{
  "kernel": "run_sabrina_p4_spherical_refined_entropy",
  "role": "post-computation assertion only",
  "schema": "ouroboros_scientific_reference_assertion_v1",
  "scientific_payload": {
    "claim_boundary": {
      "capabilities_removed": [],
      "finite_counterterm_scheme_independence_claimed": false,
      "moderate_P_monotonicity_proved": false,
      "normalization_to_field_theory_N_and_G10_fixed": false,
      "numerical_profiles_reproduced": false,
      "supergravity_domain_extended": false,
      "terms_through_order_P_minus_3_derived": false
    },
    "exact_checks": {
      "P_inverse_area_integral_exact": true,
      "all_symbolic_residuals_zero": true,
      "archive_hash_matches": true,
      "both_t_equations_exact": true,
      "lower_local_terms_annihilated": true,
      "member_hash_matches": true,
      "prior_expansion_manifest_matches": true,
      "refined_entropy_labels_unique": true,
      "refined_entropy_operator_exact": true,
      "source_blocks_match": true,
      "t_shell_matching_exact": true
    },
    "paper": {
      "arxiv_id": "2606.13889",
      "title": "Flat Space Entanglement: A Coulomb Branch Perspective"
    },
    "result_version": "sabrina_p4_spherical_refined_entropy_v1",
    "source_evidence": {
      "archive_sha256": "0c66795a0adac63d23dac9ad3207a4bd586f7453365221b95159bca9380edbc3",
      "block_hashes": {
        "area_and_matching": "1a4ecbae9b625bb0cd553031504ffd9c5c9d3da16f973e7e87afd827f92106f1",
        "degrees_of_freedom": "2c8a4bf8604eb2a36146b59ca8da1550f327eb96871479a884141ff7fde76632",
        "four_dim_refined_entropy": "99f9b70ee6d83190d0f8ff99c04babcc7a0a7a07ae5c3453be5b9a0829b1bc25",
        "p4_future_work": "48ef8f3d699b9bc045849a9cfe7ceec0aa4e5c8388d2fc1b0a24579c6d715793",
        "precedent_expansions": "a56135ef73575f190dd2e05ce7316f75e652a207bdad7a07bd59739e65b811a5",
        "spherical_eom": "809aea156968448d52e6189e6dcce138f090bcd434ea12da753fb390b14742f4",
        "three_dim_refined_entropy": "c0baeac9de982295f3f174e15cabd5e01863df355056b06a870934983b0c6a2c"
      },
      "checks": {
        "archive_hash_matches": true,
        "member_hash_matches": true,
        "prior_expansion_manifest_matches": true,
        "refined_entropy_labels_unique": true,
        "source_blocks_match": true
      },
      "member_sha256": "3612980847a10a3a07708a1af3dcee65afedc85ffc8106af673e69ae3d42585e",
      "prior_manifest_sha256": "1dc9e0a600bc5ff235fe3721a8d9e42aa9dc984bb9665b67b26d859bd8d0cd7c"
    },
    "status": "complete",
    "symbolic_derivation": {
      "asymptotic_decrease_threshold_P_over_R": "exp(1492067/1575000)",
      "profiles": {
        "t_flat": "-9*g**2*(17199*R**4 - 5600*R**2*r**2 + 304*r**4)/(112000*R**6)",
        "t_throat": "-9*g**2*(-567*R**6 + 4620*R**4*r**2 - 19250*R**2*r**4 + 9600*R*r**5 + 17500*r**6)/(112000*r**8)"
      },
      "raw_P_inverse_coefficient_over_Omega4_Omega3": "g**3*(-19683*R**8/(640000*r_uv**8) + 8019*R**6/(32000*r_uv**6) - 5859*R**4/(6400*r_uv**4) + 243*R**3/(350*r_uv**3) + 81*R**2/(128*r_uv**2) - 81*R/(70*r_uv) + 135*log(r_uv/R)/128 + 3792549/4480000)",
      "refined_entropy_area_over_Omega4_Omega3": "g**3*(45*log(P/R)/16 + 82933/560000)/P",
      "residuals": {
        "flat_t_eom": "0",
        "integrated_P_inverse": "0",
        "local_P3_and_P_annihilated": "0",
        "refined_entropy": "0",
        "shell_t_derivative": "0",
        "shell_t_value": "0",
        "throat_t_eom": "0"
      },
      "subtracted_area_through_P_inverse_over_Omega4_Omega3": "-3*P**3*R**2*g/10 + 81*P*R*g**2/35 + g**3*(135*log(P/R)/128 + 3792549/4480000)/P",
      "universal_substitution": "log(r_uv/R) -> log(P/R) after subtracting the p=4 universal logarithmic UV term"
    },
    "theorem": {
      "infrared_behavior": "positive for P>=R, tends to zero as log(P/R)/P, and decreases beyond the recorded exact threshold",
      "raw_cutoff_result": "g**3*(-19683*R**8/(640000*r_uv**8) + 8019*R**6/(32000*r_uv**6) - 5859*R**4/(6400*r_uv**4) + 243*R**3/(350*r_uv**3) + 81*R**2/(128*r_uv**2) - 81*R/(70*r_uv) + 135*log(r_uv/R)/128 + 3792549/4480000)",
      "refined_entropy_area_over_Omega4_Omega3": "g^3/P*[45/16 log(P/R)+82933/560000]+O(P^-3)",
      "refined_operator": "(P*d/dP-1)(P*d/dP-3)/3",
      "regime": "p=4, P large, rho=P+s/P+t/P^3+O(P^-5)"
    }
  },
  "scientific_payload_sha256": "391c082d381a39de409e09c5d5d1798607ab16101326c4103bafbd5f220a2345"
}