Manuscript Hawk05-A@1 · Hawk05-A.tex · lemma · 449f85bb

Lemma: Presentation degree is not an intrinsic symbol

The separate characteristic-map programme remains open › A self-contained reconstruction constraint · lines 1937–1964 · proof included or linked

Hawk05-A@1#lem:analyticnull

Suppose an adapted convention gives

Rec (M_{R}) = δ (q) \otimes R, Rec (i θ M_{R}) = δ^{'} (q) \otimes R,

and reconstructs multiplication by $q$ as the same physical coordinate multiplication. Then

Rec ((q i θ + 1) M_{R}) = 0.

For $R \neq = 0$ , its two summands reconstruct to nonzero opposite distributions.

Proof. For a test function $φ$ ,

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

Hence $q δ^{'} = - δ$ . Tensor with $R$ .

Displayed formulas in this passage

unlabeled · line 1940
$Rec (M_{R}) = δ (q) \otimes R, Rec (i θ M_{R}) = δ^{'} (q) \otimes R,$
unlabeled · line 1947
$Rec ((q i θ + 1) M_{R}) = 0.$
unlabeled · line 1956
$⟨ q δ^{'}, φ ⟩ = - \frac{d}{d q} (q φ (q))_{q = 0} = - φ (0) .$