Analytical corrections required for a coherent merge

A submission cannot preserve a false implication merely because it appeared in a predecessor. The following corrections are incorporated and their affected reports remain visible:

1. Infrared finiteness is proved. Nonnegativity alone is not used to infer a massless covariance. The Friedrichs heat estimate and the non-Friedrichs Krein bound supply the necessary estimates.

2. Image boundaries are included. The total Euclidean remainder is treated by joint ellipticity. No diagonal parameter is discarded as a measure-zero exception.

3. Current subtraction is stated correctly. The derivative difference of the direct parametrix does not vanish along arbitrary approaches to coincidence. The current is defined using the subtracted complex kernel. For the time splitting used to compute its azimuthal component, the direct contribution is identically zero.

4. Boundary charts are genuine boundary relations. An “infinite eigenvalue” is replaced by an explicit subspace and a compressed Hermitian relation. The finite-matrix small-radius limit is not asserted for every boundary chart.

5. Small-radius remainder orders are corrected. The first correction for $0<\nu <1/2$ is retained, but its remainder has additional regimes at $\nu =1/3$. The logarithmic case $\nu =1/2$ is supplied.

6. Asymptotic zeros are respected. A relative error is not asserted when a displayed leading stress coefficient vanishes.

7. Transverse and full spectra are separated. A negative transverse eigenvalue generates a full longitudinal continuous band, not a full-space $L^2$ eigenfunction.

8. State selection is not universal state uniqueness. The distinguished zero-mean spectral Fock state is specified. No classification of all algebraic ground states is claimed.

9. Projection changes the field algebra. The two projected constructions are not states with the original local canonical commutator. Their defects are stated on their actual domains.

10. Computation is not silently promoted to proof. All inherited execution claims are SUPPLIED_ NUMERIC{} and UNCERTIFIED{} as rigorous total-error bounds.

These corrections do not alter the Friedrichs polynomials, its current, the scale-invariant correction formulas, or the finite-chart Krein coefficient.