calculations.json

{
  "status": "PASS",
  "raw_reverse_forms": {
    "raw_weights": [
      100,
      10,
      1
    ],
    "reverse_weights": [
      1,
      10,
      100
    ],
    "outside_scale": 10,
    "data": {
      "regular": {
        "aggregate": [
          2,
          6,
          10
        ],
        "raw": 2700,
        "reversed": 10620
      },
      "cumulative": {
        "aggregate": [
          12,
          5,
          10
        ],
        "raw": 12600,
        "reversed": 10620
      }
    },
    "combined_rank": 2,
    "integer_kernel_generator": [
      10,
      -101,
      10
    ],
    "bounded_integer_injectivity": "Any two feasible aggregate vectors differ by at most18 in the middle column, so no nonzero integer multiple of(10,-101,10) connects them."
  },
  "reverse_equality_kernel": {
    "regular_minus_cumulative": [
      -10,
      1,
      0
    ],
    "reverse_dot": 0,
    "raw_dot": -990,
    "raw_difference": -9900,
    "full_integer_basis": [
      [
        -10,
        1,
        0
      ],
      [
        -100,
        0,
        1
      ]
    ],
    "parameterization": "delta=(-10u-100v,u,v); raw change=\u22129900u\u221299990v"
  },
  "fixed_total_possible_aggregates": {
    "regular2700": [
      {
        "aggregate": [
          2,
          6,
          10
        ],
        "reversed_total": 10620
      }
    ],
    "cumulative12600": [
      {
        "aggregate": [
          11,
          15,
          10
        ],
        "reversed_total": 11610
      },
      {
        "aggregate": [
          12,
          5,
          10
        ],
        "reversed_total": 10620
      }
    ]
  },
  "free_aggregate_constraints": {
    "variable_order": [
      "AR",
      "BR",
      "CR",
      "AC",
      "BC",
      "CC"
    ],
    "convergence_form": [
      1,
      10,
      100,
      -1,
      -10,
      -100
    ],
    "regular_weighted_form": [
      -95,
      40,
      499,
      -400,
      -40,
      -4
    ],
    "rank": 2,
    "caution": "Algebraic independence in the free aggregate register does not imply two new independent empirical witnesses when source totals and integral bounds are already fixed."
  },
  "diagnostic_controls_not_chronologies": {
    "preserve_convergence_break_weighted": {
      "regular_parts": [
        2650,
        1050
      ],
      "cumulative_parts": [
        9170,
        4430
      ],
      "regular_aggregate": [
        3,
        6,
        10
      ],
      "cumulative_aggregate": [
        13,
        5,
        10
      ],
      "regular_reversed_sum": 10630,
      "cumulative_reversed_sum": 10630,
      "regular_head": 5106,
      "cumulative_head": 15006,
      "regular_inverse_endpoint": 12036,
      "cumulative_inverse_endpoint": 12036,
      "weighted_point": "13026",
      "convergence": true,
      "regular_weighted_equality": false
    },
    "preserve_source_heads_and_weighted_break_convergence": {
      "regular_parts": [
        1650,
        1050
      ],
      "cumulative_parts": [
        9970,
        2630
      ],
      "regular_aggregate": [
        2,
        6,
        10
      ],
      "cumulative_aggregate": [
        11,
        15,
        10
      ],
      "regular_reversed_sum": 10620,
      "cumulative_reversed_sum": 11610,
      "regular_head": 4106,
      "cumulative_head": 14006,
      "regular_inverse_endpoint": 12026,
      "cumulative_inverse_endpoint": 13016,
      "weighted_point": "12026",
      "convergence": false,
      "regular_weighted_equality": true
    },
    "same_aggregate_different_ordered_regular_components": {
      "regular_parts": [
        1550,
        1150
      ],
      "cumulative_parts": [
        9170,
        3430
      ],
      "regular_aggregate": [
        2,
        6,
        10
      ],
      "cumulative_aggregate": [
        12,
        5,
        10
      ],
      "regular_reversed_sum": 10620,
      "cumulative_reversed_sum": 10620,
      "regular_head": 4106,
      "cumulative_head": 14006,
      "regular_inverse_endpoint": 12026,
      "cumulative_inverse_endpoint": 12026,
      "weighted_point": "12026",
      "convergence": true,
      "regular_weighted_equality": true
    },
    "same_aggregate_different_ordered_cumulative_components": {
      "regular_parts": [
        1650,
        1050
      ],
      "cumulative_parts": [
        9270,
        3330
      ],
      "regular_aggregate": [
        2,
        6,
        10
      ],
      "cumulative_aggregate": [
        12,
        5,
        10
      ],
      "regular_reversed_sum": 10620,
      "cumulative_reversed_sum": 10620,
      "regular_head": 4106,
      "cumulative_head": 14006,
      "regular_inverse_endpoint": 12026,
      "cumulative_inverse_endpoint": 12026,
      "weighted_point": "12026",
      "convergence": true,
      "regular_weighted_equality": true
    }
  },
  "source_hundred_place_refinements": [
    {
      "whole": 1650,
      "remaining_original_piece": 1050,
      "tail": 600,
      "hundred_digit": 6,
      "peeled_digit": 6,
      "borrow": false,
      "refinement_defect": 0
    },
    {
      "whole": 9170,
      "remaining_original_piece": 8570,
      "tail": 600,
      "hundred_digit": 1,
      "peeled_digit": 6,
      "borrow": true,
      "refinement_defect": 990
    }
  ],
  "continuation": {
    "primary": [
      12026,
      12026
    ],
    "completed": [
      14726,
      14726
    ],
    "shared_output_shift": 2700,
    "equality_at_completed_stage": "same prior equality after common addition; no extra rank"
  },
  "modular_compatibility": {
    "regular_evaluated_sum_mod23": 17,
    "tail_evaluated_mod23": 6,
    "combined_mod23": 0,
    "meaning": "17+6=23 is source-derived compatibility; equal path sums alone do not force it"
  },
  "529_dependency": {
    "primitive_dates": [
      1406,
      6,
      1446
    ],
    "computed_K": 12026,
    "computed_B": 14726,
    "measured_D": 10580,
    "derived_k": "20",
    "derived_ladder": [
      "10580",
      "11500",
      "12500"
    ],
    "reflected_coordinates": [
      "1445",
      "525",
      "-475"
    ],
    "T_inverse": 696,
    "M_inverse": 1616,
    "first_junction_form": "46+2B+2K\u221225(T+X)=0",
    "second_gap_form": "2(K\u2212X)\u221223(M\u2212T)=0",
    "two_junction_constraint_rank": 2,
    "first_junction_value": 0,
    "gap_value": 0,
    "derived_expansion_gains": [
      "920",
      "1000"
    ]
  },
  "actual_rounded_weighted_kernel": {
    "delta_C": -2,
    "delta_R": 8,
    "weighted_numerator_change": 0,
    "status": "inherited C494/C902, dependency linkage only"
  },
  "tests": {
    "fixed_total_aggregate_options": true,
    "free_constraint_rank2": true,
    "both_diagnostic_directions": true,
    "local_refinement_carry_rule": true,
    "same_tail_adds_no_equality_constraint": true,
    "all_inverse_inputs_original": true,
    "no_target_tally": true
  }
}