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

Lemma: Joint derivative budget

M.4 Contact collapse and Helmholtz conditions · lines 1020–1028 · proof included or linked

XVI-M@1#lem:joint

If $r_{h}$ of the $∣ γ ∣$ collapse derivatives hit the metric coefficient and $r_{χ}$ hit the switch, then $(2 - v + r_{h}) + (2 - s) + r_{χ} \leq 4 - N + ∣ γ ∣ \leq 4$ . Consequently $D := 4 - N + ∣ γ ∣$ , the total derivative count on $(h, σ_{ε}, χ_{I})$ , grades $Collapse$ .

Proof. $r_{h} + r_{χ} = ∣ γ ∣ \leq N$ ; add $4 - s - v = 4 - N$ .

Nearby in this section

definition: Definition: Contact collapse
remark: Remark: Single switch; preferred presentation
proposition: Proposition: Collapse rank
definition: Definition: Formal adjoint and self-adjoint subspace
lemma: Lemma: Helmholtz lemma for linear operators
section: M.4 Contact collapse and Helmholtz conditions
theorem: Theorem: Variational subspace of the contact collapse
remark: Remark: Eight third-order double-plateau variational directions