# Maintain a state

## Intention

I want to check that a state holds throughout an interval.

A one-off fact must be distinguished from complete monitoring.

## Incorrect form and why it stays silent

```text title="Incorrect form"
achieve done(p) during [@2026-09-01, @2026-09-10];
```

A one-off fact is enough for achievement, but does not certify maintenance over the whole window. The counterexample already breaks maintenance inside the window.

## Correct form

```law
language "law.core" version "0.2";
package recipes.a.r02 version "0.1.0";
namespace "urn:recipe:a-positions:02";

entity Person;
relation registered(p: Person);
relation done(p: Person);
rule R strict { for p: Person; when registered(p);
    then duty Keep { bearer p; maintain done(p) during [@2026-09-01, @2026-09-10]; };
}
```

## Frozen execution scene

| Facts and snapshot | Question | Answer |
|---|---|---|
| positive fact in the window; 2026-09-05 | `positions()` | `position(Keep, ACTIVE);` / `COMPUTED` |
| counterexample in the window; 2026-09-05 | `positions()` | `position(Keep, VIOLATED);` / `COMPUTED` |
| end without a certificate; 2026-09-13 | `positions()` | `position(Keep, UNDETERMINED);` / `COMPUTED` |

```law
test "active with supporting fact in window" {
    given {
        context {
            legal_time @2026-09-05;
            decision_time @2026-09-05T09:00:00+05:00;
            knowledge_time @2026-09-30T09:00:00+05:00;
            timezone "Asia/Almaty";
        }
        assert registered(entity_ref("urn:recipe:a-positions:02:p")); assert done(entity_ref("urn:recipe:a-positions:02:p"));
    }
    evaluate positions();
    expect position(Keep, ACTIVE);
    expect evaluation_status == COMPUTED;

}
```

```law
test "violated by counterexample in window" {
    given {
        context {
            legal_time @2026-09-05;
            decision_time @2026-09-05T09:00:00+05:00;
            knowledge_time @2026-09-30T09:00:00+05:00;
            timezone "Asia/Almaty";
        }
        assert registered(entity_ref("urn:recipe:a-positions:02:p")); assert not done(entity_ref("urn:recipe:a-positions:02:p"));
    }
    evaluate positions();
    expect position(Keep, VIOLATED);
    expect evaluation_status == COMPUTED;

}
```

```law
test "undetermined at end without certificate" {
    given {
        context {
            legal_time @2026-09-13;
            decision_time @2026-09-13T09:00:00+05:00;
            knowledge_time @2026-09-30T09:00:00+05:00;
            timezone "Asia/Almaty";
        }
        assert registered(entity_ref("urn:recipe:a-positions:02:p")); assert done(entity_ref("urn:recipe:a-positions:02:p"));
    }
    evaluate positions();
    expect position(Keep, UNDETERMINED);
    expect evaluation_status == COMPUTED;

}
```

The incorrect-form variant is executed as a separate package: `maintain` is replaced with `achieve`; one positive fact already yields SATISFIED.

```law
test "achieve variant satisfied by single fact" {
    given {
        context {
            legal_time @2026-09-05;
            decision_time @2026-09-05T09:00:00+05:00;
            knowledge_time @2026-09-30T09:00:00+05:00;
            timezone "Asia/Almaty";
        }
        assert registered(entity_ref("urn:recipe:a-positions:02:p")); assert done(entity_ref("urn:recipe:a-positions:02:p"));
    }
    evaluate positions();
    expect position(Keep, SATISFIED);
    expect evaluation_status == COMPUTED;

}
```

```python
>>> import runpy
>>> check = runpy.run_path("docs/recipes/a-positions/resources/check.py")
>>> check["check_variant"](https://github.com/arxohq/law/blob/master/docs/recipes/a-positions/2)
'А2: контрфактуал подтверждён; lawc = lawref'
```

## Counterfactual

Mutation: `maintain done(p) during [@2026-09-01, @2026-09-10];` → `maintain done(p);`; rejection LDC-E0201. Additional counterfactuals are shown as separate scenes.

## Boundary

A duty without a stated term is not always automatically maintenance: the goal kind is chosen from the content of the rule. Completeness of observations is needed for SATISFIED after the window.