# Chain

> Package `@umriss-ui/calculation`, version 0.40.0. Demo page: <https://romanhaendler.github.io/umriss-ui/calculation/chain/>. Every page in one line: [llms.txt](https://romanhaendler.github.io/umriss-ui/calculation/llms.txt); every page in full: [llms-full.txt](https://romanhaendler.github.io/umriss-ui/calculation/llms-full.txt).

A sheet read top to bottom (a running calculation): each line worked into the value before it, and interims naming the value where they stand. Reach for it for invoices, budgets and cost sheets.

```ts
import { Chain, Plus, Minus, Times, DividedBy, Interim } from "@umriss-ui/calculation";
```

Demo page: https://romanhaendler.github.io/umriss-ui/calculation/chain/

A chain has no precedence: every line works into the value before it, strictly in order. So `Times` and `DividedBy` stand alone between two named values; anything else fails on the first render.

A chain in view stands open – it is the working itself. What should show only on request goes into one line as a tree, which folds. Only an `Interim` shows the running value ([ADR-0028](https://github.com/romanhaendler/umriss-ui/blob/main/docs/adr/0028-a-calculation-is-a-tree-or-a-chain.md)).

## Examples

### Take amounts away from a first quantity

A chain starts with a quantity without operator; `Minus` and `Plus` take a label and a value directly, and an `Interim` ends it.

```tsx
import { Calculation, Chain, Given, Interim, Minus } from "@umriss-ui/calculation";

export default function NetWeight() {
  return (
    <Calculation aria-label="Net weight, shipment FP-1004223">
      <Chain>
        <Given label="Gross weight" value={1250} unit="kg" decimals={1} />
        <Minus label="Pallet" value={25} unit="kg" decimals={1} />
        <Minus label="Crates" value={144} unit="kg" decimals={1} />
        <Minus label="Packaging" value={11.5} unit="kg" decimals={1} />
        <Interim label="Net weight" unit="kg" decimals={1} />
      </Chain>
    </Calculation>
  );
}
```

### Mix additions and deductions

Where a figure is a list of items, write each as a line of its own; a credit is a `Minus` where it stands.

```tsx
import { Calculation, Chain, Given, Interim, Minus, Plus } from "@umriss-ui/calculation";

export default function TourCost() {
  return (
    <Calculation aria-label="Cost of tour T-01, Tuesday">
      <Chain>
        <Given label="Driver, 6.5 h" value={224.25} unit="€" decimals={2} />
        <Plus label="Diesel" value={13.89} unit="€" decimals={2} />
        <Plus label="Van, one day" value={58} unit="€" decimals={2} />
        <Plus label="Tolls" value={9.4} unit="€" decimals={2} />
        <Plus label="Parking" value={6} unit="€" decimals={2} />
        <Minus label="Fuel card rebate" value={0.7} unit="€" decimals={2} />
        <Interim label="Cost of the tour" unit="€" decimals={2} />
      </Chain>
    </Calculation>
  );
}
```

### Multiply between two interims

A chain has no precedence, so `Times` and `DividedBy` stand alone between two interims; after a `Plus` they fail on the first render.

```tsx
import { Calculation, Chain, Given, Interim, Plus, Times } from "@umriss-ui/calculation";

export default function MarkUpAndVat() {
  return (
    <Calculation aria-label="Price of a workshop day">
      <Chain>
        <Given label="Two facilitators, one day" value={960} unit="€" decimals={2} />
        <Plus label="Room and materials" value={180} unit="€" decimals={2} />
        <Interim label="Cost of the day" unit="€" decimals={2} />
        <Times label="Mark-up" value={1.25} />
        <Interim label="Net price" unit="€" decimals={2} />
        <Times label="VAT factor" value={1.19} />
        <Interim label="Gross price" unit="€" decimals={2} />
      </Chain>
    </Calculation>
  );
}
```

### Fold a group of lines into one

A chain in view never folds; to show items only on request, put them into one line as a tree: a `Sum` held by a `Minus` – a `Minus`, because contributions are positive by nature. Rows of either sign from data go into a `Plus` instead; the page Rows from data shows every case.

```tsx
import { Calculation, Chain, Given, Interim, Minus, Plus, Product, Ref, Sum } from "@umriss-ui/calculation";

const CONTRIBUTIONS = [
  { name: "Pension insurance", rate: 0.093 },
  { name: "Unemployment insurance", rate: 0.013 },
  { name: "Health insurance", rate: 0.082 },
  { name: "Long-term care insurance", rate: 0.017 },
];

export default function Payslip() {
  return (
    <Calculation aria-label="Payslip, March">
      <Chain>
        <Given id="gross" label="Gross salary" value={4200} unit="€" decimals={2} />
        <Minus label="Income tax" value={612.5} unit="€" decimals={2} />
        <Minus label="Church tax" value={49} unit="€" decimals={2} />
        <Minus>
          <Sum label="Social security contributions" unit="€" decimals={2}>
            {CONTRIBUTIONS.map((contribution) => (
              <Product key={contribution.name} label={contribution.name} unit="€" decimals={2}>
                <Given label={`Rate, ${contribution.name.toLowerCase()}`} value={contribution.rate} format="percent" />
                <Ref to="gross" />
              </Product>
            ))}
          </Sum>
        </Minus>
        <Interim label="Net salary" unit="€" decimals={2} />
        <Minus label="Capital-forming benefits" value={40} unit="€" decimals={2} />
        <Plus label="Travel allowance" value={60} unit="€" decimals={2} />
        <Interim label="Amount paid out" unit="€" decimals={2} />
      </Chain>
    </Calculation>
  );
}
```

### Build the lines from data

`.map` inside a chain makes each item a `Plus`, and all stand in view above their interim.

```tsx
import { Calculation, Chain, Given, Interim, Plus } from "@umriss-ui/calculation";

const ITEMS = [
  ["Compute, booking API", 4128.4],
  ["Compute, search", 2864.1],
  ["Compute, workers", 1741.9],
  ["Database, primary", 2310],
  ["Database, replicas", 1540],
  ["Object storage", 386.2],
  ["Block storage", 512.8],
  ["Data transfer out", 948.6],
  ["Load balancers", 264],
  ["Queues", 118.3],
  ["Cache cluster", 690],
  ["Log storage", 431.7],
  ["Metrics and traces", 822.5],
  ["Backups", 207.4],
  ["Support plan", 1200],
] as const;

export default function FifteenItems() {
  const [[firstName, firstAmount], ...rest] = ITEMS;
  return (
    <Calculation aria-label="Cloud bill, March">
      <Chain>
        <Given label={firstName} value={firstAmount} unit="€" decimals={2} />
        {rest.map(([name, amount]) => (
          <Plus key={name} label={name} value={amount} unit="€" decimals={2} />
        ))}
        <Interim label="Cloud bill, March" unit="€" decimals={2} />
      </Chain>
    </Calculation>
  );
}
```

### Put a chain inside a tree

As an operand a chain folds and stands for its last interim; opened, it stands whole beneath its line.

```tsx
import { Calculation, Chain, Given, Interim, Minus, Plus, Quotient, Ref } from "@umriss-ui/calculation";

export default function ChainInATree() {
  return (
    <Calculation aria-label="Delivery rate, North depot, Tuesday">
      <Quotient label="Delivery rate" format="percent" target={0.97}>
        <Chain>
          <Given id="out" label="Parcels out" value={1000} unit="parcels" />
          <Minus label="Failed attempts" value={31} unit="parcels" />
          <Minus label="Refused at the door" value={6} unit="parcels" />
          <Plus label="Delivered on a second run" value={14} unit="parcels" />
          <Interim label="Parcels delivered" unit="parcels" />
        </Chain>
        <Ref to="out" />
      </Quotient>
    </Calculation>
  );
}
```

### Hold an interim to its limits

An `Interim` takes `target` and `limits` like any quantity; here the error budget left is assessed against two lower limits.

```tsx
import { Calculation, Chain, Given, Interim, Minus, Product } from "@umriss-ui/calculation";

export default function ErrorBudget() {
  return (
    <Calculation aria-label="Error budget of Checkout, March">
      <Chain>
        <Product label="Error budget, March" unit="min" decimals={1}>
          <Given label="Minutes in March" value={44640} unit="min" />
          <Given label="Allowed downtime" value={0.0005} format="percent" decimals={2} />
        </Product>
        <Minus label="INC-1039, payment provider timeouts" value={9} unit="min" decimals={1} />
        <Minus label="INC-1036, failed deploy" value={4} unit="min" decimals={1} />
        <Minus label="INC-1048, card payments time out" value={21} unit="min" decimals={1} />
        <Interim
          label="Budget left"
          unit="min"
          decimals={1}
          limits={[
            { value: 5, side: "lower", severity: "warning" },
            { value: 0, side: "lower", severity: "alarm" },
          ]}
        />
      </Chain>
    </Calculation>
  );
}
```

## When to use something else

- A figure made of factors, folded to its formula → Tree

## Keyboard

The keys of [Calculation](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#keyboard-calculation) apply here.

## API

### `ChainProps`

| Prop | Type | Default | Description |
|---|---|---|---|
| `children` | `ReactNode` | — | The operands, top to bottom: a first quantity with no operator, then `Plus`, `Minus`, `Times` and `DividedBy` with their operands and `Interim`s naming the value where they stand. The last line is an `Interim`; a `Times` or `DividedBy` stands alone between two named values.<br>Shown in: [Take amounts away from a first quantity](https://romanhaendler.github.io/umriss-ui/calculation/chain/#net-weight), [Mix additions and deductions](https://romanhaendler.github.io/umriss-ui/calculation/chain/#tour-cost), [Multiply between two interims](https://romanhaendler.github.io/umriss-ui/calculation/chain/#mark-up-and-vat) and 22 more |

### `ChainOperandProps`

| Prop | Type | Default | Description |
|---|---|---|---|
| `label` | `string` | — | The operand's name, where the line is a given written in place. Left out where the line holds a quantity as its child.<br>Shown in: [Take amounts away from a first quantity](https://romanhaendler.github.io/umriss-ui/calculation/chain/#net-weight), [Mix additions and deductions](https://romanhaendler.github.io/umriss-ui/calculation/chain/#tour-cost), [Multiply between two interims](https://romanhaendler.github.io/umriss-ui/calculation/chain/#mark-up-and-vat) and 17 more |
| `value` | `number \| null \| `[`MetricValues`](https://romanhaendler.github.io/umriss-ui/calculation/chain/#type-MetricValues) | — | The operand's number, where the line is a given written in place. Absent as for a `Given`: the line and every interim after it are absent, with the reason. With `metrics`, an object by metric id, as on a `Given`.<br>Shown in: [Take amounts away from a first quantity](https://romanhaendler.github.io/umriss-ui/calculation/chain/#net-weight), [Mix additions and deductions](https://romanhaendler.github.io/umriss-ui/calculation/chain/#tour-cost), [Multiply between two interims](https://romanhaendler.github.io/umriss-ui/calculation/chain/#mark-up-and-vat) and 17 more |
| `children` | `ReactNode` | — | Instead of `label` and `value`: exactly one quantity - a tree, a `<Ref>` or a `<Chain>`.<br>Shown in: [Fold a group of lines into one](https://romanhaendler.github.io/umriss-ui/calculation/chain/#payslip), [Write a chain (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#invoice), [Emphasis inside a group (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#emphasis-inside-a-group) and 12 more |
| `source` | `string` | — | Where the number came from: a system, a report, a person. From `GivenProps`.<br>Shown in: [Say where a number came from (Given)](https://romanhaendler.github.io/umriss-ui/calculation/given/#where-it-came-from), [State when a number was true (Given)](https://romanhaendler.github.io/umriss-ui/calculation/given/#as-of), [Staff movement as a chain (Metrics)](https://romanhaendler.github.io/umriss-ui/calculation/metrics/#staff-movement) and 8 more |
| `asOf` | `Date \| number` | — | When the number was true - not when it was fetched. From `GivenProps`.<br>Shown in: [Say where a number came from (Given)](https://romanhaendler.github.io/umriss-ui/calculation/given/#where-it-came-from), [State when a number was true (Given)](https://romanhaendler.github.io/umriss-ui/calculation/given/#as-of), [The cost per stop of a day's tours (Worked examples)](https://romanhaendler.github.io/umriss-ui/calculation/worked-examples/#cost-per-tour) |
| `ages` | [`FreshnessAges`](https://romanhaendler.github.io/umriss-ui/calculation/chain/#type-FreshnessAges) | — | The ages at which `asOf` turns stale and lost. With both, the given carries a freshness through core; with `asOf` alone, only the time. From `GivenProps`.<br>Shown in: [Say where a number came from (Given)](https://romanhaendler.github.io/umriss-ui/calculation/given/#where-it-came-from), [The cost per stop of a day's tours (Worked examples)](https://romanhaendler.github.io/umriss-ui/calculation/worked-examples/#cost-per-tour) |
| `id` | `string` | — | Makes the quantity referable: `<Ref to>` stands for it elsewhere. Needed only for a quantity used more than once. From `QuantityProps`.<br>Shown in: [Fold a group of lines into one](https://romanhaendler.github.io/umriss-ui/calculation/chain/#payslip), [Put a chain inside a tree](https://romanhaendler.github.io/umriss-ui/calculation/chain/#chain-in-a-tree), [The availability of a service (Installation)](https://romanhaendler.github.io/umriss-ui/calculation/installation/#availability) and 10 more |
| `unit` | `string` | — | A label written after the number - "min", "pcs", "€". Never converted and never checked; the calculation does no unit algebra. From `QuantityProps`.<br>Shown in: [Take amounts away from a first quantity](https://romanhaendler.github.io/umriss-ui/calculation/chain/#net-weight), [Mix additions and deductions](https://romanhaendler.github.io/umriss-ui/calculation/chain/#tour-cost), [Multiply between two interims](https://romanhaendler.github.io/umriss-ui/calculation/chain/#mark-up-and-vat) and 42 more |
| `format` | `"percent"` | — | `percent` presents a plain ratio as per cent: 0.916 is shown as 91.6 %. The quantity stays a ratio in every operation. From `QuantityProps`.<br>Shown in: [Fold a group of lines into one](https://romanhaendler.github.io/umriss-ui/calculation/chain/#payslip), [Put a chain inside a tree](https://romanhaendler.github.io/umriss-ui/calculation/chain/#chain-in-a-tree), [Hold an interim to its limits](https://romanhaendler.github.io/umriss-ui/calculation/chain/#error-budget) and 17 more |
| `decimals` | `number` | one digit for a percentage, at most two for a derived number, a given as it was given | Fixed number of fraction digits as shown. Rounding happens only in presentation; every operation uses the full value. From `QuantityProps`.<br>Shown in: [Take amounts away from a first quantity](https://romanhaendler.github.io/umriss-ui/calculation/chain/#net-weight), [Mix additions and deductions](https://romanhaendler.github.io/umriss-ui/calculation/chain/#tour-cost), [Multiply between two interims](https://romanhaendler.github.io/umriss-ui/calculation/chain/#mark-up-and-vat) and 29 more |
| `target` | `number` | — | The value this quantity is meant to reach - missed, never violated. From `QuantityProps`.<br>Shown in: [Put a chain inside a tree](https://romanhaendler.github.io/umriss-ui/calculation/chain/#chain-in-a-tree), [The availability of a service (Installation)](https://romanhaendler.github.io/umriss-ui/calculation/installation/#availability), [Write a tree (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#oee) and 6 more |
| `limits` | `readonly `[`Limit`](https://romanhaendler.github.io/umriss-ui/calculation/chain/#type-Limit)`[]` | — | Bounds the quantity is assessed against, through core's `assess()`. From `QuantityProps`.<br>Shown in: [Hold an interim to its limits](https://romanhaendler.github.io/umriss-ui/calculation/chain/#error-budget), [Density (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#density), [Hold a figure to its limits (Tree)](https://romanhaendler.github.io/umriss-ui/calculation/tree/#limits) and 5 more |
| `explanation` | `string` | — | A sentence of plain text beside the line: why the quantity is here, or what it means. From `QuantityProps`.<br>Shown in: [Say where a number came from (Given)](https://romanhaendler.github.io/umriss-ui/calculation/given/#where-it-came-from), [A number one metric does not have (Metrics)](https://romanhaendler.github.io/umriss-ui/calculation/metrics/#not-recorded), [Staff movement as a chain (Metrics)](https://romanhaendler.github.io/umriss-ui/calculation/metrics/#staff-movement) and 2 more |
| `aside` | `ReactNode` | — | Content of the caller's own beside the line - a sparkline, a link. It never takes part in the calculation. From `QuantityProps`.<br>Shown in: [Say where a number came from (Given)](https://romanhaendler.github.io/umriss-ui/calculation/given/#where-it-came-from) |
| `emphasis` | `"strong" \| "muted"` | — | How much the line stands out among the others ([ADR-0049](https://github.com/romanhaendler/umriss-ui/blob/main/docs/adr/0049-a-sum-takes-rows-from-data.md)): `strong` to be read first, `muted` to recede - a muted line still counts in full. Not on the Result, which is already the heaviest line. From `QuantityProps`.<br>Shown in: [A stronger line (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#a-stronger-line), [A quieter line (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#a-quieter-line), [Emphasis inside a group (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#emphasis-inside-a-group) |
| `rule` | `"above"` | — | `above` rules the line off from the ones before it, where a section starts that is not an interim. Not on the Result. From `QuantityProps`.<br>Shown in: [A rule above (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#a-rule-above), [Emphasis inside a group (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#emphasis-inside-a-group) |

### `QuantityProps`

| Prop | Type | Default | Description |
|---|---|---|---|
| `label` *required* | `string` | — | What the quantity is called. It stands on its line, wherever it is an operand, and in the accessible sentence.<br>Shown in: [Take amounts away from a first quantity](https://romanhaendler.github.io/umriss-ui/calculation/chain/#net-weight), [Mix additions and deductions](https://romanhaendler.github.io/umriss-ui/calculation/chain/#tour-cost), [Multiply between two interims](https://romanhaendler.github.io/umriss-ui/calculation/chain/#mark-up-and-vat) and 50 more |
| `id` | `string` | — | Makes the quantity referable: `<Ref to>` stands for it elsewhere. Needed only for a quantity used more than once.<br>Shown in: [Fold a group of lines into one](https://romanhaendler.github.io/umriss-ui/calculation/chain/#payslip), [Put a chain inside a tree](https://romanhaendler.github.io/umriss-ui/calculation/chain/#chain-in-a-tree), [The availability of a service (Installation)](https://romanhaendler.github.io/umriss-ui/calculation/installation/#availability) and 10 more |
| `unit` | `string` | — | A label written after the number - "min", "pcs", "€". Never converted and never checked; the calculation does no unit algebra.<br>Shown in: [Take amounts away from a first quantity](https://romanhaendler.github.io/umriss-ui/calculation/chain/#net-weight), [Mix additions and deductions](https://romanhaendler.github.io/umriss-ui/calculation/chain/#tour-cost), [Multiply between two interims](https://romanhaendler.github.io/umriss-ui/calculation/chain/#mark-up-and-vat) and 42 more |
| `format` | `"percent"` | — | `percent` presents a plain ratio as per cent: 0.916 is shown as 91.6 %. The quantity stays a ratio in every operation.<br>Shown in: [Fold a group of lines into one](https://romanhaendler.github.io/umriss-ui/calculation/chain/#payslip), [Put a chain inside a tree](https://romanhaendler.github.io/umriss-ui/calculation/chain/#chain-in-a-tree), [Hold an interim to its limits](https://romanhaendler.github.io/umriss-ui/calculation/chain/#error-budget) and 17 more |
| `decimals` | `number` | one digit for a percentage, at most two for a derived number, a given as it was given | Fixed number of fraction digits as shown. Rounding happens only in presentation; every operation uses the full value.<br>Shown in: [Take amounts away from a first quantity](https://romanhaendler.github.io/umriss-ui/calculation/chain/#net-weight), [Mix additions and deductions](https://romanhaendler.github.io/umriss-ui/calculation/chain/#tour-cost), [Multiply between two interims](https://romanhaendler.github.io/umriss-ui/calculation/chain/#mark-up-and-vat) and 29 more |
| `target` | `number` | — | The value this quantity is meant to reach - missed, never violated.<br>Shown in: [Put a chain inside a tree](https://romanhaendler.github.io/umriss-ui/calculation/chain/#chain-in-a-tree), [The availability of a service (Installation)](https://romanhaendler.github.io/umriss-ui/calculation/installation/#availability), [Write a tree (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#oee) and 6 more |
| `limits` | `readonly `[`Limit`](https://romanhaendler.github.io/umriss-ui/calculation/chain/#type-Limit)`[]` | — | Bounds the quantity is assessed against, through core's `assess()`.<br>Shown in: [Hold an interim to its limits](https://romanhaendler.github.io/umriss-ui/calculation/chain/#error-budget), [Density (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#density), [Hold a figure to its limits (Tree)](https://romanhaendler.github.io/umriss-ui/calculation/tree/#limits) and 5 more |
| `explanation` | `string` | — | A sentence of plain text beside the line: why the quantity is here, or what it means.<br>Shown in: [Say where a number came from (Given)](https://romanhaendler.github.io/umriss-ui/calculation/given/#where-it-came-from), [A number one metric does not have (Metrics)](https://romanhaendler.github.io/umriss-ui/calculation/metrics/#not-recorded), [Staff movement as a chain (Metrics)](https://romanhaendler.github.io/umriss-ui/calculation/metrics/#staff-movement) and 2 more |
| `aside` | `ReactNode` | — | Content of the caller's own beside the line - a sparkline, a link. It never takes part in the calculation.<br>Shown in: [Say where a number came from (Given)](https://romanhaendler.github.io/umriss-ui/calculation/given/#where-it-came-from) |
| `emphasis` | `"strong" \| "muted"` | — | How much the line stands out among the others ([ADR-0049](https://github.com/romanhaendler/umriss-ui/blob/main/docs/adr/0049-a-sum-takes-rows-from-data.md)): `strong` to be read first, `muted` to recede - a muted line still counts in full. Not on the Result, which is already the heaviest line.<br>Shown in: [A stronger line (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#a-stronger-line), [A quieter line (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#a-quieter-line), [Emphasis inside a group (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#emphasis-inside-a-group) |
| `rule` | `"above"` | — | `above` rules the line off from the ones before it, where a section starts that is not an interim. Not on the Result.<br>Shown in: [A rule above (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#a-rule-above), [Emphasis inside a group (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#emphasis-inside-a-group) |

### Types on this page

#### `MetricValues`

A given's numbers where the calculation has metrics: one per metric id,
`null` where the number is absent.

```ts
type MetricValues = Readonly<Record<string, number | null>>;
```

#### `FreshnessAges`

From `@umriss-ui/core`.

The two ages at which a value changes its state, in milliseconds. Both
bounds belong to the older state: exactly five minutes old is already
`stale`.

`alt <= lost` is the sensible order. Stated the other way round, the
harder statement still wins - the middle state simply falls away.

| Prop | Type | Default | Description |
|---|---|---|---|
| `stale` *required* | `number` | — | From this age on the value counts as stale, but keeps its verdict. |
| `lost` *required* | `number` | — | From this age on the connection counts as disconnected. |

#### `Limit`

From `@umriss-ui/core`.

A bound: a value, a side, a severity.

No tolerance band as input. A band is derived - two limits of equal
severity on opposite sides enclose one - and as an input type it would
force a `null` on one edge in the one-sided case.

| Prop | Type | Default | Description |
|---|---|---|---|
| `value` *required* | `number` | — | <br>Shown in: [Hold an interim to its limits](https://romanhaendler.github.io/umriss-ui/calculation/chain/#error-budget), [Density (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#density), [Hold a figure to its limits (Tree)](https://romanhaendler.github.io/umriss-ui/calculation/tree/#limits) and 3 more |
| `side` *required* | [`Side`](https://romanhaendler.github.io/umriss-ui/calculation/chain/#type-Side)<br>`"upper" \| "lower"` | — | <br>Shown in: [Hold an interim to its limits](https://romanhaendler.github.io/umriss-ui/calculation/chain/#error-budget), [Density (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#density), [Hold a figure to its limits (Tree)](https://romanhaendler.github.io/umriss-ui/calculation/tree/#limits) and 3 more |
| `severity` *required* | [`Severity`](https://romanhaendler.github.io/umriss-ui/calculation/chain/#type-Severity)<br>`"warning" \| "alarm"` | — | <br>Shown in: [Hold an interim to its limits](https://romanhaendler.github.io/umriss-ui/calculation/chain/#error-budget), [Density (Calculation)](https://romanhaendler.github.io/umriss-ui/calculation/calculation/#density), [Hold a figure to its limits (Tree)](https://romanhaendler.github.io/umriss-ui/calculation/tree/#limits) and 3 more |

#### `Side`

From `@umriss-ui/core`.

Whether a limit is an upper or a lower bound.

```ts
type Side = "upper" | "lower";
```

#### `Severity`

From `@umriss-ui/core`.

How seriously a violation weighs: one severity that advises and one that
calls for action. Exactly two; for a third distinction one sets a
second limit.

```ts
type Severity = "warning" | "alarm";
```

## Known limits

- A chain in view does not fold; as an operand of a tree it folds to its last interim.

What umriss deliberately does not build, and why: [ADR-0032](https://romanhaendler.github.io/umriss-ui/what-umriss-ui-is-not/).