{
  "proof": "OA-FLOW-GDA, GDA7",
  "kind": "logical schematic; no numerical approximation",
  "hypotheses": [
    "Phi and Psi are faithful normal semifinite weights on N",
    "sigma(Phi) = sigma(Psi)",
    "C is a linear subspace of n(Phi)",
    "Lambda(Phi)(C) is dense in H(Phi)",
    "Psi(a*a) = Phi(a*a) for every a in C"
  ],
  "steps": [
    "Psi = Phi_h for a positive nonsingular central h",
    "B = pi(Phi)(h)^(1/2) is positive and closed; E = Lambda(Phi)(C)",
    "||B xi|| = ||xi|| on E",
    "xi_n -> xi implies B xi_n is Cauchy; closedness puts xi in D(B)",
    "D(B) = H(Phi) and B*B = I; positivity gives B = I",
    "Faithfulness gives h = I; hence Psi = Phi on the full positive cone"
  ],
  "domains": {
    "initial": "E is a linear dense subset of D(B)",
    "conclusion": "D(B) = H(Phi), with no Hilbert separability hypothesis"
  }
}