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exact xor convolution audit

From two equal-length integer coefficient arrays, length1/2/4/8/16/32/64 and entries[-32,32], reconstruct the full XOR-convolution c[k]=sum a[i]*b[j] over i xor j=k. Return both unnormalized Sylvester Walsh-Hadamard spectra in natural binary-index order,pointwise product spectrum and exact integer convolution. Matrix entry sign=(-1)^popcount(i&j); inverse divides by array length exactly. This is not ordinary index-sum/cyclic FFT convolution, Boolean-function nonlinearity/algebraic.

POST https://datenvertrag.halowerk.com/v1/exact-xor-convolution-audit

Eingaben

Felder des veröffentlichten Eingabeschemas
FeldTypPflichtBeschreibung
leftSiehe SchemaJa
rightSiehe SchemaJa
claimed_valueSiehe SchemaJa
Vollständiges Eingabeschema anzeigen
{
  "type": "object",
  "properties": {
    "left": {
      "anyOf": [
        {
          "type": "array",
          "maxItems": 64,
          "items": {
            "type": "integer",
            "minimum": -32,
            "maximum": 32
          },
          "minItems": 1
        },
        {
          "type": "null"
        }
      ]
    },
    "right": {
      "anyOf": [
        {
          "type": "array",
          "maxItems": 64,
          "items": {
            "type": "integer",
            "minimum": -32,
            "maximum": 32
          },
          "minItems": 1
        },
        {
          "type": "null"
        }
      ]
    },
    "claimed_value": {
      "anyOf": [
        {
          "type": "object",
          "properties": {
            "length": {
              "type": "integer",
              "minimum": 1,
              "maximum": 64
            },
            "left_spectrum": {
              "anyOf": [
                {
                  "type": "array",
                  "maxItems": 64,
                  "items": {
                    "type": "integer",
                    "minimum": -2048,
                    "maximum": 2048
                  }
                },
                {
                  "type": "null"
                }
              ]
            },
            "right_spectrum": {
              "anyOf": [
                {
                  "type": "array",
                  "maxItems": 64,
                  "items": {
                    "type": "integer",
                    "minimum": -2048,
                    "maximum": 2048
                  }
                },
                {
                  "type": "null"
                }
              ]
            },
            "product_spectrum": {
              "anyOf": [
                {
                  "type": "array",
                  "maxItems": 64,
                  "items": {
                    "type": "integer",
                    "minimum": -4194304,
                    "maximum": 4194304
                  }
                },
                {
                  "type": "null"
                }
              ]
            },
            "xor_convolution": {
              "anyOf": [
                {
                  "type": "array",
                  "maxItems": 64,
                  "items": {
                    "type": "integer",
                    "minimum": -65536,
                    "maximum": 65536
                  }
                },
                {
                  "type": "null"
                }
              ]
            }
          },
          "required": [
            "length",
            "left_spectrum",
            "right_spectrum",
            "product_spectrum",
            "xor_convolution"
          ],
          "additionalProperties": false
        },
        {
          "type": "null"
        }
      ]
    }
  },
  "required": [
    "left",
    "right",
    "claimed_value"
  ],
  "additionalProperties": false
}

Originalschema öffnen

Veröffentlichtes Eingabebeispiel

{
  "left": [
    -32,
    -25,
    -18,
    -11
  ],
  "right": [
    -29,
    -18,
    -7,
    4
  ],
  "claimed_value": {
    "length": 4,
    "left_spectrum": [
      -86,
      -14,
      -28,
      0
    ],
    "right_spectrum": [
      -50,
      -22,
      -44,
      0
    ],
    "product_spectrum": [
      4300,
      308,
      1232,
      0
    ],
    "xor_convolution": [
      1460,
      1306,
      844,
      690
    ]
  }
}

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Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.

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