# DeMark Pivot Points

`D08-F01-A09` · Geometric Chart Patterns → Pivots and Levels · archetype `record-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/geometric-chart-patterns/pivots-and-levels/demark-pivot-points/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

```ts
import { demarkPivotPoints } from "fintech-algorithms/geometric-chart-patterns/pivots-and-levels/demark-pivot-points";
```

## Signature

```ts
demarkPivotPoints(input)
```

Chooses one of three formulas for the intermediate `X` depending on whether the previous bar closed below, above, or level with its open, then reports `pivot = X / 4` with a single band pair `r1 = X / 2 - L_prev` and `s1 = X / 2 - H_prev`.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` is the required OHLCV history, strictly ordered by `timestamp` and on a single adjustment basis. This variant reads no keys from `parameters`; the branch is selected purely from the previous bar's close-versus-open relationship. `period` (default `20`) is still validated as an integer of at least 2 if supplied. |

## Returns

`TopicResult`

`series` and `latest` carry `pivot`, `r1`, `s1`, `r2` and `s2`, but DeMark defines only one band pair, so `r2` and `s2` are null at every index including the last. The warm-up is one bar.

## Warm-up

The first `1 bar` positions are `null`. Index 0 is null in every series and `ready_at` is 1; `r2` and `s2` never leave null, which is the formula and not an unfinished warm-up.

## Errors

- When a bar's `high` is below its own `open`, `close`, or `low` (or `low` is above them) — throws Error
- When `bars` is empty or is not an array — throws Error

## Complexity

Time `O(n)`, space `O(n)`.

## Worked example

Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

### Input

`input`:

```json
{
  "bars": [
    {
      "timestamp": "2024-01-02",
      "basis": "synthetic-unadjusted",
      "open": 100,
      "high": 101.45,
      "low": 98.695,
      "close": 100,
      "volume": 750000,
      "benchmark": 200
    },
    {
      "timestamp": "2024-01-03",
      "basis": "synthetic-unadjusted",
      "open": 101.49111452,
      "high": 103.38381693,
      "low": 100.05480022,
      "close": 101.78791214,
      "volume": 795117,
      "benchmark": 200.56326135
    },
    {
      "timestamp": "2024-01-04",
      "basis": "synthetic-unadjusted",
      "open": 102.45519048,
      "high": 104.6701838,
      "low": 100.91147007,
      "close": 102.9549389,
      "volume": 840234,
      "benchmark": 201.11020913
    }
  ],
  "parameters": {}
}
```

### Call

```ts
demarkPivotPoints(input)
```

### Returns

object with 9 fields: topic_id, title, state, ready, ready_at, series, latest, parameters, …

```json
{
  "topic_id": "D08-F01-A09",
  "title": "DeMark Pivot Points",
  "state": "calculated",
  "ready": true,
  "ready_at": 1,
  "series": {
    "pivot": [
      null,
      100.03625,
      102.152586555,
      103.3016941425,
      103.58734312749999,
      103.220884675
    ],
    "r1": [
      null,
      101.3775,
      104.25037289,
      105.691918215,
      106.09474635499998,
      105.64435387999998
    ],
    "s1": [
      null,
      98.62249999999999,
      100.92135618,
      101.93320448499999,
      102.15611129499999,
      101.81435779999998
    ],
    "r2": [null, null, null, null, null, null],
    "s2": [null, null, null, null, null, null]
  },
  "latest": {
    "pivot": 101.174576485,
    "r1": 102.31329422,
    "s1": 99.19207042000001,
    "r2": null,
    "s2": null
  },
  "parameters": {},
  "diagnostics": {
    "causal": true,
    "input_count": 96
  }
}
```

## Verification and provenance

Tier: **verified** (via E).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.0.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/geometric-chart-patterns/pivots-and-levels/demark-pivot-points/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/geometric-chart-patterns/pivots-and-levels/demark-pivot-points/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/geometric-chart-patterns/llms.txt