| { |
| "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" |
| } |
|
|
