Abstract

We give a local Grade S transfer of Cheung's XI-A Einstein–scalar sheet to the regular I-B conical product. The host geometry is prescribed, while all analytical equations remain on an independently declared Minkowski completion. The transfer retains the unswitched Einstein–Hilbert action, the minimally switched scalar action, the distinction between invariant and gauge-fixed Noether identities, and tensor-density covariance of the invariant metric Euler operator.

The principal obstruction is inherited, not newly claimed: for the specified free scalar input ${\varphi }_m(t)=\sin (mt)/m$, with massless value $t$, the fixed-input Einstein jet is empty for every nonzero compact switch in the frozen class. Its detector is the first source-compatibility coefficient $({\partial }_{\mu }g){T_0}^{\mu \nu }[{\varphi }_m]$. A compact bump gives a strictly positive margin, whereas the vacuum retains a nonempty jet. This distinguishes a fixed-input incompatibility from a failure of Einstein theory or of gauge-fixed wave solvability.

The contribution of this sheet is the supported transfer and its complete reporting interface, not a new gravitational covariance theorem. We identify two essential locality qualifications: the switching detector is not a plateau detector, and global completion-jet emptiness must not be renamed emptiness of every plateau-local solution space. A finite supplied catalogue is reported by destructive Enter, with surviving registers and arbitrary untouched references retained. An explicit common-interface probability encoding has an exact diamond-distance formula for rational table approximations. Finite-probe coverage and an invisible conserved-perturbation construction prevent a successful finite table from being mistaken for a distributional identity.

The potential value is an auditable separation of action identities, solution compatibility, local support, and finite readout. The fixed positive ramp width is not a worldsheet thickness. No host reconstruction, field-acquisition map, gravitational propagator, quantum multiplet, tree, BRST construction, vacuum-energy calculation, or characteristic quantum coefficient is produced.