Manuscript VII-H@1 · VII-H.tex · section · d20d2a9f

The comparison problem and the selected target

The comparison problem and the selected target · lines 180–212

VII-H@1#eq:programme, VII-H@1#eq:distinctions

The question is not whether a preferred finite part can be assigned. It is whether a response, after physical matching, has a nonzero pairing independent of every permitted prescription change:

defined response ⟶ complete response ambiguity ⟶ nonzero invariant observation .

Three distinctions govern the construction:

one graph coefficient \neq = complete response, a local numerical counterterm \neq = its propagated response image, a quotient criterion \neq = a nonzero quotient class .

Local renormalization gives extension and comparison theorems under specified hypotheses BF,HW2001,HW2002. Finite-renormalization frameworks compare interactions and observables together BDF,DF. These results do not identify the ambiguity of an unspecified nonlocal response.

Displayed formulas in this passage

VII-H@1#eq:programme · line 186
$defined response ⟶ complete response ambiguity ⟶ nonzero invariant observation .$
VII-H@1#eq:distinctions · line 197
$one graph coefficient \neq = complete response, a local numerical counterterm \neq = its propagated response image, a quotient criterion \neq = a nonzero quotient class .$