{
  "kernel": "run_sabrina_coulomb_branch_complexity_ratio",
  "role": "post-computation assertion only",
  "schema": "ouroboros_scientific_reference_assertion_v1",
  "scientific_payload": {
    "algebraic_certificate": {
      "checks": {
        "deficit_factorization_exact": true,
        "derivative_factorization_exact": true,
        "formation_is_negative": true,
        "half_plus_square_decomposition_exact": true,
        "physical_bounds_exact": true,
        "physical_table_exact": true,
        "ratio_from_source_coefficients_exact": true,
        "unique_physical_minimum_at_p3": true
      },
      "derivative": "-(p - 15)*(p - 3)/(16*(p - 9)**2)",
      "fractional_deficit": "(p - 7)*(p + 9)/(16*(p - 9))",
      "half_plus_square": "1/2 + (p - 3)**2/(144 - 16*p)",
      "physical_table": [
        {
          "flat_over_throat": "9/16",
          "fractional_deficit": "7/16",
          "p": 0
        },
        {
          "flat_over_throat": "17/32",
          "fractional_deficit": "15/32",
          "p": 1
        },
        {
          "flat_over_throat": "57/112",
          "fractional_deficit": "55/112",
          "p": 2
        },
        {
          "flat_over_throat": "1/2",
          "fractional_deficit": "1/2",
          "p": 3
        },
        {
          "flat_over_throat": "41/80",
          "fractional_deficit": "39/80",
          "p": 4
        }
      ],
      "ratio": "-(p**2 - 14*p + 81)/(16*(p - 9))"
    },
    "claim_boundary": {
      "capabilities_removed": [],
      "complexity_equals_action_claimed": false,
      "complexity_equals_volume_only": true,
      "field_theory_circuit_complexity_equality_claimed": false,
      "physical_integer_p_zero_through_four_only": true
    },
    "exact_checks": {
      "archive_hash_matches": true,
      "deficit_factorization_exact": true,
      "derivative_factorization_exact": true,
      "flat_formula_present": true,
      "formation_formula_present": true,
      "formation_is_negative": true,
      "half_plus_square_decomposition_exact": true,
      "member_hash_matches": true,
      "physical_bounds_exact": true,
      "physical_p_range_present": true,
      "physical_table_exact": true,
      "ratio_from_source_coefficients_exact": true,
      "source_blocks_match": true,
      "throat_formula_present": true,
      "unique_physical_minimum_at_p3": true
    },
    "paper": {
      "arxiv_id": "2606.13889",
      "title": "Flat Space Entanglement: A Coulomb Branch Perspective"
    },
    "result_version": "sabrina_coulomb_branch_complexity_ratio_v1",
    "source_evidence": {
      "archive_sha256": "0c66795a0adac63d23dac9ad3207a4bd586f7453365221b95159bca9380edbc3",
      "block_hashes": {
        "complexity_volume_formulas": "c7ab6918da6e15b37f48e4de2ea3403897be7be511e54772e0bc51b985e2a334"
      },
      "checks": {
        "archive_hash_matches": true,
        "flat_formula_present": true,
        "formation_formula_present": true,
        "member_hash_matches": true,
        "physical_p_range_present": true,
        "source_blocks_match": true,
        "throat_formula_present": true
      },
      "member_sha256": "3612980847a10a3a07708a1af3dcee65afedc85ffc8106af673e69ae3d42585e"
    },
    "status": "complete",
    "theorem": {
      "manifest_minimum": "ratio=1/2+(p-3)^2/[16(9-p)]",
      "maximal_reduction": "p=3 uniquely gives a one-half fractional complexity reduction",
      "parameter_cancellation": "R, r_p, G_10, Omega_(8-p), and V_p cancel from the ratio",
      "physical_bounds": "1/2 <= C_flat/C_throat <= 9/16 for p=0,1,2,3,4",
      "universal_ratio": "C_flat/C_throat=[32+(7-p)^2]/[16(9-p)]"
    }
  },
  "scientific_payload_sha256": "0a48392a955f724766d46453ed8d209ae2f1cfca84d21c71d0807b479504eb06"
}