Non-identifications and conclusion

The cone, deficit, extension, spectral state prescription, $\xi$, and $\beta$ are declared inputs. None is derived from an Enter record. No physical preference among the nonnegative extensions is claimed, and no zero-thickness relation is asserted to model a particular real string core.

A symmetric, conserved, traceless tensor need not source the prescribed background. For example, in a regular flat chart

is constant, conserved, and traceless, while the local Einstein tensor is zero. Equivalently a constant null covector gives the witness $k_{\mu }{k}_{\nu }$. This is the I-B :not-source separation CheungIB,CheungXAST.

We do not insert the expectation values into Einstein or Maxwell equations, compute a sourced magnetic field, solve backreaction, or claim spacetime emergence. Negative energy is a property of the stated field, state, and normalization, not a certification of a programme direction.

The observables are smooth tensor or scalar fields, hence distributions, on $M$. Their generic $r^{-2}$, $r^{-3}$, and $r^{-4}$ behaviours are not ordinary locally integrable completion data with transverse measure $r\mathrm{d}r$. Distributional extensions may exist, but require a prescription and may have apex-supported ambiguities. For finite nonnegative charts the leading diagonal ultraviolet powers are the scale-invariant ones; singular one-endpoint boundary data must not be confused with a universal stronger simultaneous diagonal power.

Local point splitting does not establish an interacting algebra, time-ordered product, quantum Ward identity, BRST closure, graviton or ghost sector, or apex gauge condition. A finite reporting instrument is not a continuum covariance, and finite numerical tests are not a coverage theorem.

No companion status record is updated. In particular:

• no new closure of O.1 is asserted outside any independently declared scoped result;

• any NOT_CLOSED{} status outside such a scope remains unchanged;

• the frozen XVI-N insertion is not discharged;

• XV-B's downstream quantum-admission exit is not opened;

• bulk_ symmetry_ restored{} is not promoted;

• no XVI-R or frozen-tree release is asserted.

These are non-transfer boundaries, not premises of the scalar proofs CheungO1ST,CheungXVIO,CheungXVIN,DocumentaryBoundary.

The supplied XIV-H/I/J and XV-B excerpts distinguish constructed internal kernels or off-characteristic references from an unconstructed complete characteristic quantum map. Nothing here identifies our scalar extension problem with that graph problem or supplies its missing admission. A registered technical manuscript named XV-B is not declared nonexistent; “not opened” refers only to the stated downstream admission gate.