# nb-12 solutions — Allocation in rounds

*Checkable against `law test packs/examples/language-demo/allocation`
(5 checked, 5 passed). Identifiers and code as written.*

## 1. Which single fact turns admission to NEITHER

**Answer: the resident filing; the `rounds are empty without seed`
test already proves the outcome.**

The admitting test asserts two inputs: the register filing (via
`demo.northbridge.register::filed_resident`) and the 10 points.
`Admit` needs `supported(shortlisted(a, r))` — a frozen round-1
shortlisting that only `Seed` can produce, and `Seed` fires only on
the filing. Remove the filing and round 1 closes empty, so the
`supported` conjunct fails and `admitted(ann, 2)` is NEITHER no
matter how many points are asserted. The empty-rounds test is
exactly that configuration (10 points, no filing → NEITHER).

## 2. The failing comparison and the smallest passing score

**Answer: `p >= MIN_POINTS` fails with p = 3 against MIN_POINTS = 5;
the smallest flipping score is 5.**

With `points(bob, 3)`, the conjunct `p >= MIN_POINTS` instantiates
to `3 >= 5`, which is false, so `Admit` derives nothing and
`admitted(bob, 2)` stays NEITHER. The comparison is `>=`, not `>`,
so 5 already satisfies it: re-asserting `points(bob, 5)` with the
filing kept would make all three conjuncts true (frozen shortlist,
`r < 2`, threshold met) and flip the query to TRUE_ONLY with
`applied(Admit)`.

## 3. Why the closed total reads closed tours, not input

**Answer: reading input directly would announce completion for
applicants no round ever admitted — including the seedless and
below-threshold cases the suite reports as NEITHER.**

`CloseAllocation` concludes `allocation_done()` from
`supported(admitted(a, r))`: at least one admission from a closed
tour. If it read `points(a, p)` instead, then Bob (3 points, never
admitted) and seedless Ann (10 points, never shortlisted) would each
spuriously complete the allocation — the total would no longer mean
"the rounds produced a seat". The `supported` indirection is what
ties the announcement to work the frozen rounds actually did.

## 4. Adding a procedure to the allocation package

**Answer: it fails at the static check, `law engine check`, with
`LDC-E4126` (`STAGE_PROCEDURE_UNSUPPORTED`).**

A stage and a procedure in one program are refused before any test
runs: the tour fold the stage needs is undefined alongside a
procedure automaton. The observed diagnostic on a scratch package
combining the `Allotment` stage with a minimal two-state procedure
is `error LDC-E4126: STAGE_PROCEDURE_UNSUPPORTED`. No `law test`
line is reached — the package does not compile, so there is nothing
to execute. This is an implementation-support fact about the
verified profile (`law 0.1.0`, `law.core/0.2`), not a language-wide
claim.

## How to verify

```sh
law test packs/examples/language-demo/allocation
```

Expected: `итого: 5 проверено, 5 прошли, 0 не прошли, 0 не исполнены`.
The deciding tests are `round 1 shortlists from the register`,
`rounds are empty without seed`, `round 2 admits by points`,
`insufficient points — no seat granted`, and
`closed total reads after the rounds`.
Static shape:

```sh
law engine check packs/examples/language-demo/allocation/package.law
```

Expected: `check OK: packs/examples/language-demo/allocation/package.law`.