# nb-14 solutions — Why this answer and what would change it

*Checkable against `law test packs/examples/language-demo/queries`
(6 checked, 6 passed), `law ask` on the CenterCity case, `law engine
explain`, and `law engine counterfactual` with `--verify`.
Identifiers and code as written.*

## 1. `big_bill(1)` versus `big_bill(12)`, and the explanation steps

**Answer: `big_bill(1)` is NEITHER; `big_bill(12)` is TRUE_ONLY;
`explain` lists the `BigBill` rule application and the `b12`
assertion.**

One billed month costs 10 EUR (`permit_fee` is 10 EUR per month), below
the 50 EUR bar in `BigBill`'s condition — so no rule derives
`big_bill(1)`, and with no derivation either way the status is
NEITHER, not false. Twelve months cost 120 EUR, the condition holds,
`BigBill` fires — TRUE_ONLY. The saved twelve-month vector explains
itself as exactly two proof steps: the rule application
(`urn:proof:apply:BigBill:...`) with the case assertion
(`urn:proof:assert:...#b12`) as its premise. The one-month vector
would explain with `because: []`, like the six-month one in the
article: nothing derived, nothing to list.

## 2. Calling `DoubleFee` from `law ask`

**Answer: refused with `LDC-E1105` — `DoubleFee` is not exported;
it exposes the declaration-vs-question confusion.**

`DoubleFee` is a `query` declaration: a named computation, not a
relation with truth values and not an exported symbol. `law ask`
evaluates `truth(...)` over relations (or cards); handing it a query
declaration is a category error, and the engine refuses it at the
boundary (`символ не экспортирован пакетом`). The same computation is
reachable only indirectly, through rules such as `BigBill` that call
the underlying `permit_fee` function in their conditions. If you want
the doubled number itself, read the query through its own declaration
machinery — never through `truth(...)` from another package.

## 3. The single fact that flips `big_bill(6)`

**Answer: adding `billed_months(6)` (candidate `add-b6`) at cost 1;
`--verify` reports `valid:true`.**

The CenterCity case holds `billed_months(12)` and `billed_months(1)`
but no `billed_months(6)`, so `BigBill` can never fire for `m = 6` and
the ask is NEITHER. `FlipToBig` declares `billed_months` mutable, so
adding that one assertion is a legal move; six months at 10 EUR each
reach 60 EUR ≥ 50 EUR, and the target flips to TRUE_ONLY. The solver
reports `FOUND`, solution `add-b6`, `cutoffCost 1`, one candidate
checked. The replay (`--verify` over the pinned world, case and input
hashes) re-executes the winner and reports
`{"kind":"counterfactual-verification",...,"valid":true}` — the flip
was really re-derived, not just claimed.

## 4. Two different cost-1 candidates

**Answer: two solutions, `cutoffCost` still 1.**

The solver returns *every* candidate that achieves the target at the
minimal cost; it does not pick one and hide the other. A probe with a
second equal-cost candidate (a `/tmp` copy of the input with an extra
`add-b6-alt` assertion, same literal, cost 1) returned `FOUND` with
both solutions listed, `cutoffCost 1`, two candidates checked. The
cutoff names the cheapest price at which anything flips; the solution
list names everything available at that price. A tie is reported as a
tie — choosing between the tied patches is the clerk's decision, and
the certificate keeps both options on the table.

## How to verify

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

Expected: `итого: 6 проверено, 6 прошли, 0 не прошли, 0 не исполнены`.

```sh
law ask packs/examples/language-demo/cases --case CenterCity --query 'evaluate truth(demo.northbridge.queries::big_bill(12));' --query-id big-bill-12
```

Expected: `"truthStatus":"TRUE_ONLY"`.

```sh
law ask packs/examples/language-demo/cases --case CenterCity --query 'evaluate truth(demo.northbridge.queries::big_bill(6));' --query-id big-bill-6 --format text
```

Expected: `Не установлено ни что «big_bill» (m: 6), ни обратное`.

```sh
law engine counterfactual --program packs/examples/language-demo/cases/counterfactual/flip-to-big/nb-world.json --case packs/examples/language-demo/cases/counterfactual/flip-to-big/nb-case.json --input packs/examples/language-demo/cases/counterfactual/flip-to-big/nb-input.json
```

Expected: `"status":"FOUND"` with candidate `add-b6` at `"cost":"1"`.
Append `--verify packs/examples/language-demo/cases/counterfactual/flip-to-big/nb-cf-result.json`
(with the same `--program`, `--case`, `--input`) for
`"valid":true`.

## 5. One fact moves the answer

`result.json` and `request.json` diverge; `ask.json` stays
byte-identical (the receipt has no `caseHash`). `big_bill(12)`
reports `NEITHER` — with only `billed_months(2)` and
`billed_months(1)` asserted, nothing derives the twelve-month
bill either way. `programHash` does not move
(`sha256:fa858cf463d` both runs): the program is unchanged, the
facts changed. `resultHash` moves (`172814eac88…` →
`f4197e2adb5…`) with `caseHash`. If you predicted the receipt
would change, re-read the limits — compare `result.json`, not
`ask.json`.