Manuscript XI-G@1 · XI-G.tex · section · f029bbcd

Conclusion

Decision, exclusions, and handoff › Conclusion · lines 1462–1482

v \in [u]_{sol} ⟺ v - u \in □_{1} E^{'} + □_{2} E^{'} + P_{m, 3} E^{'} ⟺ W_{v} = W_{u}; [u]_{sol} \cap F_{mc, pol} \neq = \emptyset ⟺ WF (W_{u}) \cap (V_{+}^{3} \cup V_{-}^{3}) = \emptyset; F1 data: ⟨ u, η e^{iλ k_{1} \cdot y} \otimes η e^{iλ k_{2} \cdot y} \otimes ϕ_{m} ⟩ = - iλ Λ_{f} + O (1), k_{1} + k_{2} = 2 d t, Λ_{f} < 0; [u]_{sol} \cap F_{mc, pol} = \emptyset : every representative carries \pm (k_{1♭}, k_{2♭}, 0), k_{1♭}, k_{2♭} null, co-oriented.

A reader can now see that XI-F's $\pm d t$ obstructs one kernel, and that the free-shell class does not escape it: it inherits the two null halves of that covector, one in each metric slot, and no bulk equation term removes them.

Displayed formulas in this passage

unlabeled · line 1464
$v \in [u]_{sol} ⟺ v - u \in □_{1} E^{'} + □_{2} E^{'} + P_{m, 3} E^{'} ⟺ W_{v} = W_{u}; [u]_{sol} \cap F_{mc, pol} \neq = \emptyset ⟺ WF (W_{u}) \cap (V_{+}^{3} \cup V_{-}^{3}) = \emptyset; F1 data: ⟨ u, η e^{iλ k_{1} \cdot y} \otimes η e^{iλ k_{2} \cdot y} \otimes ϕ_{m} ⟩ = - iλ Λ_{f} + O (1), k_{1} + k_{2} = 2 d t, Λ_{f} < 0; [u]_{sol} \cap F_{mc, pol} = \emptyset : every representative carries \pm (k_{1♭}, k_{2♭}, 0), k_{1♭}, k_{2♭} null, co-oriented.$