Both internal placements of K 5

Nothing in the internal construction proves that all possible such maps fail. The ending is accordingly Unresolved, not Proved obstructed.

distinction at I3{ The internal amplitude is no longer the missing H2 object. Its pole, reconstruction, uniform estimates, and finite remainder have been supplied.

The missing object is now the joint characteristic operator map for the complete grouped coefficient. Calling the precomposition sum that map would skip a different product hypothesis.

No quantum coefficient is released by moving the first missing gate from H2 to I3.}

4: joint section or prescription, not entered

Because I3 is Unresolved, I4 is not entered as a construction.

If I3 were later supplied on the same route, the selected continuation would be the joint-section and complete-remainder exit. No characteristic prescription is selected here.

That later theorem must control:

1. lower terms of every numerical line, including the massive cross-line contributions;

2. every internal vertex and its actual operator map;

3. attachment-diagonal derivatives;

4. the two geometric defect directions without treating them as integration fibers;

5. the complete actual source;

6. the derivative and mass terms of the scalar root;

7. the complete grouped cross-line difference;

8. tensor and branch summation on one justified common representation.

The finite internal remainder of Corollary cor:remainder is not that theorem. Its frequency degree is not a transverse degree of ${\mathcal{T}}_{\mathrm{form}}$.

No zero joint section is assumed, and no nonzero joint section is inferred from the $B_6$ numerator $Q\lambda$.

The results of XIV-I prove neither cancellation nor failure of cancellation of ${\mathcal{T}}_{\mathrm{form}}$.

Proof. The new amplitude reconstruction concerns $K_5$ before cross-line composition. The other new formulas identify the common internal sum. Neither constructs (eq:jointmap) at $N$ or assigns a joint principal-symbol section there.

No complete remainder for that absent joint operation is supplied. The internal homogeneous-degree splitting cannot replace it.

unentered prescription interface

The alternative prescription route remains a different construction. It would have to name all seven data:

1. ambient space;

2. reference distribution on a proved domain;

3. exact extension locus;

4. agreement with the grouped frozen prescription;

5. uniform transverse degree;

6. a closed wavefront bound retaining off-locus singularities;

7. normalization or a uniqueness theorem.

The present locus is still the codimension-eight $N={\tilde{\mathcal{N}}}_{\mathrm{att}}\subset W$. It is not converted into a codimension-four numerical problem.