references/run_sabrina_weyl_double_copy_shadow_involution.json

{
  "kernel": "run_sabrina_weyl_double_copy_shadow_involution",
  "role": "post-computation assertion only",
  "schema": "ouroboros_scientific_reference_assertion_v1",
  "scientific_payload": {
    "claim_boundary": {
      "capabilities_removed": [],
      "full_shadow_kernel_normalization_claimed": false,
      "interacting_double_copy_claimed": false,
      "naive_self_shadow_substitution_allowed": false,
      "singular_state_physics_claimed": false
    },
    "exact_checks": {
      "archive_hash_matches": true,
      "coefficient_table_present": true,
      "fixed_zero_exact": true,
      "gauge_pair_exchanged": true,
      "member_hash_matches": true,
      "pole_exchange_exact": true,
      "primary_double_copy_exact": true,
      "primary_shadow_curvatures_present": true,
      "removable_self_shadow_limits_exact": true,
      "scalar_pair_exchanged": true,
      "shadow_double_copy_exact": true,
      "source_blocks_match": true,
      "source_primary_weyl_exact": true,
      "source_shadow_weyl_exact": true,
      "tau_squared_identity": true,
      "weyl_double_copy_definition_present": true,
      "weyl_pair_exchanged": true
    },
    "involution_certificate": {
      "checks": {
        "gauge_pair_exchanged": true,
        "primary_double_copy_exact": true,
        "scalar_pair_exchanged": true,
        "shadow_double_copy_exact": true,
        "source_primary_weyl_exact": true,
        "source_shadow_weyl_exact": true,
        "tau_squared_identity": true,
        "weyl_pair_exchanged": true
      },
      "coefficients": {
        "gauge_primary": "Delta - 1",
        "gauge_shadow": "1 - Delta",
        "scalar_primary": "(2 - 2*Delta)/Delta",
        "scalar_shadow": "(2 - 2*Delta)/(Delta - 2)",
        "weyl_primary": "-Delta**2/2 + Delta/2",
        "weyl_shadow": "-Delta**2/2 + 3*Delta/2 - 1"
      },
      "tau": "2-Delta"
    },
    "paper": {
      "arxiv_id": "2012.15694",
      "title": "Shifting Spin on the Celestial Sphere"
    },
    "result_version": "sabrina_weyl_double_copy_shadow_involution_v1",
    "scope": {
      "chirality_exchange_applied": true,
      "coefficient_level_only": true,
      "universal_shadow_spacetime_factor_stripped": "2/X^2"
    },
    "singularity_certificate": {
      "fixed_zero_exact": true,
      "pole_exchange_exact": true,
      "reduced_primary_limit": "0",
      "reduced_shadow_limit": "0",
      "removable_limits_exact": true,
      "scalar_primary": {
        "pole": "Delta=0",
        "zero": "Delta=1"
      },
      "scalar_shadow": {
        "pole": "Delta=2",
        "zero": "Delta=1"
      },
      "self_shadow_point": 1,
      "unreduced_quotient_at_self_shadow": "0/0",
      "weyl_primary_zeros": [
        0,
        1
      ],
      "weyl_shadow_zeros": [
        1,
        2
      ]
    },
    "source_evidence": {
      "archive_sha256": "ff00948d397a3aaaa36cec9a65f63477b16c6315c982669e63259b0a8961fc46",
      "block_hashes": {
        "primary_shadow_curvatures": "8acb82a9be540c4a2d8eead0630fbcb8fe0c15fcbd76c81abfa1fadfcebe7a80",
        "weyl_double_copy_definition": "5cbf0c6d34e0ca8ba5607901422b27778f4b6c966fb2dae1468294d2fa0dbed4",
        "weyl_double_copy_table": "774c827ab158f3d9fbae9dbc062ceb3638202c3dc36940d488f19f968db13490"
      },
      "checks": {
        "archive_hash_matches": true,
        "coefficient_table_present": true,
        "member_hash_matches": true,
        "primary_shadow_curvatures_present": true,
        "source_blocks_match": true,
        "weyl_double_copy_definition_present": true
      },
      "member_sha256": "17ed9a4bf99bf5a3a53a11d7da5c3000c4b99db7688432072e6703a597671794"
    },
    "status": "complete",
    "theorem": {
      "divisor_exchange": "the scalar prefactor poles Delta=0 and Delta=2 are exchanged, while Delta=1 is fixed",
      "double_copy_equivariance": "C_P=f_P^2/S_P and C_S=f_S^2/S_S are preserved under tau",
      "involution": "tau(Delta)=2-Delta exchanges the stripped primary and shadow gauge, scalar, and Weyl double-copy coefficients",
      "self_shadow_boundary": "at Delta=1 the unreduced f^2/S quotient is 0/0; its reduced primary and shadow limits both equal zero"
    }
  },
  "scientific_payload_sha256": "f6243bc6dfdd05769cab60b02d4e23c53ef9c0119f2ac7a10d54eda023956fee"
}