0.02 at 20% = 0.004.

Total = 224.00 + 0.004 = 224.004 → round half up to 224.00.

Wait, R2 says "Do not round intermediate bracket products separately before summing income tax." So sum = 224.004, round to 224.00.

Net pay = 2978.74 - 178.72 - 0.00 - 224.00 = 2576.02.

Check: 2978.74 - 178.72 = 2800.02; 2800.02 - 224.00 = 2576.02.

Fields: decision calculate, currency LCR, gross_pay "2978.74", employee_contribution "178.72", allowed_deduction "0.00", taxable_pay "2800.02", income_tax "224.00", net_pay "2576.02".

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

The schedule is authoritative, replacing defaults. Second-half row: rate 0.06, cap 4500, deduction 400, free 1200, upper 2800, middle 0.14, upper 0.20.

Contribution: 0.06 * 2978.74 = 178.7244 → 178.72.

Taxable: 2800.02.

Tax: (2800.02 - 1200) = 1600.02 above free. Of that, up to upper boundary 2800: 1600 at 0.14 = 224.00. Above 2800: 0.02 at 0.20 = 0.004. Total 224.004 → 224.00.

Net: 2978.74 - 178.72 - 0.00 - 224.00 = 2576.02.

Output JSON without markdown fences. Include clauses: ["R1","R2","R3","R4","R5","R6"]. Maybe add explanation.