Manuscript En05-A@1 · En05-A.tex · proposition · f076e703

Proposition: Edgewise velocity certificate

Velocity sets and the discrete isotropy obstruction › Physical containment is an additional comparison · lines 1260–1277 · proof included or linked

En05-A@1#prop:velocity

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If every edge of a complete dependency network is physically contained, every dependency path is contained in the same convex velocity cone. Operational influence obeys that containment.

Proof. For a path with edges $(Δ_{j}, u_{j})$ ,

j \sum Δ_{j} = (j \sum u_{j}) j \sum \frac{u _{j}}{\sum _{i} u _{i}} \frac{Δ _{j}}{u _{j}} \in (j \sum u_{j}) K .

Operational influence is contained in scheduled ancestry by Corollary cor:influence.

Displayed formulas in this passage

unlabeled · line 1268
$j \sum Δ_{j} = (j \sum u_{j}) j \sum \frac{u _{j}}{\sum _{i} u _{i}} \frac{Δ _{j}}{u _{j}} \in (j \sum u_{j}) K .$

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section: Physical containment is an additional comparison
section: Physical containment is an additional comparison