Manuscript XVI-M@1 · XVI-M.tex · theorem · 7346c909

Theorem: Certified graded presentation

M.2 Numerical-kernel relations and Gate S-bv · lines 560–585 · proof included or linked

XVI-M@1#thm:M2

With Input (S-bv) certified (Theorem thm:wpA-Sbv):

$N$	labels	$dim Poly_{N}$	$d_{N} = dim H_{4 + N}$	$dim ker π_{N}$
$0$	$1$	$1$	$1$	$0$
$1$	$4$	$4$	$4$	$0$
$2$	$20$	$10$	$10$	$10$
$3$	$60$	$20$	$20$	$40$
$4$	$170$	$35$	$35$	$135$
Total	$255$		$70$	$185$

The numerator map is onto $Poly_{N}$ . A basis $B_{N}$ extends a basis of $V_{K} = H_{4} \oplus H_{5} \oplus H_{6}$ ( $dim 15$ ). Every label reconstructs as $q^{\circ}_{λ} = \sum_{b \in B_{N}} R_{λb} q^{\circ}_{b}$ with exact rational $R$ .

Proof. Propositions prop:num and prop:relations, together with the exact $Q$ -linear algebra reported in Lemma lem:M2comp.

Nearby in this section

section: M.2 Numerical-kernel relations and Gate S-bv
input: Input statement: Input (S-bv); certified by Theorem thm:wpA-Sbv
remark: Remark: Motivation for Input (S-bv)
remark: Remark: Status of Gate S-bv
lemma: Lemma: Boundary-value calculus on Ω
proposition: Proposition: Numerator representation
proposition: Proposition: Two-direction equivalence of relations
proposition: Proposition: Unconditional wave-operator family