{
  "torsor": {
    "chart": "q != 0, t_i=q^2*t_j",
    "beta": "2*dq/q",
    "horizontal_transition": "P_i=P_j-(2/q)*E",
    "parameter_transition": "P_i=P_j-(2/q)*(lambda+epsilon)",
    "Euler": "E=t*d/dt",
    "right_action_on_functions": "r_a f(t)=f(t/a)",
    "right_derivative": "dr=-E on coefficient functions",
    "defect": "M=E+dr=Lambda on invariant coefficients",
    "lift_E": "E(f tensor v)=E(f) tensor v+f tensor Lambda*v",
    "inverse": "sum_k v_k -> sum_k t^(-k) tensor t^k*v_k, weak weight k",
    "status": "Exact one-chart transition model; not a global presentation of an arbitrary G/N+",
    "proof": [
      "ND.6",
      "ND.7",
      "ND.8",
      "ND.9",
      "ND.10",
      "ND.11"
    ]
  },
  "duality": {
    "rank": 2,
    "N": 2,
    "ring": "C[x,y]/(x,y)^2",
    "basis": [
      "1",
      "x",
      "y"
    ],
    "x_matrix": [
      [
        0,
        0,
        0
      ],
      [
        1,
        0,
        0
      ],
      [
        0,
        0,
        0
      ]
    ],
    "y_matrix": [
      [
        0,
        0,
        0
      ],
      [
        0,
        0,
        0
      ],
      [
        1,
        0,
        0
      ]
    ],
    "dual_basis": [
      "1*",
      "x*",
      "y*"
    ],
    "dual_x_matrix": [
      [
        0,
        -1,
        0
      ],
      [
        0,
        0,
        0
      ],
      [
        0,
        0,
        0
      ]
    ],
    "dual_y_matrix": [
      [
        0,
        0,
        -1
      ],
      [
        0,
        0,
        0
      ],
      [
        0,
        0,
        0
      ]
    ],
    "socle_R_dimension": 2,
    "socle_dual_dimension": 1,
    "Hom_R_k_R_dimension": 2,
    "true_dual_dimension": 3,
    "true_simple_dual_dimension": 1,
    "shift": "n+r",
    "opposite_parameter": "-Lambda-2*rho",
    "density_line": "L(-2*lambda-2*rho)",
    "final_parameter": "2*lambda-Lambda",
    "deviation": "-epsilon transpose",
    "status": "Local parameter/torus-connection dualizing diagnostic; no global strong-B free-R object asserted",
    "proof": [
      "NU.1",
      "NU.2",
      "NU.3",
      "NU.4",
      "NU.6",
      "NU.7",
      "NU.8",
      "NU.9"
    ]
  },
  "projector": {
    "d": 3,
    "N": 2,
    "residue_order": [
      1,
      1,
      0
    ],
    "epsilon_block": [
      [
        0,
        1
      ],
      [
        0,
        0
      ]
    ],
    "diagonal_z_blocks": [
      "I+3*epsilon",
      "I+4*epsilon",
      "2*epsilon"
    ],
    "off_diagonal_z_blocks": "I at (1,2) and (2,3), all other off-diagonal blocks zero",
    "bound": "Q(z)=z^6*(z-1)^6=0",
    "selected_residue": 0,
    "selected_dimension": 2,
    "selected_z": "2*epsilon != 0",
    "endpoint_quotient": "q = projection to the last 2 coordinates",
    "endpoint_inverse": "i = e_0 times the canonical last-block insertion",
    "whole_parameter_deviation": "epsilon_W=diag(epsilon,epsilon,epsilon)",
    "identities": [
      "q*i=I_2",
      "i*q=e_0",
      "z*i=i*(2*epsilon)",
      "epsilon_W*i=i*epsilon"
    ],
    "status": "Exact finite module/flag calibration of NT.4; not a tensor flag of a specified group",
    "proof": [
      "NT.4",
      "NT.7",
      "NT.9",
      "NT.11",
      "NT.12"
    ]
  },
  "free_human_comparison": "https://arxiv.org/html/1209.0188v2 Remark1.2(4)",
  "licence": "CC0-1.0"
}