Review Arkansas TEA below-trigger payment formula against DHS manual

[MaxGhenis]

During Axiom Arkansas TEA encoding, the source-first pass found a likely mismatch in ar_tea.

Primary source evidence:

• Arkansas DHS Transitional Employment Assistance Policy Manual, section 2362, corpus citation path us-ar/policy/dhs/tea/manual/2024/page-93, source as of 2026-07-02.
• The manual says the family-size payment is reduced by 50% when countable monthly gross income excluding assigned child support is at least $1,026.
• Example Basic prototype #1 has $150/month gross income, below $1,026, and says the payment is the maximum grant for family size 3: $204.
• Example Run black formatting on docs #2 has $1,200/month gross income, above $1,026, and says the payment is 50% of the two-person maximum: $81.

Current PE implementation:

• policyengine_us/variables/gov/states/ar/dhs/tea/ar_tea.py
• Above trigger: maximum_benefit * (1 - reduction_rate).
• Below trigger: max_(maximum_benefit - countable_income, 0).

The below-trigger branch appears inconsistent with section 2362 / Example #1, which indicates payment remains the maximum grant when income eligible and below the gross-income trigger. Axiom encoded the source-law branch as maximum grant below trigger, reduced payment above trigger, and zero only when the income eligibility budget fails.

Related Axiom work:

• Corpus PR: Add Arkansas TEA official corpus sources TheAxiomFoundation/axiom-corpus#162
• RuleSpec PR: Encode Arkansas TEA payment rules TheAxiomFoundation/rulespec-us#513

This may affect oracle parity for the final ar_tea amount; parameter/direct components can still be compared separately.