# Decision record: EAI-D4 - premium base is tariff times insured sum, with the minimum floor

## Status

accepted

## Context

Article 17 point 1 multiplies the tariff by the contract insured sum (S), and Article 17 point 2-1 raises a base below the minimum wage to that wage. Article 16 point 1 sets S by the contract with S at or above annual payroll (F) but never S equal to F. The pre-R3 candidate computed tariff times payroll (rF) under the output name `insurance_premium_due`, with no insured-sum input and no minimum rule — finding EAI-R3. Its thirty-four green checks confirmed the chosen formula rF; they could not show that formula sufficient for the promised answer.

## Question

Payroll times rate, or insured sum times rate with the minimum-wage floor?

## Options considered

- Keep rF and narrow the promise (Variant A in the finding): rename the output to a tariff component, restrict the scope to contracts with S equal to F. Rejected: the restriction S equal to F is uncheckable from the case facts the package reads, and the finding asked for the result name to match the implemented semantics.
- Read the insured sum from the case, derive the base rS, and apply the floor (Variant B): two new case inputs, one base rule, two premium rules split by the base-to-floor comparison. Chosen: the output keeps its name because it now earns it.

## Position

The premium base is tariff times the contract insured sum; the due premium is the base when the base stands at or above the case-supplied minimum wage, else the minimum wage. The S ≥ F constraint itself stays outside the model as a recorded assumption.

## Justification

Each norm maps to one rule with its own source label: PremiumBaseFromInsuredSum and PremiumBaseStands to Article 17 point 1, PremiumMinimumFloor to Article 17 point 2-1. The two premium rules split the input space on one comparison (base ≥ floor vs base < floor), so exactly one fires per case — verified by the boundary probe, where the equal base derives once. The minimum-wage figure is case input with no conversion claimed: the source compares the computed premium to the statutory figure directly, and so does the guard.

## Distinguishing scenario

EAI-PREMIUM-SUM-DISTINGUISHES carries payroll one million with insured sum two million at class 22 and expects 59200: under the old rF rule the same case answered 29600, so the probe kills the payroll-base reading. EAI-PREMIUM-MINIMUM-FLOOR (base 120 against floor 1000) expects the floor; removing PremiumMinimumFloor on a scratch copy fails exactly this probe (36/37). EAI-PREMIUM-MINIMUM-BOUNDARY (base equal to floor at 1200) expects the base; weakening the stands-guard to strict greater-than fails exactly this probe (36/37). The min-wage figures in all probes are synthetic case inputs, not the statutory value of any year.

## Assumptions

- Each employer carries one contract insured sum, supplied by the case; the package never derives it from payroll.
- The S ≥ F constraint from Article 16 point 1 is assumed, not enforced: no check feeds an insured sum below payroll, and feeding one would still compute (see scope v3 Limits).
- The minimum-wage figure is supplied by the case for the relevant financial year; the package performs no monthly-annual conversion and pins no statutory value.
- Article 16 dynamics (sum reduced by payouts, sum following payroll) and the point 2-1 proportional sum increase stay out of scope; Article 17-1 adjustments stay out of scope.

## Consequences

Every premium-answering case must now supply the risk class, the insured sum, and the minimum wage; cases missing them stay undecided rather than defaulting. Payroll is no longer read by any premium rule — the floor and boundary probes do not pass it — though a case may still carry it alongside the assumed S ≥ F premise. Tariff edits still propagate through the base rule untouched.

## Open questions

none — the base, the floor, and the boundary are modelled and probed; the exclusions above are named in inventory v3.

## Review

Agent-reviewed with the EAI dossier on the R3 snapshot: position stands, all three probes green, both premium mutants killed on scratch copies. No human subject-matter approval.