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

Conditional finite-response certification

Finite-renormalization spaces and certificate requirements › Finite membership and separation · lines 2282–2301

VI@1#fig:VI-certificate-alternative

metric / coordinatescalarswitching defectconditional quantumsupport / uncompleted

schematic; not an evaluated matrix. No $q_S$ or $N_S$ is evaluated here.

W=\operatorname{im} N_S

q_S\in W

gives

q_S=N_S c

q_S\notin W

gives

zN_S=0

and

zq_S=1

hyperplane

\ker z

contains

W

but not

q_S

U=\operatorname{Span}\{q,n_1,\ldots,n_L\}\xrightarrow{\operatorname{ev}_S}\mathbb R^s

A finite separator excludes a global constant-coefficient identity, given catalogue coverage. A finite fit is global only when evaluation is injective on $U$ .

Conditional finite-response certification. A target vector either belongs to the counterterm response image or admits a separating row. Catalogue completeness is necessary for normalization-invariant interpretation. A fit on finitely many labels is global only when evaluation is injective on the relevant function space. The diagram contains no evaluated quantum response data.

Conditional finite-response certification

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