We need to process a payroll record for 2026-06 (first-half row per the case schedule).

Case schedule first-half: rate 0.04, cap 4500.00, deduction 400.00, free 1200.00, upper 2800.00, middle_rate 0.14, upper_rate 0.22.

Gross pay: 3468.15. Allowed deduction: 47.85.

Employee contribution: rate 0.04 × min(gross, cap) = 0.04 × 3468.15 = 138.726 → round half up to 138.73.

Check allowed deduction: must not exceed deduction cap (400.00) or gross pay minus rounded contribution: 3468.15 − 138.73 = 3329.42. 47.85 ≤ both, OK.

Taxable pay: 3468.15 − 138.73 − 47.85 = 3281.57.

Income tax: taxable 3281.57. Free = 1200.00. Upper begins at 2800.00.

Portion 1200.00 → 2800.00: 1600.00 × 0.14 = 224.00.
Portion above 2800.00: 3281.57 − 2800.00 = 481.57 × 0.22 = 105.9454 → but do not round intermediate products; sum then round: 224.00 + 105.9454 = 329.9454 → round half up = 329.95.

Net pay: 3468.15 − 138.73 − 47.85 − 329.95 = ?

3468.15 − 138.73 = 3329.42. 3329.42 − 47.85 = 3281.57. 3281.57 − 329.95 = 2951.62.

So net pay = 2951.62.

Fields: decision calculate, currency LCR, gross_pay "3468.15", employee_contribution "138.73", allowed_deduction "47.85", taxable_pay "3281.57", income_tax "329.95", net_pay "2951.62".

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

No amendment present, no contract conflict.

Output JSON only, no markdown fences.

Let me process this payroll record.

Inputs:
- gross_pay: "3468.15"
- payroll_month: "2026-06"
- allowed_deduction: "47.85"

Payroll month 2026-06 is in first-half (2026-01 through 2026-06). The case provides an authoritative reference schedule, so I must use the first-half row from the schedule:

first-half: rate = 0.04, cap = 4500.00, deduction = 400.00, free = 1200.00, upper = 2800.00, middle_rate = 0.14, upper_rate = 0.22

Step 1: Employee contribution (R3):
min(gross_pay, cap) = min(3468.15, 4500.00) = 3468.15
contribution = 0.04 × 3468.15 = 138.726
Round to two decimals (round-half-up): 138.726 → 138.73

Wait: 138.726 rounds to 138.73 (since third decimal is 6, round up). Yes, 138.73.

Step 2: Allowed deduction check (R4):
allowed_deduction = 47.85
- Must not exceed deduction cap: 47.85 ≤ 400.00 ✓
- Must not exceed gross pay minus rounded contribution: 3468.15 − 138.73 = 3329.42; 47.85 ≤ 3329.42 ✓

Step 3: Taxable pay (R4):
taxable = gross_pay − contribution − allowed_deduction = 3468.15 − 138.73 − 47.85 = 3281.57

Let me compute: 3468.15 − 138.73 = 3329.42; 3329.42 − 47.85 = 3281.57.

Step 4: Income tax (R5):
Brackets:
- Tax-free amount: 1200.00
- Middle bracket: from 1200.00 to 2800.00 (upper bracket begins at 2800.00), rate 0.14
- Upper bracket: above 2800.00, rate 0.22

Taxable pay = 3281.57

Portion up to 1200.00: 1200.00 × 0 = 0
Portion 1200.00 to 2800.00: 2800.00 − 1200.00 = 1600.00 × 0.14 = 224.00
Portion above 2800.00: 3281.57 − 2800.00 = 481.57 × 0.22 = 105.9454

Total = 224.00 + 105.9454 = 329.9454
Round to two decimals: 329.9454 → 329.95 (round-half-up: third decimal is 5, wait 329.9454 — the third decimal is 5, fourth is 4. Rounding to two decimals: 329.9454 → look at 0.0054 portion... Actually 329.9454: two decimal places means we keep 329.94 or round to 329.95. The digit after the second decimal is 5 (329.94|54), so round half up → 329.95.

Wait, let me be careful: 329.9454. The second decimal is 4, the remainder is 0.0054. Since 0.0054 > 0.005, rounds up to 329.95. Yes.

Actually, more precisely: 329.9454 → the fractional part beyond two decimals is 0.0054, which is more than 0.005, so round up: 329.95.

Hmm, but wait — 481.57 × 0.22: 481.57 × 0.22 = 105.9454. Let me verify: 481.57 × 0.22 = 481.57 × 22 / 100 = 10594.54 / 100 = 105.9454. Yes.

Total tax = 224.00 + 105.9454 = 329.9454 → 329.95.

Step 5: Net pay (R6):
net = gross − contribution − allowed_deduction − tax = 3468.15 − 138.73 − 47.85 − 329.95

3468.15 − 138.73 = 3329.42
3329.42 − 47.85 = 3281.57
3281.57 − 329.95 = 2951.62

Net pay = 2951.62

Check: taxable_pay = 3281.57, income_tax = 329.95, net = taxable − tax = 3281.57 − 329.95 = 2951.62. ✓

Output fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "3468.15"
- employee_contribution: "138.73"
- allowed_deduction: "47.85"
- taxable_pay: "3281.57"
- income_tax: "329.95"
- net_pay: "2951.62"
- clauses: R1 (schedule selection / scope), R2 (rounding), R3 (contribution), R4 (deduction and taxable pay), R5 (income tax), R6 (net pay)

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

No amendment needed, no contract conflict. No R9 citation needed.

Note: the schedule replaces defaults, so R1 covers that. The first-half schedule row applies to 2026-06.

Let me double-check the contribution rounding: 0.04 × 3468.15 = 138.726. Round half up to two decimals: 138.73. Yes.

Taxable pay check: 3468.15 − 138.73 − 47.85 = 3281.57. Correct.

Tax brackets with taxable 3281.57:
- Free: 1200.00 → 0 tax
- Middle: (2800.00 − 1200.00) = 1600.00 at 0.14 = 224.00
- Upper: (3281.57 − 2800.00) = 481.57 at 0.22 = 105.9454
- Total: 329.9454 → 329.95

Net: 3468.15 − 138.73 − 47.85 − 329.95 = 2951.62.

All good. Output JSON without markdown fences, one object.

We need to process a payroll record under rulebook version 3, with an authoritative case reference schedule that overrides defaults.

Input:
- gross_pay: 3468.15
- payroll_month: 2026-06 → first-half row (2026-01 through 2026-06)
- allowed_deduction: 47.85

Case schedule first-half:
- rate: 0.04
- cap: 4500.00
- deduction: 400.00
- free: 1200.00
- upper: 2800.00
- middle_rate: 0.14
- upper_rate: 0.22

Calculations:
1. Employee contribution (R3): rate × min(gross, cap) = 0.04 × min(3468.15, 4500.00) = 0.04 × 3468.15 = 138.726 → round to 138.73.

2. Allowed deduction check (R4): must not exceed deduction cap (400.00) or gross pay minus rounded contribution = 3468.15 − 138.73 = 3329.42. 47.85 ≤ 400.00 and ≤ 3329.42. OK.

3. Taxable pay: gross − contribution − deduction = 3468.15 − 138.73 − 47.85 = 3281.57.

Check: 3468.15 − 138.73 = 3329.42; 3329.42 − 47.85 = 3281.57. Yes.

4. Income tax (R5), marginal:
- Tax-free: 1200.00 → untaxed.
- Middle bracket: from 1200 to upper 2800: portion = 2800 − 1200 = 1600 at 0.14 = 224.00.
- Upper bracket: above 2800: 3281.57 − 2800 = 481.57 at 0.22 = 105.9454 → but do not round intermediate products separately before summing. Sum: 224.00 + 105.9454 = 329.9454 → round half-up to 329.95.

Wait, 481.57 × 0.22 = 105.9454. Total = 224 + 105.9454 = 329.9454 → rounds to 329.95.

5. Net pay: gross − contribution − deduction − tax = 3468.15 − 138.73 − 47.85 − 329.95 = ?

3468.15 − 138.73 = 3329.42
3329.42 − 47.85 = 3281.57
3281.57 − 329.95 = 2951.62.

Net pay = 2951.62.

Fields:
- decision: "calculate"
- currency: "LCR"
- gross_pay: "3468.15"
- employee_contribution: "138.73"
- allowed_deduction: "47.85"
- taxable_pay: "3281.57"
- income_tax: "329.95"
- net_pay: "2951.62"
- clauses: R1, R2, R3, R4, R5, R6. Also maybe R1 for schedule selection. The schedule is authoritative per R1. Cite R1 through R6.

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

Explanation optional; can include a brief explanation. The instructions say an optional explanation string is permitted. I'll include a short one.

Return one JSON object without markdown fences.