{
  "kind": "exact proof diagrams, no numerical samples",
  "dual_parameter_realization": {
    "coefficient_ring": "R_0: common-domain holomorphic x coefficients with |a_n|<=M C^n n!",
    "time_head_example": {
      "Q": "h^2",
      "head": "t^2 z",
      "normal_composition": "h^2 t^2 z - 4 h^3 t z + 6 h^4 z",
      "proof": "DP.9"
    },
    "division_error_norm": "at most 1/4",
    "inverse_norm": "at most 4/3",
    "remainder_support": "finite downward-closed normal monomial set B",
    "whole_module_generators": "(t^a z^beta)m_j over R_0",
    "free_locus": "g != 0, for the general smooth-support input",
    "actions": {
      "t": "h^2 partial_h + T",
      "z_i": "h partial_i + Z_i"
    },
    "curvature": [
      "h^2 partial_h Z_i - h partial_i T + [T,Z_i] = h Z_i",
      "h(partial_i Z_j-partial_j Z_i)+[Z_i,Z_j]=0"
    ],
    "principal_nilpotence": "T_0^a product Z_i,0^beta_i=0 for a+|beta|>=k",
    "proof": "DP.1--DP.6"
  },
  "stable_lattice": {
    "hypotheses": [
      "M_0 coherent finite E_0 lattice inside M",
      "E M_0=M",
      "theta and all D_xi preserve M_0"
    ],
    "residue_freeness": "at every parameter point; differential ideals of minors are zero or unit",
    "tangential_gauge": "invertible actual R_0 matrix; iterated integral bound M^k |x_i|^k/k!",
    "residue_shift": "A -> S^-1 A S + h S^-1 partial_h S; S=diag(h I_W,I_V)",
    "spectral_strip": "b-1 < Re lambda <= b",
    "recursion": "(n I+ad H)V_n = -sum_(k=1)^n A_k V_(n-k)",
    "inverse_bound": "K/n",
    "factorial_bound": "L^n n!, L=C(1+2 K M)",
    "Euler_matrix": "(H-I)^T",
    "isomorphism": "actual finite-order E-module isomorphism",
    "proof": "DP.7.1--DP.7.5",
    "resonant_example": {
      "initial": [
        [
          "0",
          "h^2"
        ],
        [
          "0",
          "2"
        ]
      ],
      "S": [
        [
          "h",
          "0"
        ],
        [
          "0",
          "1"
        ]
      ],
      "steps": 2,
      "H": [
        [
          2,
          1
        ],
        [
          0,
          2
        ]
      ],
      "Euler_matrix": [
        [
          1,
          0
        ],
        [
          1,
          1
        ]
      ]
    }
  },
  "not_claimed": [
    "ordinary numerical convergence of the h series",
    "arbitrary holonomic full-infinite regularization",
    "full real contact transport"
  ]
}