{
  "kind": "exact maps and proved bounds; no numerical samples",
  "hypotheses": [
    "T(h) converges at h=0",
    "N=T(0) nilpotent",
    "tangential relations D_x u=0"
  ],
  "normal_equation": "Y'=T(1/zeta)Y",
  "monodromy": "Y(w+2 pi i)=Y(w)M; exp(2 pi i H)=M",
  "gauge": {
    "V": "Y exp(-wH)",
    "W": "exp(wH) Y^-1",
    "products": "VW=WV=I",
    "Euler_matrix": "(H-I)^transpose",
    "proof": "CN.7–CN.20"
  },
  "growth": {
    "alpha": "1-1/max(2,largest nilpotent block length)",
    "bound": "K |zeta|^b exp(L |zeta|^alpha)",
    "proof": "CN.9–CN.16"
  },
  "comparison": {
    "top": "B tensor_E N_A -> B tensor_E M_T",
    "bottom": "C tensor_E N_A -> C tensor_E M_T",
    "horizontal_maps": "actual inverse gauge isomorphisms",
    "left_vertical": "AM.29 injective",
    "right_vertical": "CN.21 injective",
    "flatness_of_C_over_B_assumed": false
  },
  "example": {
    "P": "t^2 D_t+1",
    "N": [
      [
        0,
        0
      ],
      [
        1,
        0
      ]
    ],
    "T": [
      [
        "0",
        "-h"
      ],
      [
        "1",
        "2h"
      ]
    ],
    "alpha": "1/2",
    "proof": "CN.22–CN.23"
  }
}