Manuscript II-B@1 · II-B-v1.tex · lemma · bfd2eb3c

Lemma: The blind row

Complete contacts and the exact three-row certificate › Three admissible labels · lines 886–909 · proof included or linked

II-B@1#lem:blind

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At $β_{0}$ ,

m (β_{0}) = 0, n_{ℓ} (β_{0}) = 0 for every raw contact.

Proof. The reflection

S = diag (1, - 1, 1, 1)

fixes $k_{1}, k_{2}, A, t_{0}$ , interchanges $k_{3}, k_{4}$ , preserves $B$ , and negates the gauge vector. Follow the reflection by interchange of all data of legs three and four. Their species and physical tensors agree.

A parity-even scalar response is unchanged by these operations but is linear in the replaced tensor, which has been negated. It therefore equals its negative. This applies to each raw contact and to the complete reference tree.

Displayed formulas in this passage

unlabeled · line 889
$m (β_{0}) = 0, n_{ℓ} (β_{0}) = 0 for every raw contact.$
unlabeled · line 897
$S = diag (1, - 1, 1, 1)$

Nearby in this section

section: Three admissible labels