{
  "proof_locators": [
    "MFA.1\u2013MFA.4",
    "MFB.6\u2013MFB.11",
    "MF.6\u2013MF.11"
  ],
  "axes": {
    "horizontal": "K=Q+L",
    "vertical": "n (negative output -n)",
    "display_window": [
      0,
      10,
      0,
      10
    ],
    "negative_output_condition": "n>=1",
    "exact_boundary": "K=n",
    "negative_input": "m=K-n<0",
    "positive_input": "m=K-n>=0"
  },
  "negative_input_bound": "M*n!*C1^K*D^(n-K)",
  "positive_input_bound": "M_epsilon*n!*(3*C1)^n*(9*C1*epsilon)^(K-n)",
  "positive_output_bound": "M_epsilon*epsilon^j/j!*sum_K(4*C1*epsilon)^K",
  "constants": "C1 is the proved finite-data/common-margin constant; convergence chooses epsilon with 9*C1*epsilon<1/2; no numerical value is asserted.",
  "calibration": {
    "base": [
      "x",
      "y"
    ],
    "covariables": [
      "tau",
      "xi"
    ],
    "C_positive_j": "1/(j!)^2",
    "C_negative_minus_n": "n!",
    "R": [
      "-y",
      "x"
    ],
    "D_column": [
      "x",
      "y"
    ],
    "b": [
      "-y*C",
      "x*C+partial_tau(C)"
    ],
    "b1_times_x": "-x*y*C-y*partial_tau(C)",
    "b2_times_y": "x*y*C+y*partial_tau(C)"
  },
  "schematic_panel": "Operator splitting and exact finite matrix identities; no topology or scale represented."
}