diff --git a/research/e6-sheared-frame-seedb401/CERTIFICATE.json b/research/e6-sheared-frame-seedb401/CERTIFICATE.json new file mode 100644 index 0000000000..9bdcc82442 --- /dev/null +++ b/research/e6-sheared-frame-seedb401/CERTIFICATE.json @@ -0,0 +1,7921 @@ +{ + "schema_version": 1, + "status": "scoped-negative-result", + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "assignment_seed": "b401f2874293cab50e88e4bd7068a949", + "task_id": "complex-rank-shape-decoder", + "priority_revision": 4, + "selected_record_sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32", + "geometry": { + "root_lines": 36, + "canonical_root_sha256": "d2d26919a71a2f9a007d3c43f9806cb85a7142ebb45481ac4ad5fe6db8591263", + "basis_root_indices": [ + 0, + 1, + 2, + 4, + 6, + 20 + ], + "ambient_basis_columns": [ + 0, + 3, + 4, + 5, + 6, + 7 + ], + "basis_gram": [ + [ + "2", + "0", + "1", + "1", + "1", + "1" + ], + [ + "0", + "2", + "1", + "1", + "1", + "0" + ], + [ + "1", + "1", + "2", + "1", + "1", + "1" + ], + [ + "1", + "1", + "1", + "2", + "1", + "1" + ], + [ + "1", + "1", + "1", + "1", + "2", + "1" + ], + [ + "1", + "0", + "1", + "1", + "1", + "2" + ] + ], + "pairing_B0_rank_F2": 7, + "transvection_definition": "A=I+epsilon*E_ij; i!=j; epsilon in {-1,+1}" + }, + "controls": { + "identity_fixtures": 2, + "wrong_sign_rejections": 2, + "omitted_term_rejections": 2, + "inadmissible_edge_rejection": true + }, + "domain": { + "signed_transvections": 60, + "direction_count": 365, + "root_directions": 36, + "projective_ternary_directions": 364, + "direction_union_count": 365, + "lambda_domain": "all nonzero rational lambda, split at all exact support breakpoints", + "support_cells": 330486, + "distinct_nonzero_breakpoints": 143343, + "degenerate_cells_with_fewer_than_7_active_totals": 26 + }, + "result": { + "minimum_raw_cost": 37, + "minimum_raw_witness": { + "charged": 37, + "raw": 37, + "direction_index": 189, + "a": [ + "1", + "-1", + "1", + "0", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_fully_charged_cost": 37, + "minimum_fully_charged_witness": { + "charged": 37, + "raw": 37, + "direction_index": 189, + "a": [ + "1", + "-1", + "1", + "0", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_cost_histogram": { + "37": 6, + "38": 12, + "39": 18, + "40": 131, + "41": 369, + "42": 1397, + "43": 29259, + "44": 117297, + "45": 181997 + }, + "charged_cost_histogram": { + "37": 6, + "38": 12, + "39": 18, + "40": 131, + "41": 369, + "42": 1397, + "43": 29259, + "44": 117297, + "45": 181997 + }, + "active_total_count_histogram": { + "6": 26, + "7": 330460 + }, + "seven_active_cost_le_35_witnesses_first20_per_matrix": [], + "positive_target_witness_count": 0, + "no_seven_active_cost_le_35": true + }, + "per_transvection": [ + { + "transvection": { + "i": 0, + "j": 1, + "epsilon": -1, + "matrix": [ + [ + "1", + "-1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5496, + "distinct_nonzero_breakpoints": 2383, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "39": 1, + "40": 8, + "41": 14, + "42": 181, + "43": 5292 + }, + "charged_histogram": { + "39": 1, + "40": 8, + "41": 14, + "42": 181, + "43": 5292 + }, + "active_total_histogram": { + "7": 5496 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 1, + "epsilon": 1, + "matrix": [ + [ + "1", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5440, + "distinct_nonzero_breakpoints": 2355, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 5, + "41": 5, + "42": 14, + "43": 180, + "44": 5236 + }, + "charged_histogram": { + "40": 5, + "41": 5, + "42": 14, + "43": 180, + "44": 5236 + }, + "active_total_histogram": { + "7": 5440 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 2, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "-1", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 7, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 7, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 2, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 134, + "a": [ + "1", + "-1", + "-1", + "0", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 134, + "a": [ + "1", + "-1", + "-1", + "0", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 3, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "-1", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 6, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 6, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 3, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 152, + "a": [ + "1", + "-1", + "0", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 152, + "a": [ + "1", + "-1", + "0", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 4, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "-1", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 6, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 6, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 4, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 158, + "a": [ + "1", + "-1", + "0", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 158, + "a": [ + "1", + "-1", + "0", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 5, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "-1" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6026, + "distinct_nonzero_breakpoints": 2648, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 3, + "42": 7, + "43": 15, + "44": 215, + "45": 5785 + }, + "charged_histogram": { + "40": 1, + "41": 3, + "42": 7, + "43": 15, + "44": 215, + "45": 5785 + }, + "active_total_histogram": { + "7": 6026 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 5, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "1" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4960, + "distinct_nonzero_breakpoints": 2115, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 241, + "a": [ + "1", + "0", + "0", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 7, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 241, + "a": [ + "1", + "0", + "0", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 7, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 5, + "42": 8, + "43": 13, + "44": 152, + "45": 4780 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 5, + "42": 8, + "43": 13, + "44": 152, + "45": 4780 + }, + "active_total_histogram": { + "6": 1, + "7": 4959 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 0, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "-1", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5442, + "distinct_nonzero_breakpoints": 2356, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "39": 1, + "41": 11, + "42": 8, + "43": 186, + "44": 5236 + }, + "charged_histogram": { + "39": 1, + "41": 11, + "42": 8, + "43": 186, + "44": 5236 + }, + "active_total_histogram": { + "7": 5442 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 0, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5360, + "distinct_nonzero_breakpoints": 2315, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 1, + "42": 11, + "43": 11, + "44": 183, + "45": 5153 + }, + "charged_histogram": { + "40": 1, + "41": 1, + "42": 11, + "43": 11, + "44": 183, + "45": 5153 + }, + "active_total_histogram": { + "7": 5360 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 2, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "-1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5928, + "distinct_nonzero_breakpoints": 2599, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 6, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 6, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "charged_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "active_total_histogram": { + "7": 5928 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 2, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4998, + "distinct_nonzero_breakpoints": 2134, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 189, + "a": [ + "1", + "-1", + "1", + "0", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 189, + "a": [ + "1", + "-1", + "1", + "0", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "charged_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "active_total_histogram": { + "6": 1, + "7": 4997 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 3, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5928, + "distinct_nonzero_breakpoints": 2599, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 6, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 6, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "charged_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "active_total_histogram": { + "7": 5928 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 3, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4998, + "distinct_nonzero_breakpoints": 2134, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 171, + "a": [ + "1", + "-1", + "0", + "1", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 171, + "a": [ + "1", + "-1", + "0", + "1", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "charged_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "active_total_histogram": { + "6": 1, + "7": 4997 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 4, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "-1", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5928, + "distinct_nonzero_breakpoints": 2599, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 6, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 6, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "charged_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "active_total_histogram": { + "7": 5928 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 4, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4998, + "distinct_nonzero_breakpoints": 2134, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 165, + "a": [ + "1", + "-1", + "0", + "0", + "1", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 165, + "a": [ + "1", + "-1", + "0", + "0", + "1", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "charged_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "active_total_histogram": { + "6": 1, + "7": 4997 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 5, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "-1" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5442, + "distinct_nonzero_breakpoints": 2356, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 5, + 6 + ] + }, + "raw_histogram": { + "39": 1, + "41": 11, + "42": 8, + "43": 186, + "44": 5236 + }, + "charged_histogram": { + "39": 1, + "41": 11, + "42": 8, + "43": 186, + "44": 5236 + }, + "active_total_histogram": { + "7": 5442 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 5, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "1" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5360, + "distinct_nonzero_breakpoints": 2315, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 1, + "42": 11, + "43": 11, + "44": 183, + "45": 5153 + }, + "charged_histogram": { + "40": 1, + "41": 1, + "42": 11, + "43": 11, + "44": 183, + "45": 5153 + }, + "active_total_histogram": { + "7": 5360 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 0, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "-1", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 0, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 134, + "a": [ + "1", + "-1", + "-1", + "0", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 134, + "a": [ + "1", + "-1", + "-1", + "0", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 1, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "-1", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6032, + "distinct_nonzero_breakpoints": 2651, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "charged_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "active_total_histogram": { + "7": 6032 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 1, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5052, + "distinct_nonzero_breakpoints": 2161, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 189, + "a": [ + "1", + "-1", + "1", + "0", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 0, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 189, + "a": [ + "1", + "-1", + "1", + "0", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 0, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "charged_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "active_total_histogram": { + "6": 1, + "7": 5051 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 3, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "-1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 3, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 17, + "a": [ + "0", + "0", + "1", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 7, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 17, + "a": [ + "0", + "0", + "1", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 7, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 4, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "-1", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 4, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 23, + "a": [ + "0", + "0", + "1", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 7, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 23, + "a": [ + "0", + "0", + "1", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 7, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 5, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "-1" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 7, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 7, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 5, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "1" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 106, + "a": [ + "0", + "1", + "1", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 106, + "a": [ + "0", + "1", + "1", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 0, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "-1", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 5, + 6, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 5, + 6, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 0, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "1", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 152, + "a": [ + "1", + "-1", + "0", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 152, + "a": [ + "1", + "-1", + "0", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 1, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "-1", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6032, + "distinct_nonzero_breakpoints": 2651, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 6, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 6, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "charged_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "active_total_histogram": { + "7": 6032 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 1, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5052, + "distinct_nonzero_breakpoints": 2161, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 171, + "a": [ + "1", + "-1", + "0", + "1", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 6, + 0, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 171, + "a": [ + "1", + "-1", + "0", + "1", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 6, + 0, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "charged_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "active_total_histogram": { + "6": 1, + "7": 5051 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 2, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "-1", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 2, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 17, + "a": [ + "0", + "0", + "1", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 7, + 0, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 17, + "a": [ + "0", + "0", + "1", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 7, + 0, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 4, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "-1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 4, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 5, + "a": [ + "0", + "0", + "0", + "1", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 7, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 5, + "a": [ + "0", + "0", + "0", + "1", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 7, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 5, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "-1" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 6, + 5, + 7, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 6, + 5, + 7, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 5, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "1" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 88, + "a": [ + "0", + "1", + "0", + "1", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 88, + "a": [ + "0", + "1", + "0", + "1", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 0, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "-1", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 5, + 5, + 6, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 5, + 5, + 6, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 0, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "1", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 158, + "a": [ + "1", + "-1", + "0", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 0, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 158, + "a": [ + "1", + "-1", + "0", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 0, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 1, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "-1", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6032, + "distinct_nonzero_breakpoints": 2651, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 6, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 6, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "charged_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "active_total_histogram": { + "7": 6032 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 1, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5052, + "distinct_nonzero_breakpoints": 2161, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 165, + "a": [ + "1", + "-1", + "0", + "0", + "1", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 6, + 6, + 0, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 165, + "a": [ + "1", + "-1", + "0", + "0", + "1", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 6, + 6, + 0, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "charged_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "active_total_histogram": { + "6": 1, + "7": 5051 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 2, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "-1", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 2, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 23, + "a": [ + "0", + "0", + "1", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 7, + 6, + 0, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 23, + "a": [ + "0", + "0", + "1", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 7, + 6, + 0, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 3, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "-1", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 3, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 5, + "a": [ + "0", + "0", + "0", + "1", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 7, + 0, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 5, + "a": [ + "0", + "0", + "0", + "1", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 7, + 0, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 5, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "-1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 6, + 7, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 6, + 7, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 5, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 82, + "a": [ + "0", + "1", + "0", + "0", + "1", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 0, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 82, + "a": [ + "0", + "1", + "0", + "0", + "1", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 0, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 0, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "-1", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6026, + "distinct_nonzero_breakpoints": 2648, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 3, + "42": 7, + "43": 15, + "44": 215, + "45": 5785 + }, + "charged_histogram": { + "40": 1, + "41": 3, + "42": 7, + "43": 15, + "44": 215, + "45": 5785 + }, + "active_total_histogram": { + "7": 6026 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 0, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "1", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4960, + "distinct_nonzero_breakpoints": 2115, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 241, + "a": [ + "1", + "0", + "0", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 7, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 241, + "a": [ + "1", + "0", + "0", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 7, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 5, + "42": 8, + "43": 13, + "44": 152, + "45": 4780 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 5, + "42": 8, + "43": 13, + "44": 152, + "45": 4780 + }, + "active_total_histogram": { + "6": 1, + "7": 4959 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 1, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "-1", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5496, + "distinct_nonzero_breakpoints": 2383, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "39": 1, + "40": 8, + "41": 14, + "42": 181, + "43": 5292 + }, + "charged_histogram": { + "39": 1, + "40": 8, + "41": 14, + "42": 181, + "43": 5292 + }, + "active_total_histogram": { + "7": 5496 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 1, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5440, + "distinct_nonzero_breakpoints": 2355, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 5, + "41": 5, + "42": 14, + "43": 180, + "44": 5236 + }, + "charged_histogram": { + "40": 5, + "41": 5, + "42": 14, + "43": 180, + "44": 5236 + }, + "active_total_histogram": { + "7": 5440 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 2, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "-1", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 7, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 7, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 2, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 106, + "a": [ + "0", + "1", + "1", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 106, + "a": [ + "0", + "1", + "1", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 3, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "-1", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 6, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 6, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 3, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 88, + "a": [ + "0", + "1", + "0", + "1", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 88, + "a": [ + "0", + "1", + "0", + "1", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 4, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "-1", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 6, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 6, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 4, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 82, + "a": [ + "0", + "1", + "0", + "0", + "1", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 82, + "a": [ + "0", + "1", + "0", + "0", + "1", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + } + ], + "limits": [ + "Only the 60 signed elementary transvections A=I+epsilon E_ij are searched.", + "Only the union of the 36 root directions and projective {-1,0,1}^6 directions in the pinned basis is searched.", + "No arbitrary GL6(Q) basis change, arbitrary rational correction direction, different base decoder, or sparse pairing is covered.", + "No physical source/copy/frame/hosting/restoration/precision mapping or selected-supplier profile is established." + ] +} diff --git a/research/e6-sheared-frame-seedb401/OVERLAP.json b/research/e6-sheared-frame-seedb401/OVERLAP.json new file mode 100644 index 0000000000..dbd3b4bb5e --- /dev/null +++ b/research/e6-sheared-frame-seedb401/OVERLAP.json @@ -0,0 +1,64 @@ +{ + "schema_version": 1, + "claim": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-18938219", + "search": { + "command": "python3 scripts/find_overlap.py --refresh --task complex-rank-shape-decoder --limit 100 'E6 basis shear' 'six-term gauge' 'basis transvection' 'one-extra rank-one frame' 'full-rank E6 decoder' --json", + "searched_at": "2026-10-15T01:58:52.749494+00:00", + "status": "POSSIBLE_OVERLAP_NOT_A_NOVELTY_CERTIFICATE", + "coverage": { + "open_prs": { + "fetched_at": "2026-10-15T01:55:22.022247+00:00", + "complete_pagination": true, + "records": 477 + }, + "discussions": { + "fetched_at": "2026-10-15T01:58:52.549544+00:00", + "complete_pagination": true, + "records": 951 + } + }, + "direct_live_check": "Fresh complete overlap refresh found no other remote match for the basis-transvection terms; the only direct Discussion match was this cycle claim #18938219. PR #2240 remains open and mergeable at head c8a2b37056e766715c457f56e2dd8172f5bdbccd; PR #2241 remains open and mergeable at head 5688d8b17830dbb813fba5a509f52449383903fa. Both had checks queued at the live status query." + }, + "nearest": [ + { + "pr": 1590, + "head": "08e134b4a0c7f04869dae703f2a2e688e53c44f0", + "state": "merged", + "scope": "Root-unit model and Theorem C pricing context." + }, + { + "pr": 2228, + "head": "ad1757e319225f3a5b86e3d3fa72897bd9f6db40", + "state": "open", + "scope": "Dense root-code floors; leaves overcomplete E6 m=7 open." + }, + { + "pr": 2137, + "head": "6a022d50e21bdcf2014a26937a34d44eed3473f0", + "state": "open", + "scope": "Rank-four E6 B0 coordinate-form family." + }, + { + "pr": 2232, + "head": "3391f27dd0f226f0e1ead8b2b829eb6d3ec567d3", + "state": "open", + "scope": "Rank-four projected Gram with adapted pairing." + }, + { + "pr": 2240, + "head": "c8a2b37056e766715c457f56e2dd8172f5bdbccd", + "state": "open", + "scope": "Prior Cycle30 family fixes A=I; this census varies A over signed elementary transvections." + }, + { + "discussion": "#1167 comment #18936773", + "scope": "Active S3 rank-nine claim; different object." + }, + { + "pr": 2241, + "scope": "Recent Cycle42 sum-anchor helper inventory; different object, just completed." + } + ], + "scope_distinction": "Full-rank six-factor basis is changed by A=I+epsilon E_ij before the rank-one redundant term; fixed E6 Gram and B0; 60 matrices, 365 directions, all exact lambda support cells.", + "selected_frontier_changed": false +} diff --git a/research/e6-sheared-frame-seedb401/PROOF.md b/research/e6-sheared-frame-seedb401/PROOF.md new file mode 100644 index 0000000000..db699069c0 --- /dev/null +++ b/research/e6-sheared-frame-seedb401/PROOF.md @@ -0,0 +1,49 @@ +# Exact statement and support-cell proof + +## Finite statement + +Fix the exact E6 root lines and basis reconstructed from the pinned `ade.E6b()` ordering, their Gram matrix `H`, the coordinate matrix `X`, and the dense pairing `B0` with unit diagonal and off-diagonal ones only on orthogonal root pairs. For every signed elementary transvection + +```text +A = I + epsilon E_ij, i != j, epsilon in {-1,+1}, +``` +for every direction `a` in the union of the 36 projective E6 root directions and the 364 projective nonzero ternary vectors in the pinned basis, and for every rational `lambda != 0`, define `c=A^-1 a` and + +```text +p_j = X A e_j, q_j = X(H A^-T e_j - lambda c_j a), j=1,...,6, +p_7 = X a, q_7 = lambda X a. +``` + +The exhaustive support-cell census finds minimum raw cost 37 and minimum active-term Theorem C cost 37. Thus no seven-active decoder in this declared finite family has cost at most 35. The result is not a lower bound for all E6 seven-term decoders. + +## Identity + +As matrices in the six-dimensional coefficient space, the first six factors have sum + +```text +A (H A^-T)^T - lambda (A c) a^T + = A A^-1 H^T - lambda a a^T + = H - lambda a a^T, +``` + +using symmetry of `H` and `A c=a`. The seventh factor contributes `lambda a a^T`. Multiplying by `X` and `X^T` proves `sum_{j=1}^7 p_j q_j^T = X H X^T = G`. Each root has norm squared 2, and `B0` is one only on the diagonal or orthogonal pairs, so `B0` is admissible. The verifier checks this identity for both `A=I` and `A=I+E_01`, then rejects a reversed correction sign and an omitted seventh term. + +The first independent basis rows have root indices `[0,1,2,4,6,20]`; the first nonsingular ambient minor uses columns `[0,3,4,5,6,7]`. The canonical root digest, exact basis Gram and `rank_F2(B0)=7` are pinned in [CERTIFICATE.json](CERTIFICATE.json). + +## Exhaustive lambda cells + +For each `A,a`, the left supports are fixed. The seventh right support is fixed for nonzero lambda. Each coordinate of the remaining right factors is affine: + +```text +q_j(t) = X_t H A^-T e_j - lambda * (A^-1 a)_j * (X_t a). +``` + +A nonzero slope has one exact rational zero. A zero slope gives either an identically zero coordinate or one that never vanishes. The verifier inserts every nonzero zero with `0` as a partition cut, evaluates every nonzero breakpoint itself, and one rational point in every open interval, including both tails. This represents every allowed lambda with exactly the same support. Degenerate terms are counted by their actual active total count; no zero term is charged the floor `w=5`. + +Across the 60 signed transvections and 365 directions there are 143,343 distinct nonzero breakpoints. Including the zero cut gives `2*(60*365+143343)=330486` point/interval representatives. The search is split into two reproducible shards of 30 transvections. + +## Cost + +For each `B0[R_j,A_j]`, binary Gaussian elimination computes `r_j` exactly. The raw cost is `sum r_j`; the full Theorem C charge is `sum max(5,r_j)` over active terms. The complete cost histogram ranges from 37 through 45, with counts in [CERTIFICATE.json](CERTIFICATE.json). The least-cost witness is `A=I+E_23`, `a=(1,-1,1,0,0,1)`, `lambda=1/2`; its ranks are `(6,0,6,6,6,6,7)`, leaving six active totals at cost 37. All seven-active cells also have cost at least 37 because the full histogram contains no cost below 37. The six-term square benchmark 36 is cited from the open request and is not recomputed here. + +No source accesses, copied-information realization, frame transitions, hosting, restoration, precision, recursive children or supplier integration are supplied. The result does not change the selected frontier or establish a multiplication bound. diff --git a/research/e6-sheared-frame-seedb401/README.md b/research/e6-sheared-frame-seedb401/README.md new file mode 100644 index 0000000000..06a06ffb50 --- /dev/null +++ b/research/e6-sheared-frame-seedb401/README.md @@ -0,0 +1,45 @@ +# E6 sheared base factorization with one extra frame + +**Scoped negative result; no new κ.** For the 60 signed elementary transvections of the pinned six-coordinate E6 Gram factorization, the exact one-extra rank-one frame construction has minimum raw pairing cost **37** and minimum fully charged Theorem C cost **37**. The census covers **330,486** rational support cells across the 60 transvections and the union of 36 root directions with 364 projective ternary directions. No seven-active decoder reaches cost 35. + +The least-cost cell is degenerate to six active totals: its rank profile is `(6,0,6,6,6,6,7)`, at `A=I+E_{2,3}`, `a=(1,-1,1,0,0,1)`, `lambda=1/2`. Its charged cost 37 is still above the square-decoder benchmark 36 in the open request. The finite result does not settle arbitrary rational basis changes, other seven-term identities, sparse pairings, or the unrestricted E6 question. + +## Construction + +Let `X` be the exact 36-by-6 E6 root-coordinate matrix and `H` the Gram matrix of its pinned basis, so `G=X H X^T`. For a signed transvection `A=I+epsilon E_ij`, define `c=A^{-1}a`. For each nonzero projective direction `a` and `lambda != 0`, use + +```text +p_j = X A e_j +q_j = X(H A^{-T} e_j - lambda c_j a), j=1,...,6 +p_7 = X a +q_7 = lambda X a. +``` + +Since `A c=a`, the six correction terms sum to `-lambda X a a^T X^T`, which the seventh term restores. Hence the decoder is exactly `G`. The dense pairing `B0` stays fixed: diagonal one and off-diagonal one exactly on orthogonal root pairs. + +The direction set is the union of all 36 E6 root-line directions and all 364 projective vectors in `{-1,0,1}^6` in the pinned basis. For each transvection and direction, every rational breakpoint where a coordinate of `q_1,...,q_6` becomes zero is included, as is one exact rational representative from each complementary interval. Zero lambda is excluded. The census records degenerate terms and charges only active totals. + +The full cost histogram is `37:6, 38:12, 39:18, 40:131, 41:369, 42:1397, 43:29259, 44:117297, 45:181997`. There are 26 cells with six active totals and 330,460 with seven. The exact per-transvection records, witness, support-cell counts and root pins are in [CERTIFICATE.json](CERTIFICATE.json); the two shards are in [SHARD-0.json](SHARD-0.json) and [SHARD-1.json](SHARD-1.json). + +A hypothetical seven-active win has optimistic floor `7*5=35`, one below the square benchmark 36. The tested family’s minimum is 37 even when degenerate cells are included. This is only an algebraic root-unit cost. No supplier implementation, per-call paid profile, source/copy/frame/hosting/restoration/precision charge, or κ improvement is established. + +## Reproduce + +From repository root, with Python 3.12 and only the standard library: + +```sh +python3 scripts/research_package.py --package research/e6-sheared-frame-seedb401 --check-only +python3 scripts/research_package.py --package research/e6-sheared-frame-seedb401 +``` + +The registered replay exhausts two shards of 30 transvections each and checks their saved results plus the combined certificate. The exact verifier can also run a quick identity-control smoke check with `python3 -B research/e6-sheared-frame-seedb401/verify.py --smoke`. + +## Overlap and attribution + +The current open request is [Discussion #1166, comment #18936173](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-18936173). The completed Cycle30 [PR #2240](https://github.com/CrocSwap/integer-mult-bounds/pull/2240), head `c8a2b37056e766715c457f56e2dd8172f5bdbccd`, fixes `A=I`; this contribution changes the six-term base factorization by signed elementary transvections. Merged [PR #1590](https://github.com/CrocSwap/integer-mult-bounds/pull/1590), head `08e134b4a0c7f04869dae703f2a2e688e53c44f0`, supplies the root-unit model and Theorem C context. Open [PR #2228](https://github.com/CrocSwap/integer-mult-bounds/pull/2228) leaves overcomplete E6 at seven terms open. Open [PR #2137](https://github.com/CrocSwap/integer-mult-bounds/pull/2137) and [PR #2232](https://github.com/CrocSwap/integer-mult-bounds/pull/2232) are different rank-four families. + +The exact root ordering follows the pinned `research/root-unit-decoder-lemmas/lib/ade.py` input in [SOURCES.json](SOURCES.json). Credit the authors of PR #1590 and the cited E6 decoder work for the model and predecessors. Prepared by OpenAI Codex with substantial GPT-6 assistance in research, exact derivation, implementation, verification and writing. No independent human review is claimed. Apache-2.0. + +## Open next questions + +Can a seven-term E6 decoder outside the elementary-transvection family attain fully charged cost 35? A next step is to test one structurally different basis family, such as a two-coordinate or two-shear composition, after screening its optimistic charge. Arbitrary `GL_6(Q)` changes are unbounded, and this package supplies no physical supplier mapping. diff --git a/research/e6-sheared-frame-seedb401/SHARD-0.json b/research/e6-sheared-frame-seedb401/SHARD-0.json new file mode 100644 index 0000000000..6638ea23a3 --- /dev/null +++ b/research/e6-sheared-frame-seedb401/SHARD-0.json @@ -0,0 +1,3946 @@ +{ + "schema_version": 1, + "shard": 0, + "transvections": [ + { + "transvection": { + "i": 0, + "j": 1, + "epsilon": -1, + "matrix": [ + [ + "1", + "-1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5496, + "distinct_nonzero_breakpoints": 2383, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "39": 1, + "40": 8, + "41": 14, + "42": 181, + "43": 5292 + }, + "charged_histogram": { + "39": 1, + "40": 8, + "41": 14, + "42": 181, + "43": 5292 + }, + "active_total_histogram": { + "7": 5496 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 1, + "epsilon": 1, + "matrix": [ + [ + "1", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5440, + "distinct_nonzero_breakpoints": 2355, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 5, + "41": 5, + "42": 14, + "43": 180, + "44": 5236 + }, + "charged_histogram": { + "40": 5, + "41": 5, + "42": 14, + "43": 180, + "44": 5236 + }, + "active_total_histogram": { + "7": 5440 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 2, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "-1", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 7, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 7, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 2, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 134, + "a": [ + "1", + "-1", + "-1", + "0", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 134, + "a": [ + "1", + "-1", + "-1", + "0", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 3, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "-1", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 6, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 6, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 3, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 152, + "a": [ + "1", + "-1", + "0", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 152, + "a": [ + "1", + "-1", + "0", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 4, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "-1", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 6, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 6, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 4, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 158, + "a": [ + "1", + "-1", + "0", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 158, + "a": [ + "1", + "-1", + "0", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 5, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "-1" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6026, + "distinct_nonzero_breakpoints": 2648, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 3, + "42": 7, + "43": 15, + "44": 215, + "45": 5785 + }, + "charged_histogram": { + "40": 1, + "41": 3, + "42": 7, + "43": 15, + "44": 215, + "45": 5785 + }, + "active_total_histogram": { + "7": 6026 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 0, + "j": 5, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "1" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4960, + "distinct_nonzero_breakpoints": 2115, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 241, + "a": [ + "1", + "0", + "0", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 7, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 241, + "a": [ + "1", + "0", + "0", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 0, + 7, + 6, + 6, + 6, + 7, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 5, + "42": 8, + "43": 13, + "44": 152, + "45": 4780 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 5, + "42": 8, + "43": 13, + "44": 152, + "45": 4780 + }, + "active_total_histogram": { + "6": 1, + "7": 4959 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 0, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "-1", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5442, + "distinct_nonzero_breakpoints": 2356, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "39": 1, + "41": 11, + "42": 8, + "43": 186, + "44": 5236 + }, + "charged_histogram": { + "39": 1, + "41": 11, + "42": 8, + "43": 186, + "44": 5236 + }, + "active_total_histogram": { + "7": 5442 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 0, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "1", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5360, + "distinct_nonzero_breakpoints": 2315, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 1, + "42": 11, + "43": 11, + "44": 183, + "45": 5153 + }, + "charged_histogram": { + "40": 1, + "41": 1, + "42": 11, + "43": 11, + "44": 183, + "45": 5153 + }, + "active_total_histogram": { + "7": 5360 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 2, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "-1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5928, + "distinct_nonzero_breakpoints": 2599, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 6, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 6, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "charged_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "active_total_histogram": { + "7": 5928 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 2, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4998, + "distinct_nonzero_breakpoints": 2134, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 189, + "a": [ + "1", + "-1", + "1", + "0", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 189, + "a": [ + "1", + "-1", + "1", + "0", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "charged_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "active_total_histogram": { + "6": 1, + "7": 4997 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 3, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "-1", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5928, + "distinct_nonzero_breakpoints": 2599, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 6, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 6, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "charged_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "active_total_histogram": { + "7": 5928 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 3, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4998, + "distinct_nonzero_breakpoints": 2134, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 171, + "a": [ + "1", + "-1", + "0", + "1", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 171, + "a": [ + "1", + "-1", + "0", + "1", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "charged_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "active_total_histogram": { + "6": 1, + "7": 4997 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 4, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "-1", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5928, + "distinct_nonzero_breakpoints": 2599, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 6, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 6, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "charged_histogram": { + "41": 2, + "42": 10, + "43": 10, + "44": 221, + "45": 5685 + }, + "active_total_histogram": { + "7": 5928 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 4, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4998, + "distinct_nonzero_breakpoints": 2134, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 165, + "a": [ + "1", + "-1", + "0", + "0", + "1", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 165, + "a": [ + "1", + "-1", + "0", + "0", + "1", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 0, + 6, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "charged_histogram": { + "37": 1, + "40": 6, + "41": 6, + "42": 12, + "43": 156, + "44": 4817 + }, + "active_total_histogram": { + "6": 1, + "7": 4997 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 5, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "-1" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5442, + "distinct_nonzero_breakpoints": 2356, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 5, + 6 + ] + }, + "raw_histogram": { + "39": 1, + "41": 11, + "42": 8, + "43": 186, + "44": 5236 + }, + "charged_histogram": { + "39": 1, + "41": 11, + "42": 8, + "43": 186, + "44": 5236 + }, + "active_total_histogram": { + "7": 5442 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 1, + "j": 5, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "1" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5360, + "distinct_nonzero_breakpoints": 2315, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 1, + "42": 11, + "43": 11, + "44": 183, + "45": 5153 + }, + "charged_histogram": { + "40": 1, + "41": 1, + "42": 11, + "43": 11, + "44": 183, + "45": 5153 + }, + "active_total_histogram": { + "7": 5360 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 0, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "-1", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 0, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "1", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 134, + "a": [ + "1", + "-1", + "-1", + "0", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 134, + "a": [ + "1", + "-1", + "-1", + "0", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 1, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "-1", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6032, + "distinct_nonzero_breakpoints": 2651, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "charged_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "active_total_histogram": { + "7": 6032 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 1, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5052, + "distinct_nonzero_breakpoints": 2161, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 189, + "a": [ + "1", + "-1", + "1", + "0", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 0, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 189, + "a": [ + "1", + "-1", + "1", + "0", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 0, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "charged_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "active_total_histogram": { + "6": 1, + "7": 5051 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 3, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "-1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 3, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 17, + "a": [ + "0", + "0", + "1", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 7, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 17, + "a": [ + "0", + "0", + "1", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 7, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 4, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "-1", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 4, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 23, + "a": [ + "0", + "0", + "1", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 7, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 23, + "a": [ + "0", + "0", + "1", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 7, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 5, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "-1" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 7, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 7, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 2, + "j": 5, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "1" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 106, + "a": [ + "0", + "1", + "1", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 106, + "a": [ + "0", + "1", + "1", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 0, + 6, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + } + ], + "geometry": { + "root_lines": 36, + "canonical_root_sha256": "d2d26919a71a2f9a007d3c43f9806cb85a7142ebb45481ac4ad5fe6db8591263", + "basis_root_indices": [ + 0, + 1, + 2, + 4, + 6, + 20 + ], + "ambient_basis_columns": [ + 0, + 3, + 4, + 5, + 6, + 7 + ], + "basis_gram": [ + [ + "2", + "0", + "1", + "1", + "1", + "1" + ], + [ + "0", + "2", + "1", + "1", + "1", + "0" + ], + [ + "1", + "1", + "2", + "1", + "1", + "1" + ], + [ + "1", + "1", + "1", + "2", + "1", + "1" + ], + [ + "1", + "1", + "1", + "1", + "2", + "1" + ], + [ + "1", + "0", + "1", + "1", + "1", + "2" + ] + ], + "pairing_B0_rank_F2": 7, + "transvection_definition": "A=I+epsilon*E_ij; i!=j; epsilon in {-1,+1}" + }, + "controls": { + "identity_fixtures": 2, + "wrong_sign_rejections": 2, + "omitted_term_rejections": 2, + "inadmissible_edge_rejection": true + } +} diff --git a/research/e6-sheared-frame-seedb401/SHARD-1.json b/research/e6-sheared-frame-seedb401/SHARD-1.json new file mode 100644 index 0000000000..54d69cc2b8 --- /dev/null +++ b/research/e6-sheared-frame-seedb401/SHARD-1.json @@ -0,0 +1,3956 @@ +{ + "schema_version": 1, + "shard": 1, + "transvections": [ + { + "transvection": { + "i": 3, + "j": 0, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "-1", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 5, + 6, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 5, + 6, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 0, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "1", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 152, + "a": [ + "1", + "-1", + "0", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 152, + "a": [ + "1", + "-1", + "0", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 1, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "-1", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6032, + "distinct_nonzero_breakpoints": 2651, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 6, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 6, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "charged_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "active_total_histogram": { + "7": 6032 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 1, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5052, + "distinct_nonzero_breakpoints": 2161, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 171, + "a": [ + "1", + "-1", + "0", + "1", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 6, + 0, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 171, + "a": [ + "1", + "-1", + "0", + "1", + "0", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 6, + 0, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "charged_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "active_total_histogram": { + "6": 1, + "7": 5051 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 2, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "-1", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 2, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 17, + "a": [ + "0", + "0", + "1", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 7, + 0, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 17, + "a": [ + "0", + "0", + "1", + "-1", + "0", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 7, + 0, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 4, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "-1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 4, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 5, + "a": [ + "0", + "0", + "0", + "1", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 7, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 5, + "a": [ + "0", + "0", + "0", + "1", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 7, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 5, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "-1" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 6, + 5, + 7, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 110, + "a": [ + "0", + "1", + "1", + "0", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 6, + 5, + 7, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 3, + "j": 5, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "1" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 88, + "a": [ + "0", + "1", + "0", + "1", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 6, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 88, + "a": [ + "0", + "1", + "0", + "1", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 0, + 6, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 0, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "-1", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 5, + 5, + 6, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 7, + 6, + 5, + 5, + 6, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 0, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "1", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 158, + "a": [ + "1", + "-1", + "0", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 0, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 158, + "a": [ + "1", + "-1", + "0", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 0, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 1, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "-1", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6032, + "distinct_nonzero_breakpoints": 2651, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 6, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 6, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "charged_histogram": { + "40": 3, + "41": 7, + "42": 13, + "43": 218, + "44": 5791 + }, + "active_total_histogram": { + "7": 6032 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 1, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5052, + "distinct_nonzero_breakpoints": 2161, + "minimum_raw": { + "charged": 37, + "raw": 37, + "direction_index": 165, + "a": [ + "1", + "-1", + "0", + "0", + "1", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 6, + 6, + 0, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 37, + "raw": 37, + "direction_index": 165, + "a": [ + "1", + "-1", + "0", + "0", + "1", + "1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 6, + 6, + 6, + 0, + 6, + 7 + ] + }, + "raw_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "charged_histogram": { + "37": 1, + "39": 2, + "40": 10, + "41": 10, + "42": 152, + "43": 4877 + }, + "active_total_histogram": { + "6": 1, + "7": 5051 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 2, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "-1", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 2, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 23, + "a": [ + "0", + "0", + "1", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 7, + 6, + 0, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 23, + "a": [ + "0", + "0", + "1", + "0", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 7, + 6, + 0, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 3, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "-1", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6084, + "distinct_nonzero_breakpoints": 2677, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 363, + "a": [ + "1", + "1", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 5, + 6, + 6, + 6, + 6, + 5, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "charged_histogram": { + "40": 1, + "41": 2, + "42": 10, + "43": 12, + "44": 216, + "45": 5843 + }, + "active_total_histogram": { + "7": 6084 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 3, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4964, + "distinct_nonzero_breakpoints": 2117, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 5, + "a": [ + "0", + "0", + "0", + "1", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 7, + 0, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 5, + "a": [ + "0", + "0", + "0", + "1", + "-1", + "0" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 7, + 0, + 6, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 4, + "42": 11, + "43": 10, + "44": 153, + "45": 4784 + }, + "active_total_histogram": { + "6": 1, + "7": 4963 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 5, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "-1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 6, + 7, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 116, + "a": [ + "0", + "1", + "1", + "1", + "0", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 6, + 7, + 6 + ] + }, + "raw_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "charged_histogram": { + "41": 4, + "42": 8, + "43": 14, + "44": 214, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 4, + "j": 5, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "1" + ], + [ + "0", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 82, + "a": [ + "0", + "1", + "0", + "0", + "1", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 0, + 6, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 82, + "a": [ + "0", + "1", + "0", + "0", + "1", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 0, + 6, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "charged_histogram": { + "38": 1, + "40": 3, + "41": 9, + "42": 15, + "43": 149, + "44": 4831 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 0, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "-1", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 6026, + "distinct_nonzero_breakpoints": 2648, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 7, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 1, + "41": 3, + "42": 7, + "43": 15, + "44": 215, + "45": 5785 + }, + "charged_histogram": { + "40": 1, + "41": 3, + "42": 7, + "43": 15, + "44": 215, + "45": 5785 + }, + "active_total_histogram": { + "7": 6026 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 0, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "1", + "0", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 4960, + "distinct_nonzero_breakpoints": 2115, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 241, + "a": [ + "1", + "0", + "0", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 7, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 241, + "a": [ + "1", + "0", + "0", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 7, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "raw_histogram": { + "39": 1, + "40": 1, + "41": 5, + "42": 8, + "43": 13, + "44": 152, + "45": 4780 + }, + "charged_histogram": { + "39": 1, + "40": 1, + "41": 5, + "42": 8, + "43": 13, + "44": 152, + "45": 4780 + }, + "active_total_histogram": { + "6": 1, + "7": 4959 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 1, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "-1", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5496, + "distinct_nonzero_breakpoints": 2383, + "minimum_raw": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 39, + "raw": 39, + "direction_index": 282, + "a": [ + "1", + "0", + "1", + "1", + "1", + "1" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 5, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "39": 1, + "40": 8, + "41": 14, + "42": 181, + "43": 5292 + }, + "charged_histogram": { + "39": 1, + "40": 8, + "41": 14, + "42": 181, + "43": 5292 + }, + "active_total_histogram": { + "7": 5496 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 1, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "1" + ] + ] + }, + "cells": 5440, + "distinct_nonzero_breakpoints": 2355, + "minimum_raw": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 40, + "raw": 40, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "40": 5, + "41": 5, + "42": 14, + "43": 180, + "44": 5236 + }, + "charged_histogram": { + "40": 5, + "41": 5, + "42": 14, + "43": 180, + "44": 5236 + }, + "active_total_histogram": { + "7": 5440 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 2, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "-1", + "0", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 7, + 5, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 7, + 5, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 2, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 106, + "a": [ + "0", + "1", + "1", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 106, + "a": [ + "0", + "1", + "1", + "0", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 3, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "-1", + "0", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 6, + 5, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 6, + 5, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 3, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 88, + "a": [ + "0", + "1", + "0", + "1", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 88, + "a": [ + "0", + "1", + "0", + "1", + "0", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 4, + "epsilon": -1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "-1", + "1" + ] + ] + }, + "cells": 6052, + "distinct_nonzero_breakpoints": 2661, + "minimum_raw": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 6, + 6, + 6 + ] + }, + "minimum_charged": { + "charged": 41, + "raw": 41, + "direction_index": 92, + "a": [ + "0", + "1", + "0", + "1", + "1", + "0" + ], + "lambda": "1", + "active_totals": 7, + "ranks": [ + 6, + 6, + 6, + 5, + 6, + 6, + 6 + ] + }, + "raw_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "charged_histogram": { + "41": 5, + "42": 7, + "43": 13, + "44": 215, + "45": 5812 + }, + "active_total_histogram": { + "7": 6052 + }, + "degenerate_cells": 0, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + }, + { + "transvection": { + "i": 5, + "j": 4, + "epsilon": 1, + "matrix": [ + [ + "1", + "0", + "0", + "0", + "0", + "0" + ], + [ + "0", + "1", + "0", + "0", + "0", + "0" + ], + [ + "0", + "0", + "1", + "0", + "0", + "0" + ], + [ + "0", + "0", + "0", + "1", + "0", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "0" + ], + [ + "0", + "0", + "0", + "0", + "1", + "1" + ] + ] + }, + "cells": 5008, + "distinct_nonzero_breakpoints": 2139, + "minimum_raw": { + "charged": 38, + "raw": 38, + "direction_index": 82, + "a": [ + "0", + "1", + "0", + "0", + "1", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "minimum_charged": { + "charged": 38, + "raw": 38, + "direction_index": 82, + "a": [ + "0", + "1", + "0", + "0", + "1", + "-1" + ], + "lambda": "1/2", + "active_totals": 6, + "ranks": [ + 6, + 7, + 6, + 6, + 6, + 0, + 7 + ] + }, + "raw_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "charged_histogram": { + "38": 1, + "40": 2, + "41": 12, + "42": 12, + "43": 149, + "44": 4832 + }, + "active_total_histogram": { + "6": 1, + "7": 5007 + }, + "degenerate_cells": 1, + "seven_total_cost_le_35_count": 0, + "target_witnesses_first20": [] + } + ], + "geometry": { + "root_lines": 36, + "canonical_root_sha256": "d2d26919a71a2f9a007d3c43f9806cb85a7142ebb45481ac4ad5fe6db8591263", + "basis_root_indices": [ + 0, + 1, + 2, + 4, + 6, + 20 + ], + "ambient_basis_columns": [ + 0, + 3, + 4, + 5, + 6, + 7 + ], + "basis_gram": [ + [ + "2", + "0", + "1", + "1", + "1", + "1" + ], + [ + "0", + "2", + "1", + "1", + "1", + "0" + ], + [ + "1", + "1", + "2", + "1", + "1", + "1" + ], + [ + "1", + "1", + "1", + "2", + "1", + "1" + ], + [ + "1", + "1", + "1", + "1", + "2", + "1" + ], + [ + "1", + "0", + "1", + "1", + "1", + "2" + ] + ], + "pairing_B0_rank_F2": 7, + "transvection_definition": "A=I+epsilon*E_ij; i!=j; epsilon in {-1,+1}" + }, + "controls": { + "identity_fixtures": 2, + "wrong_sign_rejections": 2, + "omitted_term_rejections": 2, + "inadmissible_edge_rejection": true + } +} diff --git a/research/e6-sheared-frame-seedb401/SOURCES.json b/research/e6-sheared-frame-seedb401/SOURCES.json new file mode 100644 index 0000000000..67a6d2b006 --- /dev/null +++ b/research/e6-sheared-frame-seedb401/SOURCES.json @@ -0,0 +1,36 @@ +{ + "schema_version": 1, + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "e8870e5917057d59b730eb14721a778639eca050", + "sha256": "d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7" + }, + { + "path": "research/root-unit-decoder-lemmas/README.md", + "usage": "input", + "git_blob": "de305484c78226a3f8da5f3277ced78974116fbb", + "sha256": "e3c856bc361a57cc2424c829001dba94e8f3a1bc8f6616f9c2f740e9665506a9" + }, + { + "path": "research/root-unit-decoder-lemmas/lib/ade.py", + "usage": "input", + "git_blob": "7e0063d97673b7d278ac9b5b4b511df8705d5f98", + "sha256": "8185afc77fd34a599094e9f93b293a5afac61f4184ec5c5a02b81ee3c0b0053c" + }, + { + "path": "research/root-unit-decoder-lemmas/lib/dyadic.py", + "usage": "input", + "git_blob": "1456ebb7927612918bfb1a27cf580a40fa63cf74", + "sha256": "5fabeeda7023c78b00c7796af6f4b92717652f6452bc76d442ed111d4be51e8d" + } + ] +} diff --git a/research/e6-sheared-frame-seedb401/TASK.json b/research/e6-sheared-frame-seedb401/TASK.json new file mode 100644 index 0000000000..9bbfb91962 --- /dev/null +++ b/research/e6-sheared-frame-seedb401/TASK.json @@ -0,0 +1,136 @@ +{ + "schema_version": 1, + "task_id": "complex-rank-shape-decoder", + "priority_revision": 4, + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "original_card": { + "id": "complex-rank-shape-decoder", + "question": "Can a decoder deliver the local paid mass in fewer, larger-rank children (block frame climbs instead of rank-1 to rank-3 steps)?", + "starting_points": [ + "research/complex-local-word-ceiling/README.md", + "research/complex-decoder-field-extension-seed44/README.md", + "research/complex-frame-pair-decoders/README.md", + "research/selected-k8-unrestricted-ends/README.md", + "research/eisenstein-reduction-copy-floor/README.md" + ], + "methods": [ + "Find one exact small decoding identity whose frame path climbs in blocks, and price its complete per-call profile.", + "Bound the best effective child rank achievable for one fixed support alphabet, including copies, frames and restoration." + ], + "acceptance_gate": "A per-call local profile, with all copied information, frames and restoration counted, whose ceiling exceeds the selected word's by at least 5%; masked or overcomplete supports must change an assumption of the eight-term all-pairs bound.", + "first_step": { + "command": [ + "python3", + "-B", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Before any synthesis, write the candidate per-call local profile (and centre charge / unpaid coordinates if changed) and screen it with ceiling.ceiling(); reject it if even the ideal ceiling does not beat the selected word's by your stated margin. Ideal budget: rank-16 delivery is 2.31x (levers.py).", + "bottleneck_link": "Rank-1 children are about half of recursive cost; the selected word's effective child rank is about 3.9. Larger-rank delivery lowers recursive cost per unit of paid mass.", + "allowed_variations": [ + "One masked, overcomplete or block decoder family with exact labels and supports.", + "A scoped lower bound on effective rank for one alphabet.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Repacking idle remainders of an unchanged word (covered by the packing ceiling).", + "Repeating the eight-term all-pairs search inside its proved scope.", + "Only changing helper terminal subspaces and monotone frames within the fixed scalar word, entrances and cleanup contract already covered by #1995/#2013.", + "Searching below C=40 in the #2017 Eisenstein binary scalar-rectangle or fixed-support block-linear additive pairing model; specify a changed premise instead. This bound does not cover every complex decoder." + ], + "overlap_terms": [ + "rank shape", + "block climb", + "masked decoder", + "overcomplete", + "effective rank" + ] + }, + "scope_status": "changed", + "actual_scope": "Exact census of the one-extra rank-one E6 Gram decoder after each of the 60 signed elementary basis transvections A=I+epsilon E_ij; all 365 root/ternary projective directions and every nonzero rational lambda support cell are covered under fixed dense pairing B0.", + "scope_change_reason": "The selected rank-shape card led to the open E6 m=7 question from Discussion #1166. The prior Cycle30 PR #2240 fixes A=I; this cycle changes the six-term base factorization by an elementary GL6 transvection before the same rank-one correction. The work is an upstream root-unit mechanism result, not a selected-supplier profile.", + "bottleneck_link": "A seven-active E6 decoder of fully charged cost 35 could beat the stated square-decoder floor 36 by one unit in this local root-unit model. No such witness appears in the tested transvection family. No source/copy/frame realization or supplier mapping is established, so this does not change the selected paid recursive moment or kappa.", + "budget_minutes": 60, + "stop_rule": "Exhaust exactly the 60 signed elementary transvections, the 365 declared projective directions, and every exact nonzero lambda breakpoint and open interval. Do not extend to arbitrary GL6(Q) maps after this census. Reserve the final quarter of the cycle for verification, package checks, live overlap refresh and handoff.", + "outcome": "negative-result", + "evidence": "The exact two-shard verifier covers 330,486 support cells. Minimum raw and fully charged costs are 37; 26 cells have six active terms, 330,460 have seven, and no seven-active cell costs <=35. The least cell is A=I+E_23, a=(1,-1,1,0,0,1), lambda=1/2, ranks (6,0,6,6,6,6,7). Positive identity controls and wrong-sign, omitted-term and inadmissible-pairing controls pass.", + "author": "OpenAI Codex", + "ai_assistance": "Substantial OpenAI Codex GPT-6 assistance in scope selection, exact derivation, implementation, verification and writing; no independent human review.", + "open_questions": [ + { + "question": "Can another six-term E6 factorization or an arbitrary rational GL6 basis change attain a seven-active cost of 35 with B0?", + "why_it_matters": "A one-unit local improvement would meet the open E6 overcomplete target, although it still needs a physical supplier mapping.", + "first_step": "Select one structurally distinct finite basis family, derive its exact factorization, and screen the fully charged floor before any large search.", + "blocked_by": "This package only covers the 60 signed elementary transvections of one pinned basis and a finite correction-direction set." + } + ], + "assignment_seed": "b401f2874293cab50e88e4bd7068a949", + "assignment_track": "complex-mechanisms", + "scope_key": "02b31ebd160542c86299", + "catalogue_sha256": "d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7", + "selected_record_sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32", + "excluded_selector_draws": [ + { + "seed": "ff1355316fdbea3b88881994a210c24c", + "track": "verifier-engineering", + "reason": "excluded by the construction-only session rule" + } + ], + "claim_url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-18938219", + "candidates_considered": [ + { + "scope": "P104 I-G/2 side correction", + "decision": "not selected", + "reason": "Fresh overlap found active P104 correction claim #2131 and several related open PRs including #2083/#2089." + }, + { + "scope": "new complex helper inventory", + "decision": "not selected", + "reason": "Recent helper/common-sum anchor work culminated in Cycle42 PR #2241; changing only the anchor label would repeat it." + }, + { + "scope": "S3 nonabelian rank-nine block", + "decision": "not selected", + "reason": "A live claim appears in Discussion #1167 comment #18936773." + }, + { + "scope": "E6 seven-term decoder with basis shear", + "decision": "selected", + "reason": "The current open question remains; the prior A=I rank-one screen in PR #2240 does not cover the changed six-term GL6 factorization." + } + ], + "predecessors": [ + { + "reference": "PR #1590", + "head": "08e134b4a0c7f04869dae703f2a2e688e53c44f0", + "status": "merged; root-unit model and Theorem C context" + }, + { + "reference": "PR #2228", + "head": "ad1757e319225f3a5b86e3d3fa72897bd9f6db40", + "status": "open; dense-pairing root-code floor work, E6 m=7 remains open" + }, + { + "reference": "PR #2137", + "head": "6a022d50e21bdcf2014a26937a34d44eed3473f0", + "status": "open; rank-four E6 B0 coordinate-form family" + }, + { + "reference": "PR #2232", + "head": "3391f27dd0f226f0e1ead8b2b829eb6d3ec567d3", + "status": "open; rank-four projected-Gram family with adapted pairing" + }, + { + "reference": "PR #2240", + "head": "c8a2b37056e766715c457f56e2dd8172f5bdbccd", + "status": "open; Cycle30 A=I one-extra rank-one family" + }, + { + "reference": "Discussion #1166 comment #18936173", + "status": "open E6 m=7 and D5 m=6 request" + } + ] +} diff --git a/research/e6-sheared-frame-seedb401/VERIFY.json b/research/e6-sheared-frame-seedb401/VERIFY.json new file mode 100644 index 0000000000..85e15a431b --- /dev/null +++ b/research/e6-sheared-frame-seedb401/VERIFY.json @@ -0,0 +1,35 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/root-unit-decoder-lemmas/README.md", + "research/root-unit-decoder-lemmas/lib/ade.py", + "research/root-unit-decoder-lemmas/lib/dyadic.py" + ], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--shard", + "0" + ], + "timeout_seconds": 600, + "checks": "Reconstruct exact E6 geometry; positive and negative controls; exhaust the first 30 signed transvections and all lambda support cells; compare SHARD-0.json and combined certificate." + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--shard", + "1" + ], + "timeout_seconds": 600, + "checks": "Reconstruct exact E6 geometry; positive and negative controls; exhaust the remaining 30 signed transvections and all lambda support cells; compare SHARD-1.json and combined certificate." + } + ] +} diff --git a/research/e6-sheared-frame-seedb401/verify.py b/research/e6-sheared-frame-seedb401/verify.py new file mode 100644 index 0000000000..3dfcc84bd6 --- /dev/null +++ b/research/e6-sheared-frame-seedb401/verify.py @@ -0,0 +1,484 @@ +#!/usr/bin/env python3 +"""Exact bounded census of E6 Gram decoders under elementary basis shears.""" +from fractions import Fraction as F +from functools import lru_cache +from itertools import combinations, product +import hashlib +import json +from pathlib import Path +import sys + +HERE = Path(__file__).resolve().parent +TARGET = 35 + + +def require(ok, message): + if not ok: + raise SystemExit("FAIL_E6_SHEARED_FRAME: " + message) + + +def dot(x, y): + return sum((u * v for u, v in zip(x, y)), F(0)) + + +def transpose(a): + return [list(row) for row in zip(*a)] + + +def mul(a, b): + return [[sum((a[i][k] * b[k][j] for k in range(len(b))), F(0)) + for j in range(len(b[0]))] for i in range(len(a))] + + +def identity(n): + return [[F(int(i == j)) for j in range(n)] for i in range(n)] + + +def orient(v): + v = tuple(v) + return tuple(-z for z in v) if next(z for z in v if z) < 0 else v + + +def roots_e8(): + """Exact canonical E8 line list, matching the pinned ADE source ordering.""" + rows = [] + for i in range(8): + for j in range(i + 1, 8): + for s in (1, -1): + v = [F(0)] * 8 + v[i], v[j] = F(1), F(s) + rows.append(orient(v)) + for signs in product((1, -1), repeat=8): + if signs.count(-1) % 2 == 0: + rows.append(orient(F(s, 2) for s in signs)) + seen, out = set(), [] + for row in rows: + if row not in seen: + seen.add(row) + out.append(row) + return out + + +def rank_q(a): + a = [list(map(F, row)) for row in a] + nr, nc, r = len(a), (len(a[0]) if a else 0), 0 + for c in range(nc): + pivot = next((i for i in range(r, nr) if a[i][c]), None) + if pivot is None: + continue + a[r], a[pivot] = a[pivot], a[r] + d = a[r][c] + a[r] = [x / d for x in a[r]] + for i in range(nr): + if i != r and a[i][c]: + d = a[i][c] + a[i] = [x - d * y for x, y in zip(a[i], a[r])] + r += 1 + return r + + +def solve(a, b): + n = len(b) + z = [list(map(F, row)) + [F(rhs)] for row, rhs in zip(a, b)] + for c in range(n): + pivot = next((i for i in range(c, n) if z[i][c]), None) + if pivot is None: + raise ValueError("singular minor") + z[c], z[pivot] = z[pivot], z[c] + d = z[c][c] + z[c] = [x / d for x in z[c]] + for i in range(n): + if i != c and z[i][c]: + d = z[i][c] + z[i] = [x - d * y for x, y in zip(z[i], z[c])] + return [z[i][-1] for i in range(n)] + + +def inverse(a): + n = len(a) + z = [list(map(F, row)) + [F(int(i == j)) for j in range(n)] + for i, row in enumerate(a)] + for c in range(n): + pivot = next((i for i in range(c, n) if z[i][c]), None) + if pivot is None: + raise ValueError("singular frame map") + z[c], z[pivot] = z[pivot], z[c] + d = z[c][c] + z[c] = [x / d for x in z[c]] + for i in range(n): + if i != c and z[i][c]: + d = z[i][c] + z[i] = [x - d * y for x, y in zip(z[i], z[c])] + return [row[n:] for row in z] + + +def projective(v): + v = tuple(map(F, v)) + first = next(x for x in v if x) + return tuple(x / first for x in v) + + +def qstr(x): + return str(x.numerator) if x.denominator == 1 else f"{x.numerator}/{x.denominator}" + + +def e6_data(): + e8 = roots_e8() + require(len(e8) == 120, "canonical E8 roots") + alpha = e8[0] + beta = next(r for r in e8 if dot(r, alpha) in (F(1), F(-1))) + roots = [r for r in e8 if dot(r, alpha) == 0 and dot(r, beta) == 0] + require(len(roots) == 36, "E6 root lines") + + basis, basis_ids = [], [] + for i, r in enumerate(roots): + if rank_q(basis + [r]) > len(basis): + basis.append(r) + basis_ids.append(i) + if len(basis) == 6: + break + require(len(basis) == 6, "E6 rank six") + cols = next(c for c in combinations(range(8), 6) + if rank_q([[r[j] for j in c] for r in basis]) == 6) + minor = [[basis[i][j] for j in cols] for i in range(6)] + x = [solve(transpose(minor), [r[j] for j in cols]) for r in roots] + require(all(tuple(sum((x[t][i] * basis[i][j] for i in range(6)), F(0)) + for j in range(8)) == roots[t] for t in range(36)), + "exact root coordinates") + h = [[dot(basis[i], basis[j]) for j in range(6)] for i in range(6)] + g = mul(mul(x, h), transpose(x)) + require(g == [[dot(u, v) for v in roots] for u in roots], "Gram reconstruction") + require(all(g[i][i] == 2 for i in range(36)), "root norms") + b0 = [[int((1 + g[i][j]) % 2) for j in range(36)] for i in range(36)] + require(all(b0[i][j] == int(i == j or g[i][j] == 0) + for i in range(36) for j in range(36)), "B0 definition") + root_payload = [[qstr(z) for z in row] for row in roots] + digest = hashlib.sha256(json.dumps(root_payload, separators=(",", ":")).encode()).hexdigest() + return roots, x, h, g, b0, basis_ids, list(cols), digest + + +def directions(x): + root = {projective(row) for row in x} + ternary = {projective(v) for v in product((F(-1), F(0), F(1)), repeat=6) if any(v)} + union = sorted(root | ternary) + require(len(root) == 36 and len(ternary) == 364 and len(union) == 365, + "root/ternary direction domains") + return sorted(root), sorted(ternary), union + + +def shears(): + out = [] + for i in range(6): + for j in range(6): + if i == j: + continue + for eps in (-1, 1): + a = identity(6) + a[i][j] = F(eps) + out.append({"i": i, "j": j, "epsilon": eps, "A": a}) + require(len(out) == 60, "signed elementary transvection count") + return out + + +def mask(v): + return sum((1 << i) for i, z in enumerate(v) if z) + + +def masks_to_ids(value): + return [i for i in range(36) if (value >> i) & 1] + + +def rank_masks(b0): + @lru_cache(maxsize=100000) + def get(row_mask, col_mask): + cols = masks_to_ids(col_mask) + pivots = {} + for t in masks_to_ids(row_mask): + bits = 0 + for j, s in enumerate(cols): + if b0[t][s]: + bits |= 1 << j + while bits: + p = bits.bit_length() - 1 + if p in pivots: + bits ^= pivots[p] + else: + pivots[p] = bits + break + return len(pivots) + return get + + +def factors(x, h, a, lam, amap, inva, bad=None): + """Return the seven factor vectors for an arbitrary invertible 6x6 A.""" + c = [sum((inva[i][k] * a[k] for k in range(6)), F(0)) for i in range(6)] + ka = mul(h, transpose(inva)) + pcols = mul(x, amap) + qcols = mul(x, ka) + xa = [sum((x[t][k] * a[k] for k in range(6)), F(0)) for t in range(36)] + ps = [[pcols[t][j] for t in range(36)] for j in range(6)] + [xa] + qs = [[qcols[t][j] - lam * c[j] * xa[t] for t in range(36)] for j in range(6)] + [[lam * z for z in xa]] + if bad == "wrong-sign": + qs[6] = [-z for z in qs[6]] + elif bad == "omit-seventh": + qs[6] = [F(0)] * 36 + return ps, qs + + +def identity_holds(ps, qs, g, terms=7): + return all(sum((ps[j][t] * qs[j][s] for j in range(terms)), F(0)) == g[t][s] + for t in range(36) for s in range(36)) + + +def support_cells(x, h, a, amap, inva): + c = [sum((inva[i][k] * a[k] for k in range(6)), F(0)) for i in range(6)] + k = mul(h, transpose(inva)) + xa = [sum((x[t][z] * a[z] for z in range(6)), F(0)) for t in range(36)] + intercepts = [[sum((x[t][z] * k[z][j] for z in range(6)), F(0)) + for t in range(36)] for j in range(6)] + cuts = {F(0)} + for j in range(6): + for t in range(36): + slope = c[j] * xa[t] + if slope: + point = intercepts[j][t] / slope + if point: + cuts.add(point) + ordered = sorted(cuts) + samples = {z for z in ordered if z} + samples.update((u + v) / 2 for u, v in zip(ordered, ordered[1:])) + samples.add(ordered[0] - 1) + samples.add(ordered[-1] + 1) + require(F(0) not in samples and len(samples) == 2 * len(ordered), "exact lambda cell representatives") + return sorted(samples), len(ordered) - 1, intercepts, c, xa + + +def admissible(pairing, gram): + return (all(pairing[i][i] == 1 for i in range(36)) + and all(pairing[i][j] == pairing[j][i] for i in range(36) for j in range(36)) + and all(not pairing[i][j] or i == j or gram[i][j] == 0 + for i in range(36) for j in range(36))) + + +def search_matrix(x, h, g, b0, rank, directions_all, frame): + a_map = frame["A"] + inva = inverse(a_map) + pcols = mul(x, a_map) + p_masks_by_dir = [] + for a in directions_all: + xa = [sum((x[t][k] * a[k] for k in range(6)), F(0)) for t in range(36)] + p_masks_by_dir.append([mask([pcols[t][j] for t in range(36)]) for j in range(6)] + [mask(xa)]) + hist_raw, hist_charged, term_counts = {}, {}, {} + cells_total = breakpoints_total = 0 + min_row = None + min_raw = None + target_witnesses = [] + target_count = 0 + degenerate = 0 + for ai, a in enumerate(directions_all): + samples, nbreak, intercepts, c, xa = support_cells(x, h, a, a_map, inva) + cells_total += len(samples) + breakpoints_total += nbreak + p_masks = p_masks_by_dir[ai] + for lam in samples: + col_masks = [mask([intercepts[j][t] - lam * c[j] * xa[t] for t in range(36)]) + for j in range(6)] + [mask([lam * z for z in xa])] + ranks = [rank(p_masks[j], col_masks[j]) for j in range(7)] + active = sum(bool(p_masks[j]) and bool(col_masks[j]) for j in range(7)) + raw = sum(ranks) + charged = sum(max(5, ranks[j]) for j in range(7) + if p_masks[j] and col_masks[j]) + hist_raw[raw] = hist_raw.get(raw, 0) + 1 + hist_charged[charged] = hist_charged.get(charged, 0) + 1 + term_counts[active] = term_counts.get(active, 0) + 1 + degenerate += (active < 7) + row = {"charged": charged, "raw": raw, "direction_index": ai, + "a": [qstr(z) for z in a], "lambda": qstr(lam), + "active_totals": active, "ranks": ranks} + if min_row is None or (charged, raw, ai, lam) < (min_row["charged"], min_row["raw"], min_row["direction_index"], F(min_row["lambda"])): + min_row = row + if min_raw is None or raw < min_raw["raw"]: + min_raw = row + if charged <= TARGET and active == 7 and len(target_witnesses) < 20: + target_witnesses.append(row) + if charged <= TARGET and active == 7: + target_count += 1 + return { + "transvection": {**{k: frame[k] for k in ("i", "j", "epsilon")}, + "matrix": [[qstr(z) for z in row] for row in frame["A"]]}, + "cells": cells_total, + "distinct_nonzero_breakpoints": breakpoints_total, + "minimum_raw": min_raw, + "minimum_charged": min_row, + "raw_histogram": {str(k): hist_raw[k] for k in sorted(hist_raw)}, + "charged_histogram": {str(k): hist_charged[k] for k in sorted(hist_charged)}, + "active_total_histogram": {str(k): term_counts[k] for k in sorted(term_counts)}, + "degenerate_cells": degenerate, + "seven_total_cost_le_35_count": target_count, + "target_witnesses_first20": target_witnesses, + } + + +def check_controls(roots, x, h, g, b0, directions_all): + # Exact decoder identities at A=I and a nontrivial elementary transvection. + frames = [identity(6), identity(6)] + frames[1][0][1] = F(1) + a = directions_all[0] + for amap in frames: + inva = inverse(amap) + ps, qs = factors(x, h, a, F(1), amap, inva) + require(identity_holds(ps, qs, g), "positive exact decoder identity") + badp, badq = factors(x, h, a, F(1), amap, inva, "wrong-sign") + require(not identity_holds(badp, badq, g), "wrong-sign negative control") + badp, badq = factors(x, h, a, F(1), amap, inva, "omit-seventh") + require(not identity_holds(badp, badq, g), "omitted seventh-term negative control") + require(admissible(b0, g), "B0 positive admissibility control") + bad = [row[:] for row in b0] + edge = next((i, j) for i in range(36) for j in range(i + 1, 36) if g[i][j]) + i, j = edge + bad[i][j] = bad[j][i] = 1 + require(not admissible(bad, g), "inadmissible-pairing negative control") + return {"identity_fixtures": 2, "wrong_sign_rejections": 2, + "omitted_term_rejections": 2, "inadmissible_edge_rejection": True} + + +def json_cost_hist(items, field): + out = {} + for item in items: + for k, v in item[field].items(): + out[int(k)] = out.get(int(k), 0) + v + return {str(k): out[k] for k in sorted(out)} + + +def aggregate(shard_results, meta, controls): + all_results = [r for part in shard_results for r in part["transvections"]] + raw_hist = json_cost_hist(all_results, "raw_histogram") + charged_hist = json_cost_hist(all_results, "charged_histogram") + active_hist = json_cost_hist(all_results, "active_total_histogram") + best_charged = min(all_results, key=lambda r: (r["minimum_charged"]["charged"], r["minimum_charged"]["raw"])) + best_raw = min(all_results, key=lambda r: (r["minimum_raw"]["raw"], r["minimum_raw"]["charged"])) + witnesses = [w for r in all_results for w in r["target_witnesses_first20"]] + target_count = sum(r["seven_total_cost_le_35_count"] for r in all_results) + return { + "schema_version": 1, + "status": "completed" if target_count else "scoped-negative-result", + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "assignment_seed": "b401f2874293cab50e88e4bd7068a949", + "task_id": "complex-rank-shape-decoder", + "priority_revision": 4, + "selected_record_sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32", + "geometry": meta, + "controls": controls, + "domain": { + "signed_transvections": len(all_results), + "direction_count": 365, + "root_directions": 36, + "projective_ternary_directions": 364, + "direction_union_count": 365, + "lambda_domain": "all nonzero rational lambda, split at all exact support breakpoints", + "support_cells": sum(r["cells"] for r in all_results), + "distinct_nonzero_breakpoints": sum(r["distinct_nonzero_breakpoints"] for r in all_results), + "degenerate_cells_with_fewer_than_7_active_totals": sum(r["degenerate_cells"] for r in all_results), + }, + "result": { + "minimum_raw_cost": best_raw["minimum_raw"]["raw"], + "minimum_raw_witness": best_raw["minimum_raw"], + "minimum_fully_charged_cost": best_charged["minimum_charged"]["charged"], + "minimum_fully_charged_witness": best_charged["minimum_charged"], + "raw_cost_histogram": raw_hist, + "charged_cost_histogram": charged_hist, + "active_total_count_histogram": active_hist, + "seven_active_cost_le_35_witnesses_first20_per_matrix": witnesses, + "positive_target_witness_count": target_count, + "no_seven_active_cost_le_35": target_count == 0, + }, + "per_transvection": all_results, + "limits": [ + "Only the 60 signed elementary transvections A=I+epsilon E_ij are searched.", + "Only the union of the 36 root directions and projective {-1,0,1}^6 directions in the pinned basis is searched.", + "No arbitrary GL6(Q) basis change, arbitrary rational correction direction, different base decoder, or sparse pairing is covered.", + "No physical source/copy/frame/hosting/restoration/precision mapping or selected-supplier profile is established.", + ], + } + + +def run_shard(shard_id): + roots, x, h, g, b0, basis_ids, cols, digest = e6_data() + root_dirs, ternary_dirs, all_dirs = directions(x) + controls = check_controls(roots, x, h, g, b0, all_dirs) + frames = shears() + require(shard_id in (0, 1), "shard id must be 0 or 1") + chunk = frames[shard_id * 30:(shard_id + 1) * 30] + rank = rank_masks(b0) + results = [search_matrix(x, h, g, b0, rank, all_dirs, frame) for frame in chunk] + meta = { + "root_lines": 36, + "canonical_root_sha256": digest, + "basis_root_indices": basis_ids, + "ambient_basis_columns": cols, + "basis_gram": [[qstr(z) for z in row] for row in h], + "pairing_B0_rank_F2": rank((1 << 36) - 1, (1 << 36) - 1), + "transvection_definition": "A=I+epsilon*E_ij; i!=j; epsilon in {-1,+1}", + } + return {"schema_version": 1, "shard": shard_id, "transvections": results, + "geometry": meta, "controls": controls} + + +def run_pilot(): + roots, x, h, g, b0, *_ = e6_data() + _, _, all_dirs = directions(x) + rank = rank_masks(b0) + frame = shears()[0] + result = search_matrix(x, h, g, b0, rank, all_dirs, frame) + print("PILOT", json.dumps({"transvection": result["transvection"], + "cells": result["cells"], + "min_raw": result["minimum_raw"], + "min_charged": result["minimum_charged"], + "target_count": result["seven_total_cost_le_35_count"]}, sort_keys=True)) + + +def main(): + args = sys.argv[1:] + if args == ["--smoke"]: + roots, x, h, g, b0, *_ = e6_data() + _, _, all_dirs = directions(x) + controls = check_controls(roots, x, h, g, b0, all_dirs) + print("PASS_E6_SHEARED_FRAME_SMOKE", controls) + return + if args == ["--pilot"]: + run_pilot() + return + if args == ["--aggregate"]: + s0 = json.loads((HERE / "SHARD-0.json").read_text()) + s1 = json.loads((HERE / "SHARD-1.json").read_text()) + certificate = aggregate([s0, s1], s0["geometry"], s0["controls"]) + (HERE / "CERTIFICATE.json").write_text(json.dumps(certificate, indent=2) + "\n") + print("WROTE_CERTIFICATE", certificate["domain"]["support_cells"], + "minimum_charged", certificate["result"]["minimum_fully_charged_cost"], + "targets", certificate["result"]["positive_target_witness_count"]) + return + if len(args) != 2 or args[0] not in ("--emit-shard", "--shard") or args[1] not in ("0", "1"): + raise SystemExit("usage: verify.py --smoke | --pilot | --emit-shard {0,1} | --aggregate | --shard {0,1}") + shard_id = int(args[1]) + computed = run_shard(shard_id) + shard_path = HERE / f"SHARD-{shard_id}.json" + if args[0] == "--emit-shard": + shard_path.write_text(json.dumps(computed, indent=2) + "\n") + print("WROTE", shard_path, "cells", sum(x["cells"] for x in computed["transvections"])) + return + require(shard_path.exists(), f"SHARD-{shard_id}.json missing") + expected = json.loads(shard_path.read_text()) + require(computed == expected, f"shard {shard_id} differs from its certificate") + cert_path = HERE / "CERTIFICATE.json" + require(cert_path.exists(), "CERTIFICATE.json missing") + s0 = json.loads((HERE / "SHARD-0.json").read_text()) + s1 = json.loads((HERE / "SHARD-1.json").read_text()) + combined = aggregate([s0, s1], computed["geometry"], computed["controls"]) + require(combined == json.loads(cert_path.read_text()), "aggregate certificate mismatch") + print("PASS_E6_SHEARED_FRAME_SHARD", shard_id, + "transvections", len(computed["transvections"]), + "cells", sum(x["cells"] for x in computed["transvections"])) + + +if __name__ == "__main__": + main()