{
  "panel_A": {
    "group_map": "surjective; no group isomorphism asserted",
    "a_U": "I_U ker(rho_U)",
    "dimension_bound": "1+m q^2",
    "U_star": "a product attaining the maximum finite quotient dimension",
    "algebra_map": "A_U'/a_U' -> A_Ustar/a_Ustar; surjective and equal dimension",
    "proof": [
      "EV.13",
      "EV.14",
      "EV.15"
    ]
  },
  "panel_B": {
    "coordinates": [
      "independent output parameter u",
      "input time s",
      "spatial x"
    ],
    "source_covector": "nu_u=0, tau_s=1",
    "C_tr": "D_infinity_(u,s,x) / D_infinity_(u,s,x) D_u",
    "w": "e_Phi^[u](D_s^-1 kappa(v))",
    "identity": "D_s w = (C_tr tensor_R e_Phi)(v)",
    "tensor": "ordinary algebraic; finitely many elementary factors",
    "proof": [
      "EV.28",
      "EV.29",
      "EV.30",
      "EV.31",
      "EV.32"
    ]
  },
  "panel_C": {
    "top_arrow": "Psi(s)=1 tensor e(s)",
    "right_vertical": "balanced full B action via j:K_infinity->C",
    "left_vertical": "the entire finite directional Hom evaluation",
    "commutes": true,
    "injectivity_input": "SE.1",
    "scalar_reconstruction": "B tensor_T N = N by ISR.8--ISR.10",
    "unproved_mixed_flatness_used": false,
    "proof": [
      "EV.36",
      "EV.37",
      "EV.38",
      "EV.39",
      "EV.40"
    ]
  },
  "diagram_has_no_geometric_scale": true,
  "source_context": "https://www.kurims.kyoto-u.ac.jp/~kenkyubu/kashiwara/HolIII.pdf"
}