Let me start by listing the documents to get the case inputs.

Payroll: gross_pay 850.21, payroll_month 2026-01, allowed_deduction 125.58. Contract gross pay 850.21 matches, so no conflict.

Month 2026-01 is in the first half of 2026. I need to look up the reference row. The rules mention a reference_tables schedule available through lookup_reference. Let me look up first-half.

The first-half row covers 2026-01 through 2026-06 (months ["2026-01", "2026-06"] presumably meaning the range). Rate 0.06, cap 4500.00, deduction cap 400.00, free 1100.00, upper 2800.00, middle_rate 0.12, upper_rate 0.18.

Now compute:
- Employee contribution = 0.06 * min(850.21, 4500.00) = 0.06 * 850.21 = 51.0126 → round to 51.01.
- Allowed deduction = 125.58. Check cap: must not exceed 400.00 or gross pay minus rounded contribution = 850.21 - 51.01 = 799.20. 125.58 ≤ both. OK.
- Taxable pay = 850.21 - 51.01 - 125.58 = 673.62.
- Income tax: taxable 673.62 ≤ free 1100.00, so tax = 0.00.
- Net pay = 850.21 - 51.01 - 125.58 - 0.00 = 673.62.

Let me verify with calculate.

All checks pass:
- gross_pay 850.21, month 2026-01 covered by first-half row.
- Contract gross pay 850.21 matches payroll gross pay — no conflict, no amendment needed.
- Employee contribution = 51.01.
- Allowed deduction 125.58 ≤ 400.00 (deduction cap) and ≤ 850.21 - 51.01 = 799.20. Valid.
- Taxable pay = 673.62, below the 1100.00 free amount, so income tax = 0.00.
- Net pay = 673.62.

Citations: R1 (month selection/row), R2 (rounding), R3 (contribution), R4 (deduction and taxable pay), R5 (tax), R6 (net pay). No R9 needed since contract matches.

Let me start by listing documents and looking up the reference tables. Actually, I need to first list documents to find the case inputs, then read them. The lookup_reference calls are independent of the documents, but I don't know which half to look up until I know the payroll month. However, I could look up both halves in parallel with list_documents. Let me do that: list_documents + lookup_reference(first-half) + lookup_reference(second-half) in one block.

Now read both documents to get the payroll record and contract.

Payroll month 2026-01 → first-half row: rate 0.06, cap 4500.00, deduction cap 400.00, free 1100.00, upper 2800.00, middle_rate 0.12, upper_rate 0.18.

Inputs: gross_pay = 850.21, allowed_deduction = 125.58 (≤ 400.00 cap). Contract gross_pay matches payroll gross_pay (850.21), so no conflict, no amendment needed.

Employee contribution = min(850.21, 4500.00) * 0.06 = 51.0126 → round half up to 51.01.

Taxable pay = 850.21 − 51.01 − 125.58 = 673.62.

Taxable pay 673.62 ≤ free 1100.00 → income tax = 0.00.

Net pay = 850.21 − 51.01 − 125.58 − 0.00 = 673.62.

Let me verify with calculate.

All checks:
- gross_pay present: 850.21 (valid, two decimals)
- payroll_month: 2026-01 → first-half row applies (rate 0.06, cap 4500.00, deduction 400.00, free 1100.00, upper 2800.00, middle 0.12, upper 0.18)
- No contract conflict: contract gross_pay 850.21 equals payroll gross_pay → no amendment needed, no R9 citation.
- allowed_deduction 125.58 ≤ min(400.00 cap, 850.21 − 51.01 = 799.20) → valid.
- Contribution: min(850.21, 4500.00) × 0.06 = 51.0126 → 51.01.
- Taxable: 673.62 ≤ free 1100.00 → tax 0.00.
- Net: 673.62.

Return R6 JSON with clauses R1, R2, R3, R4, R5, R6.

Let me start by listing the documents and looking up the reference tables. The task says reference rows are available only through lookup_reference. I need to know the payroll month first, though. Let me list documents first, then read the document, then lookup the reference based on the month.

Independent calls: list_documents can be done first. lookup_reference requires knowing which half to use — depends on the payroll month. So first call list_documents alone (or I could call both halves, but better to know the month first).

Let me call list_documents.

Let me read both documents in parallel since they're independent.

Payroll month is 2026-01, which is in the first half of 2026. Let me look up the first-half reference.

Payroll month 2026-01 is covered by the first-half reference row.

Inputs:
- gross_pay = 850.21
- allowed_deduction = 125.58
- contract gross_pay = 850.21 — matches, no conflict, no amendment needed.

Check R4: allowed_deduction must not exceed the selected deduction cap (400.00) or gross pay minus the rounded employee contribution.

Employee contribution (R3): rate 0.06 × min(850.21, 4500.00) = 0.06 × 850.21 = 51.0126 → round half up to 51.01.

Allowed deduction check: min(400.00, 850.21 − 51.01 = 799.20) = 400.00. 125.58 ≤ 400.00 and ≤ 799.20. Valid.

Taxable pay (R4): 850.21 − 51.01 − 125.58 = 673.62.

Income tax (R5): taxable 673.62.
- Free amount: 1100.00. Taxable pay 673.62 ≤ 1100.00, so all untaxed. Tax = 0.00.

Net pay (R6): 850.21 − 51.01 − 125.58 − 0.00 = 673.62.

Let me verify with the calculator.

The calculator doesn't accept a line like `contribution` alone as output — every line must be an assignment. Let me restructure: assign each output to a name, and the last line's value... Actually it says "Returns the value of every assigned name." So I just need each line to be an assignment. Let me fix.

Results:
- Employee contribution: 51.01 (0.06 × 850.21 = 51.0126 → 51.01)
- Allowed deduction: 125.58 (valid: ≤ 400.00 cap and ≤ 799.20 available)
- Taxable pay: 673.62
- Income tax: 0.00 (taxable ≤ 1100.00 free amount)
- Net pay: 673.62

Contract gross (850.21) matches payroll gross, so no conflict, no R9 citation needed.

Return R6 JSON with clauses R1–R6.