{
  "task": {
    "id": "case_129",
    "name": "check_multiple_of_n",
    "summary": "Checks if all elements are a multiple of n (default n=2).",
    "examples": [
      {
        "input": [
          "BOS",
          0,
          28,
          2,
          6,
          22,
          16,
          26,
          20,
          10
        ],
        "output": [
          "BOS",
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ]
      },
      {
        "input": [
          "BOS",
          0,
          8,
          2,
          26,
          9,
          6,
          20,
          24,
          12
        ],
        "output": [
          "BOS",
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
        ]
      },
      {
        "input": [
          "BOS",
          4,
          10,
          14,
          0,
          6,
          9,
          12,
          8,
          18
        ],
        "output": [
          "BOS",
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
        ]
      },
      {
        "input": [
          "BOS",
          0,
          22,
          8,
          6,
          26,
          4,
          2,
          16,
          24
        ],
        "output": [
          "BOS",
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ]
      },
      {
        "input": [
          "BOS",
          2,
          26,
          8,
          14,
          29,
          18,
          0,
          10,
          16
        ],
        "output": [
          "BOS",
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0,
          0
        ]
      }
    ],
    "is_categorical": true
  },
  "program": "checks = rasp.Map(lambda x: 1 if x % n == 0 else 0, rasp.tokens).named(f\"check_multiple_of_{n}\")\nzero_selector = rasp.Select(checks, rasp.Map(lambda x: 0, rasp.indices), rasp.Comparison.EQ)\nreturn rasp.Map(lambda x: 0 if x > 0 else 1, rasp.SelectorWidth(zero_selector))",
  "components": [
    {
      "id": "L0_MLP",
      "hook": "blocks.0.mlp.hook_post",
      "role": {
        "tag": "INDICATOR",
        "note": "Computes a per-element pass/fail flag indicating whether each value is divisible by n."
      },
      "rasp_vars": [
        "checks"
      ],
      "labels": [
        "check_multiple_of_2_4",
        "map_5"
      ]
    },
    {
      "id": "L1H0_ATTN",
      "hook": "blocks.1.attn.hook_result[0]",
      "role": {
        "tag": "AGGREGATOR",
        "note": "Aggregates positions where the divisibility flag is zero, producing a per-position count of non-multiple occurrences."
      },
      "rasp_vars": [
        "zero_selector"
      ],
      "labels": [
        "selector_width_2_selector_width_attn_output"
      ]
    },
    {
      "id": "L1_MLP",
      "hook": "blocks.1.mlp.hook_post",
      "role": {
        "tag": "MAPPER",
        "note": "Summarizes the mismatch count signal into a single global indicator shared across positions."
      },
      "rasp_vars": [
        "mismatch_count"
      ],
      "labels": [
        "selector_width_2"
      ]
    },
    {
      "id": "L2_MLP",
      "hook": "blocks.2.mlp.hook_post",
      "role": {
        "tag": "INDICATOR",
        "note": "Converts the global mismatch indicator into the final decision: all-multiples vs not-all-multiples."
      },
      "rasp_vars": [
        "all_multiples"
      ],
      "labels": [
        "map_1"
      ]
    }
  ]
}