File size: 3,764 Bytes
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"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"
}
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