Derive Arkansas 2026+ minus adjustments from the indexed statutory tables

[MaxGhenis]

Summary

From 2027, Arkansas income tax projections were internally inconsistent:

• rates/main/rate.yaml thresholds uprate (gov.irs.uprating, rounded down to $100).
• rates/main/reduction.yaml, the minus-adjustment scale in tax = rate × TI − reduction, had no uprating, so its thresholds and amounts stayed at their 2026 values.

As a result, 2027+ tax fell as income crossed each 2026 bound: −$111.98 at $11,200, −$63.97 at $16,000 and −$79.17 at $26,400 (and −$112 at $5,600 before the $0 floor). Tax was also wrong between the old and uprated bounds.

This PR stops storing the 2026+ minus adjustments and derives them from the tables that A.C.A. § 26-51-201(a)(4) (Act 1 of 2026) sets out and that § 26-51-201(a)(5) and (d) index each year:

• (A) table (net income ≤ the high-income threshold): rate.yaml, taxed at marginal rates, each from its row's "From" bound.
• (B) table (above the threshold): new high_income/rate.yaml, 2% to $4,700 and 3.7% above, applied to all of the filer's net income.
• (C) bracket adjustment: new high_income/bracket_adjustment.yaml, $290 falling $10 per $100 row to $0. It is subtracted from (B).
• High-income threshold: new high_income/threshold.yaml, $94,700.

ar_main_income_tax (new, in ar_income_tax_helpers.py) now computes the schedule for ar_income_tax_before_non_refundable_credits_indiv, …_joint and ar_uses_low_income_tax_tables, which each used to repeat rate × TI − reduction.

• 2014–2025 keep the published DFA-card path behind a new switch, use_published_reduction (true through 2025). Results are unchanged.
• 2026 results are unchanged at every whole-dollar income. The derived schedule equals Act 1 of 2026 to within 1e-12, including the −$2.66 step at $94,700 → $94,701 that the Act itself creates. The one change is for fractional taxable income strictly between a row's upper bound and the next row's start, such as $94,800.50, a gap under $1 that the statute's whole-dollar rows skip. Such income now falls in the higher row. That is the ceiling convention Fix Arkansas 2025 and 2024 income tax minus-adjustment schedules against the DFA cards #9624's own reference implementation uses.
• 2027+ is consistent by construction. Because the reduction is derived, it also follows parameter reforms. A reform that moves a rate-table bound no longer makes tax jump at the old bound.

What § 26-51-201(d) indexes, and how it rounds

Quoted from the enacted Acts. Act 1 of 2026 changed only (a)(4) and added (a)(5); it left (d) as amended by Act 532 of 2023.

(d)(1) … The secretary shall increase the minimum and maximum dollar amounts for each rate bracket, rounding to the nearest one hundred dollars ($100), for which a tax is imposed under the table by the cost-of-living adjustment for each calendar year and by not changing the rate applicable to any rate bracket as adjusted.
— Act 532 of 2023, § 2

(5) The tables set forth in subdivisions (a)(1)-(4) of this section shall be adjusted annually in accordance with the method set forth in subsection (d) of this section.
— Act 1 of 2026 (1st Ext. Sess.), § 1

What that means for each amount, and what this PR does:

Amount	Indexed?	Basis
(A) row bounds	Yes	Bracket minimums and maximums in an (a)(4) table
$94,700 threshold	Yes	It is the (A) top bracket's maximum. DFA indexed it on every card: 89,600 → 92,300 (2024), 92,300 → 94,700 (2025)
(B) $4,700 2% top	Yes	Bracket bound. The cards' final minus adjustments imply 4,500 → 4,600 → 4,700 (87.40 = 1.9% × 4,600; 89.30 = 1.9% × 4,700)
(C) row bounds	Yes, each row	DFA's 2023 and 2024 cards: "Ark. Code Ann. 26-51-201(d)(1) requires each bracket to be increased annually by the cost-of-living adjustment, rounding to the nearest $100", which produced their asterisked $200 rows
(C) dollar amounts ($290 … $10)	No	Not bracket bounds. Every 2022–2025 card kept the enacting Act's $10 steps ($460, $430, $310 start)
Rates	No	"by not changing the rate"

Rounding. The statute says nearest $100, but rate.yaml rounded down, so this PR switches it to nearest. DFA's cards follow the statute. Act 532 of 2023's TY2023 table starts its rows at $5,100 / $10,300 / $14,700 / $24,300 and tops out at $87,000. The 2023 card has $5,300 / $10,600 / $15,100 / $25,000 / $89,600. That is each amount × 1.03 (the COLA cap) rounded to the nearest $100: 5,100 × 1.03 = 5,253 → 5,300. Rounding down would need a 3.9% COLA, above the 3% cap. rate.yaml brackets 5 and 6, which are .inf in every year since 2021/2022, drop their uprating metadata: core rounds nearest with Python's round, which overflows on infinity.

Row keys. Each (C) row is keyed on the round "Less Than or Equal To" bound of the row before it (94,700, 94,800, …, 97,600) and evaluated with calc(right=True). Rounding those round numbers to the nearest $100 keeps every row starting exactly one dollar above the prior bound. The first row always shares the high-income threshold's value, and a test checks this for every year.

Before and after (2027)

ar_income_tax_before_non_refundable_credits_indiv, 2027:

Taxable income	Base	This PR	Change	Why
$5,750	3.00	0.00	−3.00	The 2% row now starts at $5,800 (5,600 × 1.0298 = 5,767, nearest $100)
$11,300	2.00	110.00	+108.00	Base took 2% × 11,300 − the frozen $224
$16,200	198.00	255.00	+57.00	Base took 3% × 16,200 − the frozen $288
$26,800	544.00	614.20	+70.20	Base took 3.4% × 26,800 − the frozen $367.20
$50,000	1,482.80	1,471.40	−11.40	Derived (A) reduction is $378.60, not the frozen $367.20
$97,000	3,439.10	3,210.40	−228.70	Below the indexed $97,500 threshold, so table (A) applies; base applied the un-indexed 2026 ladder
$97,550	3,519.45	3,237.75	−281.70	First indexed (C) row ($290 adjustment); base was in the frozen ladder's last row ($10)
$150,000	5,470.10	5,468.40	−1.70	The (B) 2% top indexes to $4,800

Every integer taxable income from $0 to $200,000:

Year	Incomes that change	This PR higher by up to	This PR lower by up to	Incomes where tax falls, base	…this PR
2027	194,301	$108.00	$281.70	4 (worst −$111.98)	0
2030	193,901	$102.00	$320.50	4 (worst −$111.98)	0
2035	193,301	$90.00	$361.70	4 (worst −$111.98)	0

"Base" is main before this PR: the 2027+ rate thresholds rounded down, with the minus adjustments frozen at 2026.

Invariants

policyengine_us/tests/test_ar_income_tax_schedule.py (extended from #9624) checks, at every integer taxable income:

1. Differential. The model matches an independent transcription of each source:
   • 2021–2025: the DFA cards.
   • 2026: Act 1 of 2026.
   • 2027–2035: Act 1's tables with every bound indexed from 2026 and rounded to the nearest $100, written in the test from the Act's numbers.
   • Tolerance is half a cent.
2. Non-negative in 2021–2040, 2050, 2075 and 2100.
3. Never falls as income rises, same years, except where the statute's (A) and (B)–(C) tables meet. In 2026 that step is −$2.66, pinned exactly. Once indexing raises the (A) bounds, the step becomes a rise (+$7.04 in 2027).
4. Structure, 2026–2040, 2050, 2075 and 2100:
   • the (C) ladder starts at the threshold;
   • its bounds rise in $100 multiples;
   • its amounts stay $290…$10, $0;
   • the (B) top rate equals the (A) top rate.
5. Property tests on 200 seeded random table sets. The derived (A) tax equals the card form (rate × TI − Σ rate step × row start), is continuous at every row start, and never falls within either regime. Hypothesis is not a dependency of this repo, and uv.lock is committed, so these use seeded numpy generators instead.
6. Reform robustness. A 2027 reform moves the 2% row to $7,000 and cuts the top rates to 3.5%. Tax still never falls except where (A) meets (B)–(C). Continuity holds at every (A) and (B) row bound; the statute's own steps remain: the seam, and +$10 at each (C) row.

The 2027 YAML cases use only incomes whose tax survives a one-step change in the projected uprating factor. The (B)–(C) rows next to the indexed threshold sit within about 0.03% of a nearest-$100 flip, and a routine C-CPI-U refresh could move them. The index-relative Python tests cover those rows instead, and test_state_uprating_rounding.py now derives its expected 2027–2035 bounds from the loaded index.

Verification

• Base vs this branch, parameter level. Every integer taxable income from 0 to 200,000, plus 20,000 random fractional incomes, bound±0.5 points, −5, 1e6, 1e7 and 1e9:
  • 2014–2025: identical at every point.
  • 2026: identical at every whole-dollar income. The only differences are 40 fractional incomes inside the sub-$1 gaps described above.
  • 2012–2013: $0 on both sides. The switch starts at 0000-01-01, so years before rate.yaml's first value still take the published path. An independent reviewer caught that the first version raised ParameterNotFoundError there; a test now pins it.
• Local runs on the final head:
  • test_ar_income_tax_schedule.py plus tests/core/test_state_uprating_rounding.py: 309 passed.
  • The whole tests/policy/baseline/gov/states/ar YAML folder: 718 passed.
• Mutation testing of the new tests: the pytest suite kills all 14 mutants. The 2027 YAML cases also kill 10 of them; the three they miss only touch mid-ladder rows, which the YAML leaves to the index-relative pytest.
  • Rounding back to downwards.
  • An unindexed threshold, (B) top, ladder, or 3% row.
  • right=False on the ladder, and < for <= at the threshold.
  • DFA's "Less Than or Equal To" convention in (A).
  • One ladder amount changed, or one ladder row dropped.
  • A different (B) rate, threshold, or 2% top.
  • Restoring the old frozen-2026 reduction.
• Adversarial review in three lenses (statute and claims, numerical, conventions and CI), with a skeptic re-running each finding:
  • Three findings confirmed, all wording: the helper docstring overclaimed continuity, the changelog said the new bounds were previously "rounded down", and the (B) description. All fixed.
  • Three more, unverified when the skeptics hit a usage limit, were checked by hand and also fixed: the withholding side effect, four 2027 YAML cases one C-CPI-U refresh from a rounding flip, and the rate-table description.
  • Five were refuted:
    • A reform to the (A) top rate doesn't reach incomes above the threshold. That is intended: (A) and (B) are separate statutory tables.
    • (A) is indexed on "From" while DFA counts from "Less Than or Equal To". That convention predates this PR (Reconcile Arkansas TY2026 with DFA's 2026 Indexed Tax Brackets card when it is published #9639).
    • Reference titles say (a)(5) was "added". The Act's markup supports that wording.
    • A textual conflict with Fix fused reference URLs repo-wide and correct Arkansas DFA page anchors #9609. It predated this PR.
    • Placeholders in the draft PR body. Now filled.
• Independent review (Opus, Subfleet): APPROVE at cc053d30ff, then APPROVE on the final head's delta (e00c01eba7, the pre-2014 fix). Both reviews were read-only, so they didn't run anything; the runs above are mine.
• Rebase. Rebased onto main after Fix Arkansas 2025 and 2024 income tax minus-adjustment schedules against the DFA cards #9624, Fix Arkansas 2014-2020 income tax rate schedules #9611, Give Arkansas 2015-2020 income tax parameters their own values #9615, Use Arkansas's own medical expense deduction floor #9612 and Use Arkansas's own miscellaneous and casualty loss itemized deduction rules #9625 merged. Main's 2025–2027 AR schedule values are the same as Fix Arkansas 2025 and 2024 income tax minus-adjustment schedules against the DFA cards #9624's head, so the before/after tables above describe main.

API note. From 2026, gov.states.ar.tax.income.rates.main.reduction has no effect: its 2025 values carry forward but go unused. Reform rates.main.rate and rates.main.high_income.* instead.

Not changed (follow-ups)

• Index series. § 26-51-201(d)(2) uses CPI-U: 12-month averages ending August 31, year over year, capped at 3%. The model still uses gov.irs.uprating (chained CPI-U). Index IRS parameters to the 12-months-ending-August chained CPI-U, with CBO's tax-year projections #9621 is reworking the CPI projection series, so switching AR to a statutory COLA index is Index Arkansas income tax brackets by the statutory CPI-U COLA, capped at 3% #9638. DFA's 2025 card fits unadjusted CPI-U: 92,300 → 94,700 needs a factor in [1.02546, 1.02654); unadjusted CPI-U gives 1.026531 and gov.irs.uprating gives 1.028831.
• TY2026 values. DFA has not published a 2026 Indexed Tax Brackets card. Its 2026 withholding formula uses Act 1's unindexed bounds. In 2022, 2023 and 2024, though, DFA's card indexed each newly enacted table by that year's COLA. DFA's minus adjustments also count from the "Less Than or Equal To" bound (111.98, not 112). Both are tracked in Reconcile Arkansas TY2026 with DFA's 2026 Indexed Tax Brackets card when it is published #9639 for when the card appears. This PR keeps 2026 exactly as before.
• (C) row method. DFA indexed the ladder row by row in 2020–2024 but regenerated uniform $100 rows from the indexed threshold on its 2025 card. This PR indexes row by row, because (d)(1) and DFA's asterisk note both read that way. Either method stays consistent with the threshold.
• Withholding. ar_withheld_income_tax applies the marginal rate to all of reduced AGI with no minus adjustment. That predates this PR: ar_withheld_income_tax ignores Arkansas's minus adjustments and exemption credit #9640. It reads rate.yaml, so the nearest-$100 rounding does move its 2027+ bounds, e.g. from $5,700 to $5,800.

axiom: TheAxiomFoundation/rulespec-us#1418 debt (the rulespec-us AR pilot is bounded to TY2026 "because section 26-51-201(a)(5) provides for later annual adjustment"; TY2027+ indexing under (d) is unencoded)

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✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (909176a) to head (e00c01e).
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[MaxGhenis]

Admin-merged (squash, --match-head-commit e00c01e) under Max's 2026-09-26 ruling (d399: obvious improvements need no permission; admin-merge when the only block is a required review only Max could give). Gates on head e00c01e: gh pr checks exit 0 (37 pass), MERGEABLE, no CHANGES_REQUESTED. Approvals: an independent Opus 5.5 review on Subfleet (APPROVE at cc053d3; a delta review of the pre-2014 fix, APPROVE at e00c01e), and an in-session adversarial review with statute, numerical and conventions lenses; all its confirmed findings are fixed in cc053d3 and e00c01e. Local runs on the final head: 309 pytest, 718 AR YAML; all 14 mutants killed; 2014-2025 identical to main at every tested income.