{
  "title": "Noncommutative Information Measurement Aqec Failure Map",
  "question": "Which dropped hypothesis first invalidates a channel, divergence, recovery, localization, or finite-regime information claim?",
  "takeaway": "Ancilla positivity, normal state domains, modularly compatible recovery, compact causal coupling, and split or finite-index control are independent requirements with distinct counterexamples.",
  "figure_type": "failure",
  "schematic": true,
  "scale": "not to scale",
  "nodes": [
    {
      "id": "a0",
      "row": "licensed checkpoints",
      "label": "normal UCP channel\\\\predual normal-state action"
    },
    {
      "id": "a1",
      "row": "licensed checkpoints",
      "label": "modular divergence\\\\support and proved parameter range"
    },
    {
      "id": "a2",
      "row": "licensed checkpoints",
      "label": "exact sufficiency or QEC\\\\equality and compatible reference"
    },
    {
      "id": "a3",
      "row": "licensed checkpoints",
      "label": "localized instrument\\\\compact coupling and causal order"
    },
    {
      "id": "a4",
      "row": "licensed checkpoints",
      "label": "finite-regime task\\\\split collar, finite index, or energy class"
    },
    {
      "id": "b0",
      "row": "first broken step",
      "label": "transpose or singular update\\\\not CP or not normal"
    },
    {
      "id": "b1",
      "row": "first broken step",
      "label": "incompatible support or illegal $\\alpha$\\\\divergence infinite or theorem absent"
    },
    {
      "id": "b2",
      "row": "first broken step",
      "label": "modularly moved subalgebra\\\\no reference-preserving recovery"
    },
    {
      "id": "b3",
      "row": "first broken step",
      "label": "spacelike tail or unordered regions\\\\remote action or order dependence"
    },
    {
      "id": "b4",
      "row": "first broken step",
      "label": "zero collar or infinite index\\\\no canonical density matrix or finite bound"
    }
  ],
  "edges": [
    {
      "from": "a0",
      "to": "a1",
      "label": "divergence",
      "logical_status": "ordered diagnostic sequence, not a universal implication chain"
    },
    {
      "from": "a1",
      "to": "a2",
      "label": "recovery",
      "logical_status": "ordered diagnostic sequence, not a universal implication chain"
    },
    {
      "from": "a2",
      "to": "a3",
      "label": "localize",
      "logical_status": "ordered diagnostic sequence, not a universal implication chain"
    },
    {
      "from": "a3",
      "to": "a4",
      "label": "scope",
      "logical_status": "ordered diagnostic sequence, not a universal implication chain"
    },
    {
      "from": "a0",
      "to": "b0",
      "label": "lose ancilla or predual",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a1",
      "to": "b1",
      "label": "leave domain",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a2",
      "to": "b2",
      "label": "break compatibility",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a3",
      "to": "b3",
      "label": "drop causal support",
      "logical_status": "failure under removed or overstated hypothesis"
    },
    {
      "from": "a4",
      "to": "b4",
      "label": "force finite structure",
      "logical_status": "failure under removed or overstated hypothesis"
    }
  ]
}