Manuscript XI-A@1 · XI-A.tex · section · b8211ecc

Decision table and handoff

Decision table and handoff · lines 1244–1300

Gate	Result
Signature, curvature, coupling normalization	Frozen
Positive TT kinetic sign	Proved
Attractive Newtonian comparison	Proved
Quadratic action and de Donder term	Explicit
Metric Euler derivative through $κ^{2}$	Proved; no $\partial g$ in the minimal metric variation
Scalar and source-divergence switch derivatives	Displayed
Invariant nonlinear Noether identity	Proved with the correct adjoint gauge operator and coupling factors
Gauge-fixed unbroken Noether identity	Proved false; breaking term retained
Invariant metric Euler covariance on $g_{U}$	Proved as tensor-density covariance
Nonlinear Fierz–Pauli-only replacement	Proved insufficient
Fixed-input Einstein jet $J_{g} (ϕ_{m})$	Empty
Universal emptiness for all inputs	False; vacuum counterexample
Gauge-fixed wave equation	Different equation; not an Einstein-jet repair
Quantum metric, propagator, tree, BRST class	Not constructed

The corrected sheet reaches Constructed. The specified on-shell Einstein reading reaches Proved obstructed. The literal demand for a nonlinear covariant, gauge-fixed Fierz–Pauli-only sheet cannot receive a construction theorem.

XI-B receives:

the signed quadratic operator $2 G_{lin} + e_{gf} = - □ γ ˉ$ ;
the explicit de Donder term and its breaking;
the stress-tensor vertex (eq:vertex);
the unswitched Einstein action and the order bookkeeping needed for its nonlinear identities;
the Noether identity (eq:noether), including its background-switch defect;
the empty fixed-input Einstein fiber and its distinction from gauge-fixed wave solvability.

It receives no propagator, ghost, antifield, tree, or quantum state. The algebra $g_{U}$ acts on classical configurations; it has not been shown to act on a quantum graviton. Establishing a BRST description of gauge fixing would be a later construction, not a consequence of naming the de Donder term BFR.