Let me process this payroll record.

Inputs:
- gross_pay: 4484.82
- payroll_month: 2026-11
- allowed_deduction: 395.18
- contract gross_pay: 4728.75 (differs from payroll gross_pay)
- amendment: gross_pay 4484.82, approved: true, effective_month: 2026-05

Reference schedule (authoritative case schedule):
- second-half (2026-07 through 2026-12): rate 0.04, cap 4500.00, deduction 400.00, free 900.00, upper 3600.00, middle_rate 0.10, upper_rate 0.18

Step 1: Check required inputs per R7.
- gross_pay present: 4484.82 ✓
- payroll_month present: 2026-11 ✓
- Month has reference row: 2026-11 is in 2026-07 through 2026-12, second-half row ✓
- contract_gross_pay 4728.75 differs from gross_pay 4484.82. Check amendment: approved=true, effective_month 2026-05 ≤ 2026-11, amount 4484.82 equals payroll gross_pay 4484.82. So amendment resolves conflict under R9. ✓

Step 2: Employee contribution (R3).
- Contribution rate: 0.04 (second-half from case schedule)
- Wage cap: 4500.00
- min(4484.82, 4500.00) = 4484.82
- Contribution = 4484.82 × 0.04 = 179.3928 → round to 179.39

Let me compute: 4484.82 × 0.04 = 179.3928. Round half-up to two decimals: 179.39.

Step 3: Allowed deduction (R4).
- Deduction cap: 400.00
- Gross pay minus contribution: 4484.82 − 179.39 = 4305.43
- allowed_deduction = 395.18 ≤ 400.00 ✓ and ≤ 4305.43 ✓
- So allowed deduction = 395.18

Step 4: Taxable pay.
- Taxable pay = gross − contribution − deduction = 4484.82 − 179.39 − 395.18 = 3910.25

Compute: 4484.82 − 179.39 = 4305.43; 4305.43 − 395.18 = 3910.25.

Step 5: Income tax (R5).
- Tax-free amount: 900.00
- Upper bracket begins: 3600.00
- Middle rate: 0.10, upper rate: 0.18

Taxable pay = 3910.25.
- Portion up to 900: untaxed.
- Portion 900 to 3600: 2700.00 × 0.10 = 270.00
- Portion above 3600: 3910.25 − 3600 = 310.25 × 0.18 = 55.845

Total tax = 270.00 + 55.845 = 325.845 → round half-up: 325.85.

Wait: 55.845 rounds... but we don't round intermediate products; sum first: 270.00 + 55.845 = 325.845, round to 325.85 (round half-up: 325.845 → third decimal is 5, so round up: 325.85). Actually 325.845 → two decimals: look at third decimal 5, round half up → 325.85. Yes.

Hmm, but wait — the exact decimal: 310.25 × 0.18 = 55.845. 2700 × 0.10 = 270. Sum = 325.845. Round half-up → 325.85.

Step 6: Net pay (R6).
- Net = gross − contribution − deduction − tax = 4484.82 − 179.39 − 395.18 − 325.85

Compute: 4484.82 − 179.39 = 4305.43; 4305.43 − 395.18 = 3910.25; 3910.25 − 325.85 = 3584.40.

Net pay = 3584.40.

Answer fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "4484.82"
- employee_contribution: "179.39"
- allowed_deduction: "395.18"
- taxable_pay: "3910.25"
- income_tax: "325.85"
- net_pay: "3584.40"
- clauses: R1 (row selection), R2 (rounding), R3 (contribution), R4 (deduction), R5 (tax), R6 (net pay), R9 (amendment resolves conflict).

Citations: "Calculated answers cite R1 through R6, and also R9 only when an amendment is needed to resolve a conflict." Here the amendment was needed to resolve the contract conflict, so include R9.

Clauses: ["R1","R2","R3","R4","R5","R6","R9"]

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

Let me process this payroll record.

Inputs:
- gross_pay: "4484.82"
- payroll_month: "2026-11"
- allowed_deduction: "395.18"
- contract gross_pay: "4728.75"
- amendment: gross_pay "4484.82", approved true, effective_month "2026-05"

Case schedule (authoritative, replaces defaults):
- second-half (2026-11 falls in 2026-07 through 2026-12): rate 0.04, cap 4500.00, deduction cap 400.00, free 900.00, upper 3600.00, middle_rate 0.10, upper_rate 0.18

Check R7 order:
1. gross_pay present: "4484.82" ✓
2. payroll_month present: "2026-11" ✓
3. Month has reference row: 2026-11 → second-half ✓
4. Contract conflict: contract gross_pay "4728.75" differs from payroll gross_pay "4484.82". Amendment: approved true, effective_month "2026-05" ≤ "2026-11", amount "4484.82" equals payroll record's gross_pay "4484.82". So amendment resolves conflict under R9. Cite R9 in calculated answer.

Now calculate:

Employee contribution (R3): rate 0.04 × min(4484.82, 4500.00) = 0.04 × 4484.82 = 179.3928 → round to 179.39.

Wait, R2 says round monetary calculation results to two decimal places using round-half-up. 0.04 × 4484.82 = 179.3928 → 179.39.

Allowed deduction (R4): 395.18. Check: must not exceed deduction cap 400.00 ✓ and gross pay minus rounded contribution: 4484.82 − 179.39 = 4305.43. 395.18 ≤ 4305.43 ✓. So allowed deduction = 395.18.

Taxable pay (R4): gross − contribution − deduction = 4484.82 − 179.39 − 395.18 = 3910.25.

Let me compute: 4484.82 − 179.39 = 4305.43. 4305.43 − 395.18 = 3910.25.

Income tax (R5): progressive brackets with free = 900.00, upper = 3600.00, middle_rate 0.10, upper_rate 0.18.

Taxable pay 3910.25.
- Portion up to 900.00: untaxed.
- Portion 900.00 to 3600.00: 2700.00 × 0.10 = 270.00.
- Portion above 3600.00: 3910.25 − 3600.00 = 310.25 × 0.18 = 55.845.

Total = 270.00 + 55.845 = 325.845 → round half-up to 325.85? Wait, 325.845 rounds to 325.85 (round-half-up: third decimal 5 rounds up). Actually 325.845 → the digit after second decimal is 5, so round up: 325.85.

Hmm, but "Do not round intermediate bracket products separately before summing income tax." So sum 270.00 + 55.845 = 325.845, then round → 325.85.

Wait, let me double-check 310.25 × 0.18 = 55.845. Yes.

Total tax = 325.845 → 325.85.

Net pay (R6): gross − contribution − deduction − tax = 4484.82 − 179.39 − 395.18 − 325.85.

4484.82 − 179.39 = 4305.43.
4305.43 − 395.18 = 3910.25.
3910.25 − 325.85 = 3584.40.

Net pay = 3584.40.

Fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "4484.82"
- employee_contribution: "179.39"
- allowed_deduction: "395.18"
- taxable_pay: "3910.25"
- income_tax: "325.85"
- net_pay: "3584.40"
- clauses: R1, R2, R3, R4, R5, R6, R9 (amendment resolves conflict)

Citation: "Calculated answers cite R1 through R6, and also R9 only when an amendment is needed to resolve a conflict." Here the amendment is needed to resolve the contract conflict (contract differs from payroll gross). So include R9.

Clauses: ["R1", "R2", "R3", "R4", "R5", "R6", "R9"].

Optional explanation string permitted. I could add brief explanation noting amendment resolves conflict.

Output one JSON object, no markdown fences.

Let me process this payroll record.

Inputs:
- Payroll record: gross_pay = 4484.82, payroll_month = 2026-11, allowed_deduction = 395.18
- Contract gross_pay = 4728.75 (conflicts with payroll gross_pay 4484.82)
- Amendment: gross_pay = 4484.82, approved = true, effective_month = 2026-05

Case reference schedule (authoritative, replaces defaults):
- first-half (2026-01 through 2026-06): rate 0.06, cap 4000.00, deduction 400.00, free 1100.00, upper 3600.00, middle_rate 0.14, upper_rate 0.24
- second-half (2026-07 through 2026-12): rate 0.04, cap 4500.00, deduction 400.00, free 900.00, upper 3600.00, middle_rate 0.10, upper_rate 0.18

Payroll month 2026-11 → second-half row.

Check order per R7:
1. Missing gross_pay? No, present (4484.82).
2. Missing payroll_month? No, 2026-11.
3. Month without reference row? 2026-11 is covered by second-half row. OK.
4. Contract conflict: contract gross_pay 4728.75 differs from payroll gross_pay 4484.82. Check amendment under R9: approved = true, effective_month 2026-05 ≤ 2026-11, amount 4484.82 equals payroll record's gross pay 4484.82. So the amendment resolves the conflict. Use gross_pay = 4484.82. Cite R9.

Now calculate:

Employee contribution (R3): rate 0.04 × min(4484.82, 4500.00) = 0.04 × 4484.82 = 179.3928 → round to 179.39.

Allowed deduction (R4): 395.18. Check cap: 400.00 (second-half deduction cap). 395.18 ≤ 400.00 OK. Check gross pay minus rounded contribution: 4484.82 − 179.39 = 4305.43. 395.18 ≤ 4305.43 OK.

Taxable pay: 4484.82 − 179.39 − 395.18 = 3910.25.

Let me compute: 4484.82 − 179.39 = 4305.43. 4305.43 − 395.18 = 3910.25.

Income tax (R5), second-half: free = 900.00, upper boundary = 3600.00, middle_rate = 0.10, upper_rate = 0.18.

- Portion up to 900.00: untaxed.
- Portion 900.00 to 3600.00: 2700.00 × 0.10 = 270.00.
- Portion above 3600.00: 3910.25 − 3600.00 = 310.25 × 0.18 = 55.845.

Total tax = 270.00 + 55.845 = 325.845 → round half-up to 325.85.

Wait — R2 says round monetary calculation results to two decimal places using round-half-up. Do not round intermediate bracket products separately before summing income tax. So sum first: 270.00 + 55.845 = 325.845, then round → 325.85. Hmm, 325.845 rounds to 325.85 with round-half-up (the third decimal is 5, round up the second decimal: 325.84 + 0.01 = 325.85). Actually 325.845 → the digit after hundredths is 5, so round up: 325.85. Yes.

Net pay (R6): 4484.82 − 179.39 − 395.18 − 325.85 = ?

4484.82 − 179.39 = 4305.43.
4305.43 − 395.18 = 3910.25.
3910.25 − 325.85 = 3584.40.

Net pay = 3584.40.

Fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "4484.82"
- employee_contribution: "179.39"
- allowed_deduction: "395.18"
- taxable_pay: "3910.25"
- income_tax: "325.85"
- net_pay: "3584.40"
- clauses: R1, R2, R3, R4, R5, R6, R9 (amendment resolves conflict).

Citation requirements: Calculated answers cite R1 through R6, and also R9 only when an amendment is needed to resolve a conflict. Here the amendment was needed (contract conflict), so include R9.

Also mention the case schedule in R1? Clauses are identifiers like R3. I'll include ["R1","R2","R3","R4","R5","R6","R9"].

Optional explanation string permitted. I can add a brief explanation noting the amendment resolved the conflict and the second-half schedule row applies.

Do not include input-only fields like payroll_month, contract_gross_pay, amendment.

Money as strings with two decimals. Good.

Double-check contribution: 0.04 × 4484.82 = 179.3928. Round half-up to two decimals: 179.39 (third decimal 2 < 5). Yes.

Check wage cap: 4500.00; min(4484.82, 4500.00) = 4484.82. Correct.

Taxable pay 3910.25 > upper boundary 3600.00, so upper bracket applies to 310.25.

Tax: 2700.00 × 0.10 = 270.00; 310.25 × 0.18 = 55.845. Sum 325.845 → 325.85.

Net: 3584.40.

JSON only, no markdown fences.