{ "classification": "Exact local construction/admission checks; no RH candidate certified", "arithmetic": "Python Fraction and integers; no floating-point comparisons", "workers": 2, "case_count": 165, "all_checks_consistent": true, "controls": { "composite_labels": "Same local geometry with 4 or 6; local weight pass is insufficient to identify prime support", "dimension_lift": "Unit-rate 6D lift fails; chosen normalized rates/parity can restore weight algebra only", "davenport_heilbronn": "Not applicable to local determinant/deck/individual Euler-factor algebra: the analogue lacks the specified prime-product geometry. No generic completed-function positivity inference is tested or passed.", "ns94_ns100_ns101": "No circle-count or theta-positivity inference attempted; their broader symmetry-only warnings retained" }, "rows": [ { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 2, "label_is_prime": true, "actual_repetition_m": 2, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/2", "target_without_log_label": "-1/2", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 2, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/4", "target_without_log_label": "-1/4", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 2, "label_is_prime": true, "actual_repetition_m": 6, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/8", "target_without_log_label": "-1/8", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 2, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/16", "target_without_log_label": "-1/16", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 3, "label_is_prime": true, "actual_repetition_m": 2, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/3", "target_without_log_label": "-1/3", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 3, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/9", "target_without_log_label": "-1/9", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 3, "label_is_prime": true, "actual_repetition_m": 6, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/27", "target_without_log_label": "-1/27", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 3, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/81", "target_without_log_label": "-1/81", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 5, "label_is_prime": true, "actual_repetition_m": 2, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/5", "target_without_log_label": "-1/5", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 5, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/25", "target_without_log_label": "-1/25", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 5, "label_is_prime": true, "actual_repetition_m": 6, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/125", "target_without_log_label": "-1/125", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 5, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/625", "target_without_log_label": "-1/625", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 7, "label_is_prime": true, "actual_repetition_m": 2, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/7", "target_without_log_label": "-1/7", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 7, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/49", "target_without_log_label": "-1/49", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 7, "label_is_prime": true, "actual_repetition_m": 6, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/343", "target_without_log_label": "-1/343", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 7, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/2401", "target_without_log_label": "-1/2401", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 11, "label_is_prime": true, "actual_repetition_m": 2, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/11", "target_without_log_label": "-1/11", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 11, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/121", "target_without_log_label": "-1/121", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 11, "label_is_prime": true, "actual_repetition_m": 6, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/1331", "target_without_log_label": "-1/1331", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 11, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/14641", "target_without_log_label": "-1/14641", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 4, "label_is_prime": false, "actual_repetition_m": 2, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/4", "target_without_log_label": "-1/4", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 4, "label_is_prime": false, "actual_repetition_m": 4, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/16", "target_without_log_label": "-1/16", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 4, "label_is_prime": false, "actual_repetition_m": 6, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/64", "target_without_log_label": "-1/64", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 4, "label_is_prime": false, "actual_repetition_m": 8, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/256", "target_without_log_label": "-1/256", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 6, "label_is_prime": false, "actual_repetition_m": 2, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/6", "target_without_log_label": "-1/6", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 6, "label_is_prime": false, "actual_repetition_m": 4, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/36", "target_without_log_label": "-1/36", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 6, "label_is_prime": false, "actual_repetition_m": 6, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/216", "target_without_log_label": "-1/216", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 4, "label": 6, "label_is_prime": false, "actual_repetition_m": 8, "rates": [ "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/1296", "target_without_log_label": "-1/1296", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 2, "label_is_prime": true, "actual_repetition_m": 2, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/4", "target_without_log_label": "-1/2", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 2, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/16", "target_without_log_label": "-1/4", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 2, "label_is_prime": true, "actual_repetition_m": 6, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/64", "target_without_log_label": "-1/8", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 2, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/256", "target_without_log_label": "-1/16", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 3, "label_is_prime": true, "actual_repetition_m": 2, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/9", "target_without_log_label": "-1/3", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 3, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/81", "target_without_log_label": "-1/9", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 3, "label_is_prime": true, "actual_repetition_m": 6, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/729", "target_without_log_label": "-1/27", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 3, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/6561", "target_without_log_label": "-1/81", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 5, "label_is_prime": true, "actual_repetition_m": 2, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/25", "target_without_log_label": "-1/5", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 5, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/625", "target_without_log_label": "-1/25", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 5, "label_is_prime": true, "actual_repetition_m": 6, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/15625", "target_without_log_label": "-1/125", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 5, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/390625", "target_without_log_label": "-1/625", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 7, "label_is_prime": true, "actual_repetition_m": 2, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/49", "target_without_log_label": "-1/7", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 7, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/2401", "target_without_log_label": "-1/49", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 7, "label_is_prime": true, "actual_repetition_m": 6, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/117649", "target_without_log_label": "-1/343", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 7, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/5764801", "target_without_log_label": "-1/2401", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 11, "label_is_prime": true, "actual_repetition_m": 2, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/121", "target_without_log_label": "-1/11", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 11, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/14641", "target_without_log_label": "-1/121", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 11, "label_is_prime": true, "actual_repetition_m": 6, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/1771561", "target_without_log_label": "-1/1331", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 11, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/214358881", "target_without_log_label": "-1/14641", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 4, "label_is_prime": false, "actual_repetition_m": 2, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/16", "target_without_log_label": "-1/4", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 4, "label_is_prime": false, "actual_repetition_m": 4, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/256", "target_without_log_label": "-1/16", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 4, "label_is_prime": false, "actual_repetition_m": 6, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/4096", "target_without_log_label": "-1/64", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 4, "label_is_prime": false, "actual_repetition_m": 8, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/65536", "target_without_log_label": "-1/256", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 6, "label_is_prime": false, "actual_repetition_m": 2, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/36", "target_without_log_label": "-1/6", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 6, "label_is_prime": false, "actual_repetition_m": 4, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/1296", "target_without_log_label": "-1/36", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 6, "label_is_prime": false, "actual_repetition_m": 6, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/46656", "target_without_log_label": "-1/216", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 6, "label_is_prime": false, "actual_repetition_m": 8, "rates": [ "1", "1" ], "grading_shift": 0, "normalized_weight_without_log_label": "1/1679616", "target_without_log_label": "-1/1296", "exterior_trace_equals_determinant": true, "candidate_condition_holds": false, "symbolic_rate_and_parity_condition": false, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 2, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/4", "target_without_log_label": "-1/4", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 2, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/16", "target_without_log_label": "-1/16", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 2, "label_is_prime": true, "actual_repetition_m": 12, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/64", "target_without_log_label": "-1/64", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 2, "label_is_prime": true, "actual_repetition_m": 16, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/256", "target_without_log_label": "-1/256", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 3, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/9", "target_without_log_label": "-1/9", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 3, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/81", "target_without_log_label": "-1/81", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 3, "label_is_prime": true, "actual_repetition_m": 12, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/729", "target_without_log_label": "-1/729", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 3, "label_is_prime": true, "actual_repetition_m": 16, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/6561", "target_without_log_label": "-1/6561", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 5, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/25", "target_without_log_label": "-1/25", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 5, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/625", "target_without_log_label": "-1/625", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 5, "label_is_prime": true, "actual_repetition_m": 12, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/15625", "target_without_log_label": "-1/15625", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 5, "label_is_prime": true, "actual_repetition_m": 16, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/390625", "target_without_log_label": "-1/390625", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 7, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/49", "target_without_log_label": "-1/49", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 7, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/2401", "target_without_log_label": "-1/2401", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 7, "label_is_prime": true, "actual_repetition_m": 12, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/117649", "target_without_log_label": "-1/117649", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 7, "label_is_prime": true, "actual_repetition_m": 16, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/5764801", "target_without_log_label": "-1/5764801", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 11, "label_is_prime": true, "actual_repetition_m": 4, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/121", "target_without_log_label": "-1/121", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 11, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/14641", "target_without_log_label": "-1/14641", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 11, "label_is_prime": true, "actual_repetition_m": 12, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/1771561", "target_without_log_label": "-1/1771561", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 11, "label_is_prime": true, "actual_repetition_m": 16, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/214358881", "target_without_log_label": "-1/214358881", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 4, "label_is_prime": false, "actual_repetition_m": 4, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/16", "target_without_log_label": "-1/16", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 4, "label_is_prime": false, "actual_repetition_m": 8, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/256", "target_without_log_label": "-1/256", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 4, "label_is_prime": false, "actual_repetition_m": 12, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/4096", "target_without_log_label": "-1/4096", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 4, "label_is_prime": false, "actual_repetition_m": 16, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/65536", "target_without_log_label": "-1/65536", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 6, "label_is_prime": false, "actual_repetition_m": 4, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/36", "target_without_log_label": "-1/36", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 6, "label_is_prime": false, "actual_repetition_m": 8, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/1296", "target_without_log_label": "-1/1296", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 6, "label_is_prime": false, "actual_repetition_m": 12, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/46656", "target_without_log_label": "-1/46656", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 6, "label": 6, "label_is_prime": false, "actual_repetition_m": 16, "rates": [ "1/2", "1/2" ], "grading_shift": 1, "normalized_weight_without_log_label": "-1/1679616", "target_without_log_label": "-1/1679616", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 2, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/16", "target_without_log_label": "-1/16", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 2, "label_is_prime": true, "actual_repetition_m": 16, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/256", "target_without_log_label": "-1/256", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 2, "label_is_prime": true, "actual_repetition_m": 24, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/4096", "target_without_log_label": "-1/4096", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 2, "label_is_prime": true, "actual_repetition_m": 32, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/65536", "target_without_log_label": "-1/65536", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 3, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/81", "target_without_log_label": "-1/81", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 3, "label_is_prime": true, "actual_repetition_m": 16, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/6561", "target_without_log_label": "-1/6561", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 3, "label_is_prime": true, "actual_repetition_m": 24, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/531441", "target_without_log_label": "-1/531441", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 3, "label_is_prime": true, "actual_repetition_m": 32, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/43046721", "target_without_log_label": "-1/43046721", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 5, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/625", "target_without_log_label": "-1/625", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 5, "label_is_prime": true, "actual_repetition_m": 16, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/390625", "target_without_log_label": "-1/390625", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 5, "label_is_prime": true, "actual_repetition_m": 24, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/244140625", "target_without_log_label": "-1/244140625", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 5, "label_is_prime": true, "actual_repetition_m": 32, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/152587890625", "target_without_log_label": "-1/152587890625", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 7, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/2401", "target_without_log_label": "-1/2401", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 7, "label_is_prime": true, "actual_repetition_m": 16, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/5764801", "target_without_log_label": "-1/5764801", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 7, "label_is_prime": true, "actual_repetition_m": 24, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/13841287201", "target_without_log_label": "-1/13841287201", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 7, "label_is_prime": true, "actual_repetition_m": 32, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/33232930569601", "target_without_log_label": "-1/33232930569601", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 11, "label_is_prime": true, "actual_repetition_m": 8, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/14641", "target_without_log_label": "-1/14641", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 11, "label_is_prime": true, "actual_repetition_m": 16, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/214358881", "target_without_log_label": "-1/214358881", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 11, "label_is_prime": true, "actual_repetition_m": 24, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/3138428376721", "target_without_log_label": "-1/3138428376721", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 11, "label_is_prime": true, "actual_repetition_m": 32, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/45949729863572161", "target_without_log_label": "-1/45949729863572161", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 4, "label_is_prime": false, "actual_repetition_m": 8, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/256", "target_without_log_label": "-1/256", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 4, "label_is_prime": false, "actual_repetition_m": 16, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/65536", "target_without_log_label": "-1/65536", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 4, "label_is_prime": false, "actual_repetition_m": 24, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/16777216", "target_without_log_label": "-1/16777216", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 4, "label_is_prime": false, "actual_repetition_m": 32, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/4294967296", "target_without_log_label": "-1/4294967296", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 6, "label_is_prime": false, "actual_repetition_m": 8, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/1296", "target_without_log_label": "-1/1296", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 6, "label_is_prime": false, "actual_repetition_m": 16, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/1679616", "target_without_log_label": "-1/1679616", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 6, "label_is_prime": false, "actual_repetition_m": 24, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/2176782336", "target_without_log_label": "-1/2176782336", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "hyperbolic_local_weight", "dimension_real": 8, "label": 6, "label_is_prime": false, "actual_repetition_m": 32, "rates": [ "1/4", "1/4", "1/2" ], "grading_shift": 0, "normalized_weight_without_log_label": "-1/2821109907456", "target_without_log_label": "-1/2821109907456", "exterior_trace_equals_determinant": true, "candidate_condition_holds": true, "symbolic_rate_and_parity_condition": true, "test_passed": true, "scope": "Exact finite algebra only; composite labels can also match. No global trace, gamma/poles, positivity or RH transfer." }, { "kind": "independent_passive_prime_port", "label": 2, "a": "1/2", "y": "2", "ratio": "7/6", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 2, "a": "1", "y": "5/2", "ratio": "5/4", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 2, "a": "3/2", "y": "3", "ratio": "31/24", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 3, "a": "1/2", "y": "2", "ratio": "13/12", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 3, "a": "1", "y": "5/2", "ratio": "10/9", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 3, "a": "3/2", "y": "3", "ratio": "121/108", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 5, "a": "1/2", "y": "2", "ratio": "31/30", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 5, "a": "1", "y": "5/2", "ratio": "26/25", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 5, "a": "3/2", "y": "3", "ratio": "781/750", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 7, "a": "1/2", "y": "2", "ratio": "57/56", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 7, "a": "1", "y": "5/2", "ratio": "50/49", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 7, "a": "3/2", "y": "3", "ratio": "2801/2744", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 11, "a": "1/2", "y": "2", "ratio": "133/132", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 11, "a": "1", "y": "5/2", "ratio": "122/121", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 11, "a": "3/2", "y": "3", "ratio": "16105/15972", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 4, "a": "1/2", "y": "2", "ratio": "21/20", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 4, "a": "1", "y": "5/2", "ratio": "17/16", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 4, "a": "3/2", "y": "3", "ratio": "341/320", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 6, "a": "1/2", "y": "2", "ratio": "43/42", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 6, "a": "1", "y": "5/2", "ratio": "37/36", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "independent_passive_prime_port", "label": 6, "a": "3/2", "y": "3", "ratio": "1555/1512", "candidate_condition_holds": false, "test_passed": true, "scope": "Rejects this independently passive Euler-factor architecture; says nothing against a coupled completed system." }, { "kind": "elliptic_deck_map", "label": 2, "power": 1, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 2, "power": 2, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 2, "power": 3, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 2, "power": 4, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 3, "power": 1, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 3, "power": 2, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 3, "power": 3, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 3, "power": 4, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 5, "power": 1, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 5, "power": 2, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 5, "power": 3, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 5, "power": 4, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 7, "power": 1, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 7, "power": 2, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 7, "power": 3, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 7, "power": 4, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 11, "power": 1, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 11, "power": 2, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 11, "power": 3, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 11, "power": 4, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 4, "power": 1, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 4, "power": 2, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 4, "power": 3, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 4, "power": 4, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 6, "power": 1, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 6, "power": 2, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 6, "power": 3, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "elliptic_deck_map", "label": 6, "power": 4, "reduced_shift_in_period_units": "0", "candidate_condition_holds": false, "test_passed": true, "scope": "Ordinary quotient map is the identity; labeled return/groupoid data would be extra structure." }, { "kind": "primitive_support", "labels": [ 2, 3, 5 ], "faults": [], "repeated_primitive_labels": false, "candidate_condition_holds": true, "test_passed": true, "scope": "Exact support check on the supplied finite primitive list, not a global construction or analytic continuation." }, { "kind": "primitive_support", "labels": [ 2, 3, 4 ], "faults": [ { "primitive_label": 4, "extra_log_coefficient": { "2": 2 }, "type": "duplicates_prime_power" } ], "repeated_primitive_labels": false, "candidate_condition_holds": false, "test_passed": true, "scope": "Exact support check on the supplied finite primitive list, not a global construction or analytic continuation." }, { "kind": "primitive_support", "labels": [ 2, 3, 6 ], "faults": [ { "primitive_label": 6, "extra_log_coefficient": { "2": 1, "3": 1 }, "type": "extra_primitive_support" } ], "repeated_primitive_labels": false, "candidate_condition_holds": false, "test_passed": true, "scope": "Exact support check on the supplied finite primitive list, not a global construction or analytic continuation." }, { "kind": "primitive_support", "labels": [ 2, 2, 3 ], "faults": [], "repeated_primitive_labels": true, "candidate_condition_holds": false, "test_passed": true, "scope": "Exact support check on the supplied finite primitive list, not a global construction or analytic continuation." } ] }