Manuscript Hawk02-A@1 · Hawk02-A.tex · lemma · 7fbae745

Lemma: A null presentation

Stage 4: renormalization and characteristic admission › Reconstruction descent is a necessary test · lines 1298–1323 · proof included or linked

Hawk02-A@1#lem:null

For a one-dimensional normal coordinate $q$ ,

q δ^{'} (q) + δ (q) = 0.

Consequently, for any existing nonzero distribution $R (r)$ ,

(q δ^{'} (q) + δ (q)) \otimes R (r) = 0,

although the two summands are separately nonzero. Presentation degree alone therefore need not define a degree filtration of reconstructed kernels.

Proof. For a test $φ$ ,

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

Tensor with $R$ .

Displayed formulas in this passage

unlabeled · line 1301
$q δ^{'} (q) + δ (q) = 0.$
unlabeled · line 1305
$(q δ^{'} (q) + δ (q)) \otimes R (r) = 0,$
unlabeled · line 1315
$⟨ q δ^{'}, φ ⟩ = - \partial_{q} (q φ (q))_{q = 0} = - φ (0) .$