{
  "statement": "the derived p-adic height is p-adic height data; no theorem in the sources sends it to the real Néron–Tate regulator",
  "equated": false,
  "what_MCS_section_4_proves": "Bertolini–Darmon's derived p-adic height equals (up to sign) Nekovář's — two p-adic constructions identified with each other",
  "what_it_does_not_prove": [
    "that either is nondegenerate",
    "that either computes Reg_NT",
    "anything about a real-valued regulator"
  ],
  "DAG_C_controlled_by": "C_NT (Rounds 031/035 define C as Mordell–Weil determinant ⟶ classical Néron–Tate regulator)",
  "C_p_pass_does_not_imply_C_NT": true,
  "agrees": true
}