Unified extension and state ledger

Any relation with $H_W\ngeqq 0$ & Excluded as stationary finite-moment state & Theorems thm:spectrum and thm:nogo.

Massive extensions, including ${\mathsf{L}}_L$ with $m\ge {\kappa }_L$ & Open here & A massive baseline and covariance analysis are not supplied. At equality, nonnegativity is insufficient because of the longitudinal threshold infrared divergence.

Non-product or longitudinal-momentum-dependent extensions & Open & Boundary data are infinite dimensional and require an operator-valued relation and Weyl function. Generic choices need not preserve longitudinal boosts.

Geometrically twisted tensor sectors, spinors, gauge fields & Open & No spin structure, constrained gauge domain, or multiplet state is constructed.

Thermal and other non-ground states & Open & Not constructed. Their infrared conditions are separate from the ground-state estimates.

Apex-supported extensions of the observables & Open & No distributional completion or apex counterterm class is chosen.

Global microlocal spectrum analysis & Open & Local Hadamard form is proved; global diffractive propagation is not classified here.