Both internal placements of K 5

The internal amplitude is now more than the assertion that a tree kernel exists. Its frequency singularity is explicitly a fixed retarded simple pole plus its regular companion. Its estimates hold on tests crossing that pole, and its inverse transform reconstructs both the diagonal chart and the separated cone chart.

Both placements and every finite lower differential term are retained with $z$ untested.

The remaining problem has changed, but it has not disappeared: compose the complete reconstructed sum with the grouped cross-lines on the characteristic domain. No internal Fourier identity supplies that missing product theorem.

Successor package

A successor receives:

1. the unchanged XIV-H package;

2. the finite retarded-pole module and its exact normalization;

3. the pole identity, uniform estimates, and reconstruction map;

4. the two complete $K_5$ amplitude maps with $z$ retained;

5. their exact finite lower-degree remainder and internal wavefront bounds;

6. the common precomposition sum and its canonical-domain value;

7. the precise missing I3 joint operator map;

8. the still closed I4–I6 and J3–J5 gates.

It receives no transverse degree of ${\mathcal{T}}_{\mathrm{form}}$, no cancellation theorem, and no permission to call either seventeen-dimensional count an excess. It receives no ${R_1}^{(1)}$.

The remaining chain is

Aiming at XV-B does not replace any arrow by a name.

Conclusion

An internal pole amplitude is not a cross-line prescription. A reconstructed tree sum is not its characteristic product. A frequency remainder is not the quantum remainder theorem. An undefined quantum coefficient is not an anomaly.

Declarations

scope. The new construction is an explicit finite distribution-valued internal amplitude module. It includes a proved pole identity, uniform annular estimates, reconstruction, finite lower-degree remainder, and internal wavefront bounds. No general intersecting-Lagrangian calculus is claimed.

common product phase. Separate Fourier transformations represent existing independent internal tensor factors. No sum of the retarded and quantum cross-line phases is formed or declared nondegenerate.