| { |
| "kernel": "run_sabrina_projective_simplex_rank_theorem", |
| "role": "post-computation assertion only", |
| "schema": "ouroboros_scientific_reference_assertion_v1", |
| "scientific_payload": { |
| "claim_boundary": { |
| "capabilities_removed": [], |
| "compatibility_required": true, |
| "integer_witness_matrices_claimed_as_physical_null_momenta": false, |
| "non_square_distributional_jacobian_derived": false, |
| "rank_deficiency_allowed_but_not_unique": true, |
| "simplex_positivity_required": true, |
| "source_error_claimed": false |
| }, |
| "classification": "all_D_projective_simplex_localization_rank_theorem_exact_with_support_and_positivity_boundaries", |
| "counterexamples": { |
| "incompatible": { |
| "augmented_rank": 2, |
| "matrix_rank": 1 |
| }, |
| "rank_deficient_compatible": { |
| "nullity": 1, |
| "rank": 2 |
| }, |
| "unique_but_not_simplex_positive": { |
| "solution": [ |
| "1", |
| "1", |
| "-1" |
| ] |
| } |
| }, |
| "exact_checks": { |
| "D4_n2_through_n5_have_zero_affine_moduli": true, |
| "D4_n3_has_two_external_compatibility_constraints": true, |
| "D4_n4_has_one_external_compatibility_constraint": true, |
| "D4_n5_is_square_unique_on_support": true, |
| "D4_n6_has_one_affine_modulus": true, |
| "all_99_integer_witnesses_have_expected_rank": true, |
| "archive_hash_matches": true, |
| "finite_grid_has_99_points": true, |
| "incompatible_example_fails_rank_test": true, |
| "localization_statement_hash_matches": true, |
| "localization_statement_unique": true, |
| "member_hash_matches": true, |
| "predecessor_manifest_hash_matches": true, |
| "rank_deficient_example_has_one_modulus": true, |
| "rank_deficient_example_is_compatible": true, |
| "source_equation_blocks_match": true, |
| "source_equation_markers_unique": true, |
| "unique_solution_can_fail_simplex_positivity": true |
| }, |
| "finite_exact_grid": [ |
| { |
| "D": 2, |
| "affine_solution_dimension_on_support": 0, |
| "expected_rank": 2, |
| "external_compatibility_codimension": 1, |
| "full_rank": true, |
| "n": 2, |
| "rank": 2 |
| }, |
| { |
| "D": 2, |
| "affine_solution_dimension_on_support": 0, |
| "expected_rank": 3, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 3, |
| "rank": 3 |
| }, |
| { |
| "D": 2, |
| "affine_solution_dimension_on_support": 1, |
| "expected_rank": 3, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 4, |
| "rank": 3 |
| }, |
| { |
| "D": 2, |
| "affine_solution_dimension_on_support": 2, |
| "expected_rank": 3, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 5, |
| "rank": 3 |
| }, |
| { |
| "D": 2, |
| "affine_solution_dimension_on_support": 3, |
| "expected_rank": 3, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 6, |
| "rank": 3 |
| }, |
| { |
| "D": 2, |
| "affine_solution_dimension_on_support": 4, |
| "expected_rank": 3, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 7, |
| "rank": 3 |
| }, |
| { |
| "D": 2, |
| "affine_solution_dimension_on_support": 5, |
| "expected_rank": 3, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 8, |
| "rank": 3 |
| }, |
| { |
| "D": 2, |
| "affine_solution_dimension_on_support": 6, |
| "expected_rank": 3, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 9, |
| "rank": 3 |
| }, |
| { |
| "D": 2, |
| "affine_solution_dimension_on_support": 7, |
| "expected_rank": 3, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 10, |
| "rank": 3 |
| }, |
| { |
| "D": 2, |
| "affine_solution_dimension_on_support": 8, |
| "expected_rank": 3, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 11, |
| "rank": 3 |
| }, |
| { |
| "D": 2, |
| "affine_solution_dimension_on_support": 9, |
| "expected_rank": 3, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 12, |
| "rank": 3 |
| }, |
| { |
| "D": 3, |
| "affine_solution_dimension_on_support": 0, |
| "expected_rank": 2, |
| "external_compatibility_codimension": 2, |
| "full_rank": true, |
| "n": 2, |
| "rank": 2 |
| }, |
| { |
| "D": 3, |
| "affine_solution_dimension_on_support": 0, |
| "expected_rank": 3, |
| "external_compatibility_codimension": 1, |
| "full_rank": true, |
| "n": 3, |
| "rank": 3 |
| }, |
| { |
| "D": 3, |
| "affine_solution_dimension_on_support": 0, |
| "expected_rank": 4, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 4, |
| "rank": 4 |
| }, |
| { |
| "D": 3, |
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| "expected_rank": 4, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 5, |
| "rank": 4 |
| }, |
| { |
| "D": 3, |
| "affine_solution_dimension_on_support": 2, |
| "expected_rank": 4, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 6, |
| "rank": 4 |
| }, |
| { |
| "D": 3, |
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| "expected_rank": 4, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 7, |
| "rank": 4 |
| }, |
| { |
| "D": 3, |
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| "expected_rank": 4, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 8, |
| "rank": 4 |
| }, |
| { |
| "D": 3, |
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| "expected_rank": 4, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 9, |
| "rank": 4 |
| }, |
| { |
| "D": 3, |
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| "expected_rank": 4, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 10, |
| "rank": 4 |
| }, |
| { |
| "D": 3, |
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| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 11, |
| "rank": 4 |
| }, |
| { |
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| "expected_rank": 4, |
| "external_compatibility_codimension": 0, |
| "full_rank": true, |
| "n": 12, |
| "rank": 4 |
| }, |
| { |
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| "full_rank": true, |
| "n": 2, |
| "rank": 2 |
| }, |
| { |
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| "full_rank": true, |
| "n": 3, |
| "rank": 3 |
| }, |
| { |
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| "n": 4, |
| "rank": 4 |
| }, |
| { |
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| "n": 5, |
| "rank": 5 |
| }, |
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| "n": 6, |
| "rank": 5 |
| }, |
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| "rank": 5 |
| }, |
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| }, |
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| "rank": 5 |
| }, |
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| }, |
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| "rank": 2 |
| }, |
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| }, |
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| "rank": 4 |
| }, |
| { |
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| }, |
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| "n": 6, |
| "rank": 6 |
| }, |
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| }, |
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| }, |
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| }, |
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| }, |
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| }, |
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| "rank": 6 |
| }, |
| { |
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| "rank": 2 |
| }, |
| { |
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| }, |
| { |
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| }, |
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| }, |
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| "rank": 6 |
| }, |
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| "rank": 7 |
| }, |
| { |
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| }, |
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| }, |
| { |
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| }, |
| { |
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| }, |
| { |
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| }, |
| { |
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| "rank": 2 |
| }, |
| { |
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| "rank": 3 |
| }, |
| { |
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| "rank": 4 |
| }, |
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| }, |
| { |
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| }, |
| { |
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| "rank": 7 |
| }, |
| { |
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| "full_rank": true, |
| "n": 8, |
| "rank": 8 |
| }, |
| { |
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| }, |
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| }, |
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| }, |
| { |
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| }, |
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| }, |
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| }, |
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| }, |
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| }, |
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| { |
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| } |
| ], |
| "paper": { |
| "arxiv_id": "1706.03917", |
| "title": "Gluon Amplitudes as 2d Conformal Correlators" |
| }, |
| "result_version": "sabrina_projective_simplex_rank_theorem_v1", |
| "source_evidence": { |
| "archive_sha256": "af2756072965c969be2a74c492fe25a797fe9f85e24d61605cf088e355d06244", |
| "block_hashes": { |
| "delta_product_rewrite": "8a2029c1a1fe7989bbb77b99449ca37fd43965e0b9169abe60c01d969c5f6f20", |
| "simplex_result": "24194f455371e8599a13a472c41489b7a6ccdbfa6911705547e0adb3ec882a9e" |
| }, |
| "checks": { |
| "archive_hash_matches": true, |
| "localization_statement_hash_matches": true, |
| "localization_statement_unique": true, |
| "member_hash_matches": true, |
| "predecessor_manifest_hash_matches": true, |
| "source_equation_blocks_match": true, |
| "source_equation_markers_unique": true |
| }, |
| "localization_line_sha256": "56cabb68b24099425e4158af718ec6b892423facfa4910a1878990f84cc769e6", |
| "member_sha256": "88253eb755b1b2418d0ac3480c1d4b67d9bb3985f8f6f6c3b0f79c85784f4bfe" |
| }, |
| "status": "complete", |
| "theorem": { |
| "constraint_matrix_shape": "(D+1) by n", |
| "external_compatibility_codimension": "D+1-r", |
| "generic_n_above_D_plus_1": "n-D-1 unfixed simplex moduli", |
| "generic_n_at_most_D_plus_1": "unique sigma on compatible support; D+1-n residual external constraints", |
| "generic_rank": "r=min(D+1,n)", |
| "on_support_affine_solution_dimension": "n-r", |
| "square_distributional_jacobian": "for n=D+1 and det(M)!=0 only: delta(M sigma-b)=delta(sigma-sigma*)/abs(det(M))" |
| } |
| }, |
| "scientific_payload_sha256": "a4be65bfe6724693b679405e1985b33302d94ec8113edf75512620fcc58045f7" |
| } |
|
|
