# TeX82 Math Noad Binary Reclassification & Inter-atom Glue Recovery

> TeX82 Math Noad Binary Reclassification & Inter-atom Glue Recovery 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).

Recovers effective TeX noad classes and all inserted inter-atom math glue, including binary-operator reclassification and style-dependent transitions, then verifies the result against a SHA-256 claim.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-DOCUMENTS-15/tex82-math-noad-binary-reclassification-style-dependent-interatom-glue?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/tex82-math-noad-binary-reclassification-inter-atom-glue-recovery-f081a766
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_w6YXGeJmp785GMXrifm6V

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 tex82-math-noad-binary-reclassification-inter-atom-glue-recovery-f081a766 -d '<json body>'
```

Example prompt: I have a TeX math noad sequence in display style with thin glue (width 3.33, stretch 1.66, shrink 1), medium glue (width 4.44, stretch 2.22, shrink 1), and thick glue (width 5, stretch 2.5, shrink 1), containing these noads: ord, bin, ord, rel, open, ord, close — can you recover all the effective noad classes and inserted inter-atom glue, including any binary reclassification, and verify the result against SHA-256 claim 'a3f2...64hexchars'?

## When to prefer this

Use this endpoint when you need to faithfully simulate TeX82's inter-atom math glue algorithm, including binary-operator reclassification rules and style-dependent spacing transitions, and optionally validate the result against a known SHA-256 hash. Prefer this over generic TeX renderers when you need the raw glue values and noad class assignments rather than rendered output.

## Known failure modes

- Invalid noad class enum value returns schema validation error
- SHA-256 claim mismatch returns failed verification status
- Item array exceeding 96 items is rejected
- Glue width/stretch/shrink values outside [-1000, 1000] / [0, 1000] bounds are rejected
- Null claim skips verification step
- Malformed hex string in claim field fails pattern validation

## How this service works

Recover effective TeX noad classes and every inserted math glue, including binary-operator reclassification and style transitions.. Compare the complete typed result SHA256.

## Output

Returns the complete sequence of effective noad classes after binary-operator reclassification and all inter-atom glue values inserted between atoms for each style transition encountered, plus a boolean or status indicating whether the SHA-256 claim matches the typed result.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "$defs": {
    "a": {
     "type": "object",
     "required": [
      "width",
      "stretch",
      "shrink"
     ],
     "properties": {
      "width": {
       "type": "number",
       "maximum": 1000,
       "minimum": -1000
      },
      "shrink": {
       "type": "number",
       "maximum": 1000,
       "minimum": 0
      },
      "stretch": {
       "type": "number",
       "maximum": 1000,
       "minimum": 0
      }
     },
     "additionalProperties": false
    }
   },
   "required": [
    "texMath"
   ],
   "properties": {
    "texMath": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "style",
        "glues",
        "items"
       ],
       "properties": {
        "glues": {
         "type": "object",
         "required": [
          "thin",
          "medium",
          "thick"
         ],
         "properties": {
          "thin": {
           "$ref": "#/properties/input/properties/body/properties/artifact/%24defs/a"
          },
          "thick": {
           "$ref": "#/properties/input/properties/body/properties/artifact/%24defs/a"
          },
          "medium": {
           "$ref": "#/properties/input/properties/body/properties/artifact/%24defs/a"
          }
         },
         "additionalProperties": false
        },
        "items": {
         "type": "array",
         "items": {
          "anyOf": [
           {
            "type": "object",
            "required": [
             "kind",
             "class"
            ],
            "properties": {
             "kind": {
              "const": "noad"
             },
             "class": {
              "enum": [
               "ord",
               "op",
               "bin",
               "rel",
               "open",
               "close",
               "punct",
               "inner"
              ]
             }
            },
            "additionalProperties": false
           },
           {
            "type": "object",
            "required": [
             "kind",
             "value"
            ],
            "properties": {
             "kind": {
              "const": "style"
             },
             "value": {
              "enum": [
               "display",
               "text",
               "script",
               "scriptscript"
              ]
    
… (truncated)
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/tex82-math-noad-binary-reclassification-inter-atom-glue-recovery-f081a766/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)