{
  "proof_locators": [
    "DS.1",
    "DS.3",
    "DS.6",
    "DS.7",
    "DS.8",
    "DS.13",
    "DS.14",
    "DS.17",
    "DS.20",
    "DS.21",
    "DS.23"
  ],
  "standing_scope": "Hausdorff second-countable locally compact etale groupoids; original C0(T) anchors",
  "range_sum": {
    "g": "x->z",
    "h": "y->z",
    "h^-1g": "x->y",
    "common_range": "z",
    "xi_h_fibre": "E1_z",
    "eta_hinv_g_fibre": "E2_y",
    "transported_eta_fibre": "E2_z"
  },
  "source_matrix": {
    "g": "x->z",
    "l": "x->y",
    "g l^-1": "y->z",
    "entry": "pi_x(alpha_g^-1(a(g l^-1)))",
    "domain": "E_x",
    "codomain": "E_x"
  },
  "compact_extension": "theta_(e b),(f c) tensor 1 = theta_(e tensor i_B b),(f tensor i_B c)",
  "quotient_square": "[q_A] tensor j_r(x) = j_m(x) tensor [q_B] in KK(A_m,B_r)",
  "module_base_change": "X_E,m tensor_(B_m,q_B) B_r is isomorphic to X_E,r",
  "diagram_coordinates": "Normalized page layout only, no mathematical metric coordinates asserted",
  "not_inferred": [
    "reduced exactness",
    "global norm-continuity of unlocalized F",
    "coefficient-free quotient inverse",
    "original-unit Dirac factors"
  ],
  "product_existence_provider": "ANCHORED-KK-FOUNDATIONS.md KG.1-KG.4"
}