Manuscript XV-E@1 · XV-E.tex · section · a3dc45f5
Erratum to XV-D's coefficient proposition
Erratum to XV-D's coefficient proposition · lines 965–978
XV-D, Section 6, Proposition prop:reduction, item (iii),
states under hypothesis (H1) () that if
XV-C's estimate fails for ,
, then (a) has no extension to ,
and (b) “the failure sequence of XV-C for is
then a failure witness for the trace itself.” Clause (a)
is correct under (H1). Clause (b) overstates: the normalized form of
XV-C's witness is not preserved under multiplication by .
The proposed XV-E plan suggested instead that (a) requires an
invertibility hypothesis; that suggestion conflates (a) with its
converse. The following proposition settles all directions.