{
  "schema": "HELIX.SWITCHYARD.CANDIDATE_CENSUS.PUBLIC.v1",
  "source": {
    "paper": "The Helix Operator: The Exact Integer Helix on the Coprime Substrate",
    "doi": "10.5281/zenodo.21611872",
    "paper_section": "13.4",
    "results_audit": "247e0eddc53580ef"
  },
  "comparison": {
    "reference": "exhaustive unordered pair census on the same switch floor",
    "lattice_os": "LEVEL support-shadow candidate census before route-policy evaluation",
    "metric": "exact candidate count",
    "projected": false,
    "timing_claim": false
  },
  "floors": [
    {
      "atoms": [
        3,
        5,
        7,
        11
      ],
      "modulus": 1155,
      "exhaustive_unordered_pairs": 114960,
      "level_support_shadow_pairs": 496,
      "exact_reduction": 231.7741935483871,
      "kernel_dimension": 31,
      "residual_dimension": 0,
      "periodic_reanchor_invariant": true
    },
    {
      "atoms": [
        3,
        5,
        11,
        13
      ],
      "modulus": 2145,
      "exhaustive_unordered_pairs": 460320,
      "level_support_shadow_pairs": 1770,
      "exact_reduction": 260.06779661016947,
      "kernel_dimension": 52,
      "residual_dimension": 0,
      "periodic_reanchor_invariant": true
    },
    {
      "atoms": [
        3,
        7,
        11,
        13
      ],
      "modulus": 3003,
      "exhaustive_unordered_pairs": 1036080,
      "level_support_shadow_pairs": 4005,
      "exact_reduction": 258.69662921348316,
      "kernel_dimension": 79,
      "residual_dimension": 0,
      "periodic_reanchor_invariant": true
    },
    {
      "atoms": [
        3,
        7,
        13,
        17
      ],
      "modulus": 4641,
      "exhaustive_unordered_pairs": 2653056,
      "level_support_shadow_pairs": 6903,
      "exact_reduction": 384.3337679269883,
      "kernel_dimension": 108,
      "residual_dimension": 0,
      "periodic_reanchor_invariant": true
    },
    {
      "atoms": [
        3,
        11,
        13,
        17
      ],
      "modulus": 7293,
      "exhaustive_unordered_pairs": 7370880,
      "level_support_shadow_pairs": 45150,
      "exact_reduction": 163.2531561461794,
      "kernel_dimension": 171,
      "residual_dimension": 0,
      "periodic_reanchor_invariant": true
    }
  ],
  "scope": {
    "grade": "verified five-floor execution adapter; candidate-count reduction, not hardware runtime or mass throughput",
    "meaning": "exact candidate-space reduction under the registered support policy",
    "not_claimed": [
      "hardware runtime",
      "mass throughput",
      "physical actuator mapping",
      "advantage for unconstrained Abelian route existence"
    ]
  },
  "audit": "0635e6bf32928c8f"
}