{
  "schema": "HELIX.SUPERHIGHWAY.SCALING.PUBLIC.v1",
  "source": {
    "paper": "The Helix Operator: The Exact Integer Helix on the Coprime Substrate",
    "doi": "10.5281/zenodo.21611872",
    "paper_sections": ["13.5", "13.6"],
    "results_audit": "aacd94752a079c5e"
  },
  "comparison": {
    "input": "the same registered path-dependent target family at each horizon",
    "reference": "standard exact 26-state stream",
    "lattice_os": "compiled order-five TRANSPORT",
    "metric": "exact ring multiplications",
    "projected": false,
    "fixed_width_modulus": 2147483647
  },
  "horizon_ladder": [
    {"horizon": 600, "standard_exact_stream_multiplications": 9349, "lattice_os_transport_multiplications": 179, "measured_ratio": 52.229050279329606},
    {"horizon": 6000, "standard_exact_stream_multiplications": 94399, "lattice_os_transport_multiplications": 459, "measured_ratio": 205.66230936819173},
    {"horizon": 60000, "standard_exact_stream_multiplications": 944899, "lattice_os_transport_multiplications": 618, "measured_ratio": 1528.962783171521},
    {"horizon": 600000, "standard_exact_stream_multiplications": 9449899, "lattice_os_transport_multiplications": 798, "measured_ratio": 11841.978696741855}
  ],
  "same_target_elapsed_measurement": {
    "horizon": 18,
    "exact_multiplicity": "1522646264372231232",
    "generic_exact_frontier_seconds": 70.8707415999379,
    "lattice_os_ten_skeleton_median_nanoseconds": 23122.39,
    "measured_ratio": 3065026.6516539985,
    "projected": false,
    "recurrence_seed_lookup_excluded": true
  },
  "scope": {
    "streaming_law": "Theta(L) sparse exact ring operations",
    "lattice_os_law": "O(5^2 log L) exact ring operations after compilation",
    "full_integer_boundary": "Theta(L) output bits",
    "address_book_construction": "problem-owned"
  }
}