# Standard Skew Young Tableau Jeu de Taquin Rectification Verifier

> Standard Skew Young Tableau Jeu de Taquin Rectification Verifier is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

Performs jeu de taquin rectification on a skew standard Young tableau and verifies the resulting straight standard Young tableau.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-REST-B20/standard-skew-young-tableau-jeu-de-taquin-rectification?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/standard-skew-young-tableau-jeu-de-taquin-rectification-verifier-293a95c1
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_sqNVXTdfOijyZbChRw3sp

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability standard-skew-young-tableau-jeu-de-taquin-rectification-verifier-293a95c1 -d '<json body>'
```

Example prompt: Rectify this skew standard Young tableau with outer shape [3,2,1] and inner shape [1] and cells [[1,0,2],[2,1,1],[3,2,0]] using jeu de taquin, and verify that the resulting straight standard Young tableau matches the expected claim.

## When to prefer this

Use this endpoint when you need to algorithmically rectify a skew standard Young tableau via jeu de taquin and verify the resulting straight tableau, particularly in mathematical research pipelines, combinatorics education tools, or automated theorem-checking systems that require validated RSK-type computations.

## Known failure modes

- Invalid skew shape where inner partition does not fit inside outer partition
- Cell coordinates outside the skew shape boundaries
- Non-standard filling violating the increasing row/column conditions
- Outer or inner partition arrays exceeding maximum length of 6
- Cells array exceeding maximum of 12 entries
- Malformed input JSON missing required fields such as outer, inner, or cells
- Claim mismatch returning a validation failure

## How this service works

Verify the entire straight standard tableau obtained by rectifying a supplied skew standard Young tableau.

## Output

Returns a verification of the full rectified straight standard Young tableau obtained from the supplied skew Young tableau via jeu de taquin slides, along with validation of any provided claim about the rectification outcome.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "rectify"
   ],
   "properties": {
    "rectify": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "outer",
        "inner",
        "cells"
       ],
       "properties": {
        "cells": {
         "type": "array",
         "items": {
          "type": "array",
          "items": {
           "type": "integer",
           "maximum": 255,
           "minimum": 0
          },
          "maxItems": 3,
          "minItems": 3
         },
         "maxItems": 12,
         "minItems": 0
        },
        "inner": {
         "type": "array",
         "items": {
          "type": "integer",
          "maximum": 255,
          "minimum": 0
         },
         "maxItems": 6,
         "minItems": 0
        },
        "outer": {
         "type": "array",
         "items": {
          "type": "integer",
          "maximum": 255,
          "minimum": 0
         },
         "maxItems": 6,
         "minItems": 1
        }
       },
       "additionalProperties": false
      },
      "claim": {}
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/standard-skew-young-tableau-jeu-de-taquin-rectification-verifier-293a95c1/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
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