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

Example: A null presentation with nonzero summands

Propagation and reconstruction before observation · lines 471–486

For a one-dimensional coordinate $q$ ,

q δ^{'} (q) + δ (q) = 0.

Indeed,

⟨ q δ^{'}, ψ ⟩ = - \partial_{q} (q ψ (q)) ∣_{q = 0} = - ψ (0) .

Tensoring with a nonzero distribution in other variables leaves the identity unchanged. A rule extracting a highest polynomial degree from the two summands need not descend to their zero reconstruction. This is the elementary mechanism used in XIV-J's null-presentation test CheungXIVJ.

Displayed formulas in this passage

unlabeled · line 473
$q δ^{'} (q) + δ (q) = 0.$
unlabeled · line 477
$⟨ q δ^{'}, ψ ⟩ = - \partial_{q} (q ψ (q)) ∣_{q = 0} = - ψ (0) .$

Nearby in this section

proposition: Proposition: Propagated ambiguity
section: Propagation and reconstruction before observation
theorem: Theorem: Reconstruction descent
section: Propagation and reconstruction before observation