Manuscript VI@1 · VI.tex · figure · b5b60afb

Two different certificates

The finite obstruction certificate › The evaluated two-representative table · lines 2765–2782

VI@1#fig:VI-two-certificates

metric / coordinatescalarswitching defectconditional quantumsupport / uncompleted

Established classical certificate

h=0:\quad \mathcal A^{(1)}=0

h=K\xi:\quad \mathcal A^{(1)}=-a_f,\qquad a_f\geq\tfrac12

both have

gh=0

and zero forced response

-a_f

analytic inequality, not a simulation: $\max\{|F|,|F+a_f|\}\geq a_f/2\geq 1/4$

Unconstructed quantum certificate

empty

q_S

empty

N_S

empty complete catalogue

empty Ward-compatible products

RG-open

The two-representative obstruction table is not a counterterm-response matrix.

Different certificates. The two classical representatives share a proposed quotient label but have candidate values separated by $a_{f} \geq 1/2$ . Any common quotient value therefore incurs error at least $1/4$ on one representative. This obstruction is established without constructing a radiative target vector or a counterterm response matrix; the quantum problem remains RG-open.

Two different certificates

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