Let me work through this.

Payroll month: 2026-05 → first-half row of the case schedule (since 2026-01 through 2026-06 is first-half).

Case schedule first-half: rate 0.06, cap 5000.00, deduction 400.00, free 1100.00, upper 3300.00, middle_rate 0.10, upper_rate 0.18.

Gross pay: 5000.02. Allowed deduction: 0.00 (given).

Employee contribution: rate 0.06 × min(gross, cap) = 0.06 × min(5000.02, 5000.00) = 0.06 × 5000.00 = 300.00.

Allowed deduction check: must not exceed deduction cap (400.00) and gross minus contribution (5000.02 − 300.00 = 4700.02). 0.00 is fine.

Taxable pay: 5000.02 − 300.00 − 0.00 = 4700.02.

Income tax:
- Free: 1100.00 → tax 0.
- Middle portion: from 1100.00 to 3300.00 → 2200.00 × 0.10 = 220.00.
- Upper portion: 4700.02 − 3300.00 = 1400.02 × 0.18 = 252.0036 → round to 252.00? Wait — do not round intermediate bracket products separately before summing income tax (R2 and R5). So sum: 220.00 + 252.0036 = 472.0036 → round half up to two decimals = 472.00.

Net pay: gross − contribution − deduction − tax = 5000.02 − 300.00 − 0.00 − 472.00 = 4228.02.

Check: 5000.02 − 300.00 = 4700.02; 4700.02 − 472.00 = 4228.02. Yes.

Clues to cite: R1 (row selection, schedule), R2 (rounding), R3 (contribution), R4 (deduction and taxable pay), R5 (tax), R6 (net pay/answer). No amendment needed, so not R9.

Monetary fields as two-decimal strings:
- gross_pay: "5000.02"
- employee_contribution: "300.00"
- allowed_deduction: "0.00"
- taxable_pay: "4700.02"
- income_tax: "472.00"
- net_pay: "4228.02"

Decision: calculate, currency LCR.

Return one JSON object without markdown fences.

We need to process a payroll record.

Record: gross_pay = "5000.02", payroll_month = "2026-05", allowed_deduction = "0.00".

Authoritative case reference schedule supplied: first-half: rate 0.06, cap 5000.00, deduction 400.00, free 1100.00, upper 3300.00, middle_rate 0.10, upper_rate 0.18. second-half: rate 0.07, cap 4000.00, deduction 400.00, free 1100.00, upper 3600.00, middle_rate 0.12, upper_rate 0.22.

Payroll month 2026-05 is in first half (2026-01 through 2026-06). So use first-half row per the schedule.

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

Employee contribution (R3): rate 0.06 × min(gross 5000.02, cap 5000.00) = 0.06 × 5000.00 = 300.00.

Allowed deduction: 0.00. Check: not exceeding deduction cap (400.00), and not exceeding gross pay minus contribution: 5000.02 − 300.00 = 4700.02. 0.00 ≤ both. Fine.

Taxable pay: gross − contribution − deduction = 5000.02 − 300.00 − 0.00 = 4700.02.

Income tax (R5): taxable 4700.02.
- Tax-free amount: 1100.00 → untaxed portion 1100.00.
- Middle bracket: from 1100.00 up to upper 3300.00 → amount = 3300.00 − 1100.00 = 2200.00 at 0.10 = 220.00.
- Upper bracket: above 3300.00 → 4700.02 − 3300.00 = 1400.02 at 0.18 = 252.0036.

Total = 220.00 + 252.0036 = 472.0036 → round half-up to 472.00.

Net pay: gross − contribution − deduction − tax = 5000.02 − 300.00 − 0.00 − 472.00 = 4228.02.

Check rounding: taxable pay 4700.02 exactly two decimals. Contribution 300.00. Tax 472.00. Net 4228.02.

Let me double check the multiplication: 1400.02 × 0.18 = 252.00... 1400.02 × 0.18 = 252.0036. Yes.

Also 2200 × 0.10 = 220. Yes.

Round total: 472.0036 → 472.00.

Net: 5000.02 − 300.00 = 4700.02; − 0 = 4700.02; − 472.00 = 4228.02.

Answer fields: decision: calculate, currency: LCR, gross_pay "5000.02", employee_contribution "300.00", allowed_deduction "0.00", taxable_pay "4700.02", income_tax "472.00", net_pay "4228.02".

Clauses: Calculated answers cite R1 through R6. Also R9 only when amendment needed — no amendment here. So cite R1, R2, R3, R4, R5, R6.

Explanation optional — I can include a brief one. Include the note that the case schedule replaces defaults and 2026-05 is first half.

Should I include explanation? Optional. I'll include a short one.

We need to process a payroll record for 2026-05 with an authoritative case reference schedule.

Payroll month: 2026-05 → first-half row per R1 period boundaries. The case schedule gives first-half: rate 0.06, cap 5000.00, deduction cap 400.00, free 1100.00, upper 3300.00, middle_rate 0.10, upper_rate 0.18.

Gross pay: 5000.02.

Employee contribution: rate × min(gross, cap) = 0.06 × min(5000.02, 5000.00) = 0.06 × 5000.00 = 300.00.

Allowed deduction: 0.00, within cap 400.00 and ≤ gross − contribution = 5000.02 − 300.00 = 4700.02. OK.

Taxable pay: 5000.02 − 300.00 − 0.00 = 4700.02.

Income tax: progressive marginal.
- Free amount: 1100.00 untaxed.
- Portion above free up to upper boundary (3300.00): 3300.00 − 1100.00 = 2200.00 at 0.10 = 220.00.
- Portion above 3300.00: 4700.02 − 3300.00 = 1400.02 at 0.18 = 252.0036 → but don't round intermediate products separately before summing; sum raw: 220.00 + 252.0036 = 472.0036 → round half up to 472.00.

Net pay: 5000.02 − 300.00 − 0.00 − 472.00 = 4228.02.

Check: gross 5000.02, contribution 300.00, deduction 0.00, tax 472.00 → net 4228.02.

All fields as two-decimal strings. Currency LCR. Clauses: R1 (row selection, schedule), R2 (rounding), R3 (contribution), R4 (deduction/taxable), R5 (tax), R6 (net/pay fields). No amendment needed.

Output JSON without markdown fences.