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    {
      "symbol": "tnfr.math.symbolic.evaluate_bifurcation_risk",
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        "tnfr.math.evaluate_bifurcation_risk",
        "tnfr.mathematics.evaluate_bifurcation_risk"
      ],
      "reason": "An arbitrary absolute threshold on the nodal product-rule acceleration establishes neither bifurcation nor stability and cannot admit THOL/IL or certify U4. No source consumer exists except the duplicated module demonstration and public re-exports.",
      "replacement": [
        "src/tnfr/math/symbolic.py::compute_second_derivative_symbolic (symbolic product rule only)",
        "src/tnfr/operators/operator_contracts.py (registered operator contracts)",
        "src/tnfr/operators/grammar_canon.py (grammar admission)"
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    {
      "owner": "src/tnfr/math/symbolic.py",
      "contract": "docs/API_CONTRACTS.md#removed-unsupported-helpers",
      "change": "The normalized exponential pressure improper integral converges iff growth_rate < 0. At zero rate, finite increment equals elapsed horizon and the form grows linearly. Finite input admission and unavailable numerical projections are explicit."
    },
    {
      "owner": "src/tnfr/validation/__init__.py",
      "change": "Required compatibility imports now propagate failures; no empty-table or always-good fallback masks a missing implementation."
    },
    {
      "owner": "theory/GAUGE_SYMMETRY_AND_UNIFICATION.md",
      "change": "Distinguish real wrapped-edge cycle sum 2*pi*k from its final wrapped closure residual."
    }
  ]
}