We need answer JSON only. Need calculate. Need follow rules. Need inspect.

Payroll month 2026-05 -> first-half. Authoritative case schedule supplied, numeric values replace defaults for case only. First-half: rate 0.04, cap 5000.00, deduction cap 400.00, free 1000.00, upper begins 3600.00, middle_rate 0.10, upper_rate 0.24.

Record gross_pay 8370.45, allowed_deduction 370.62. No contract_gross_pay, no amendment. Need calculate.

R3 employee contribution = rate * min(gross, wage cap). min(8370.45, 5000.00)=5000.00. rate 0.04 => 200.00. Round 200.00.

R4 allowed_deduction defaults but provided 370.62. Must not exceed deduction cap 400.00, or gross minus rounded employee contribution = 8370.45 - 200.00 = 8170.45. 370.62 <= both. Taxable pay = gross - employee contribution - allowed_deduction = 8370.45 - 200.00 - 370.62 = 7799.83? Let's compute: 8370.45 - 200 = 8170.45. -370.62 = 7799.83. Yes.

R5 income tax progressive. Taxable pay 7799.83. Free 1000.00. Upper bracket begins 3600.00. Middle on portion above free up to upper: 3600.00 - 1000.00 = 2600.00 * 0.10 = 260.00. Upper on portion above 3600: 7799.83 - 3600.00 = 4199.83 * 0.24 = ? 4199.83*0.24 = 1007.9592? Compute: 4199.83*24/100 = 100795.92/100 = 1007.9592. Sum = 1267.9592. Round half-up to 1267.96. Need not round intermediate bracket products separately before summing. Actually we computed products exact decimal. 260 + 1007.9592 = 1267.9592 -> 1267.96.

Net pay = gross - employee contribution - allowed deduction - income tax = 8370.45 - 200.00 - 370.62 - 1267.96 = 6531.87? Compute: 8370.45 - 200 = 8170.45. -370.62 = 7799.83. -1267.96 = 6531.87. Yes.

Need clauses supporting calculation. Calculated answers cite R1 through R6, and also R9 only when amendment needed. No amendment. So clauses ["R1","R2","R3","R4","R5","R6"] maybe exactly. Need include? "Every monetary expected answer exact..." provide clause references. Allowed fields: calculate uses decision, currency, gross_pay, employee_contribution, allowed_deduction, taxable_pay, income_tax, net_pay, clauses. Optional explanation permitted. Need output JSON object no Markdown. Money strings two decimals. Should we include explanation? Probably not necessary. Need no input-only fields.

Need ensure allowed_deduction 370.62. Employee contribution 200.00. taxable 7799.83. income 1267.96. net 6531.87. Currency LCR. Decision calculate.

Let's double-check R4: allowed deduction must not exceed selected deduction cap or gross minus rounded employee contribution. 370.62 <= 400, <=8170.45. Good.

Potential issue: Authoritative schedule "first-half" has rate 0.04, cap 5000.00, deduction 400.00. Yes.

Need final exact JSON. No Markdown. Use clauses maybe include R1-R6. The rule says "Calculated answers cite R1 through R6" meaning all. Should include R1,R2,R3,R4,R5,R6. Could include R2 arithmetic. Good.

Let's produce.

We need answer JSON only. Need calculate using authoritative schedule. Need parse record. gross_pay 8370.45, payroll_month 2026-05 -> first-half. allowed_deduction 370.62.

Authoritative first-half values: rate 0.04, cap 5000.00, deduction cap 400.00, tax-free 1000, upper bracket begins 3600, middle 0.10, upper 0.24.

Need compute employee_contribution = rate * min(gross, cap) = 0.04 * 5000.00 = 200.00. Rounded.

Allowed deduction must not exceed deduction cap 400.00 or gross minus rounded employee contribution = 8370.45 - 200.00 = 8170.45. 370.62 <=400 and <=8170.45, so allowed 370.62.

Taxable_pay = gross - employee_contribution - allowed_deduction = 8370.45 - 200.00 - 370.62 = 7799.83? Let's compute: 8370.45 - 200 = 8170.45. -370.62 = 7799.83 yes.

Income tax progressive:
Tax-free amount 1000 untaxed.
Upper bracket begins 3600. Portion above free up to upper = 3600 - 1000 = 2600 at middle rate 0.10 = 260.00.
Portion above upper = taxable_pay - 3600 = 7799.83 - 3600 = 4199.83 at upper rate 0.24.
4199.83 * 0.24 = 1007.9592? Compute 4199.83*24/100 = 100795.92/100? Let's do: 4199.83 * 0.2 = 839.966. *0.04 = 167.9932. Sum = 1007.9592. Round half-up to two decimals = 1007.96 (third decimal 9? 1007.9592 -> hundredths: 1007.95 with third decimal 9? Let's see 1007.9592: digits after decimal 9592. To two decimals: 1007.96 because third digit 9 >=5. Yes).

Total income tax = 260.00 + 1007.9592 = 1267.9592. Round total under R2 = 1267.96. Note R2 says do not round intermediate bracket products separately before summing. So total 1267.9592 -> 1267.96. Same as if sum unrounded. If rounded each: 260 + 1007.96 = 1267.96.

Net pay = gross - employee contribution - allowed deduction - rounded income tax = 8370.45 - 200.00 - 370.62 - 1267.96 = 6531.87? Let's compute: 8370.45 - 200 = 8170.45. -370.62 = 7799.83. -1267.96 = 6531.87. Yes.

Need clauses. Calculated answers cite R1 through R6. Also R9 only if amendment needed. No amendment. So clauses maybe ["R1","R2","R3","R4","R5","R6"]. Need exact required fields: decision, currency, gross_pay, employee_contribution, allowed_deduction, taxable_pay, income_tax, net_pay, clauses. Optional explanation permitted. Money strings two decimals. Ensure JSON object no markdown. Use "calculate".

Need ensure allowed_deduction input 370.62 within cap 400.00. yes.

Let's final.

We need answer only JSON object no markdown. Need process payroll. Need inspect. We have record gross_pay 8370.45, month 2026-05, allowed_deduction 370.62. Authoritative case reference schedule first-half applies (2026-01 through 2026-06). Values replace defaults: rate 0.04, cap 5000.00, deduction cap 400.00, free 1000.00, upper 3600.00, middle_rate 0.10, upper_rate 0.24.

Need calculate employee contribution: rate * min(gross, cap) = 0.04 * min(8370.45,5000) = 0.04*5000 = 200.00. Round 200.00.

Allowed deduction: input 370.62. Must not exceed deduction cap 400.00 or gross - rounded employee contribution = 8370.45 - 200.00 = 8170.45. 370.62 <= both. allowed_deduction = 370.62.

Taxable pay = gross - employee contribution - allowed deduction = 8370.45 - 200.00 - 370.62 = 7799.83? Compute: 8370.45-200=8170.45; -370.62=7799.83 yes.

Income tax progressive:
Taxable pay 7799.83.
Tax-free up to 1000.00 untaxed.
Portion above free up to upper boundary 3600.00: amount = 3600 - 1000 = 2600.00 taxed at middle rate 0.10 = 260.00.
Portion above upper boundary: 7799.83 - 3600 = 4199.83 taxed at upper rate 0.24 = ? 4199.83 * 0.24 = 1007.9592. Round? Need not round intermediate bracket products separately before summing. Sum = 260.00 + 1007.9592 = 1267.9592. Round total to two decimals half-up = 1267.96. If separately round upper product 1007.96 plus 260 =1267.96 same. Okay.

Net pay = gross - employee contribution - allowed deduction - income tax = 8370.45 - 200.00 - 370.62 - 1267.96 = 6531.87? Compute: 8370.45 - 200 = 8170.45; -370.62=7799.83; -1267.96=6531.87. Yes.

Need clauses. For calculate cite R1 through R6. Also R9 only when amendment needed. No amendment. So clauses ["R1","R2","R3","R4","R5","R6"] maybe include R1-R6. The instruction: Calculated answers cite R1 through R6. Use exactly required answer fields and only clauses that directly govern. Answer fields: decision, currency, gross_pay, employee_contribution, allowed_deduction, taxable_pay, income_tax, net_pay, clauses. Optional explanation permitted. Do not include input-only fields. Need all monetary strings with two decimals. decision "calculate". currency "LCR".

Need ensure no Markdown. Return JSON object. Let's produce.

Potential issue: Authoritative schedule says "schedule must include rate, cap, deduction, free, upper, middle_rate, and upper_rate in each row." They provided. In tool mode available only through lookup_reference. Here supplied authoritative schedule. Use it. Yes.

Let's final.