Manuscript XIII-C@1 · XIII-C.tex · section · e6556893

The parallel-line primitive

C3: scaling degrees and their exact scope › The parallel-line primitive · lines 907–938

For the stress–stress contraction in $B_{10}$ or $B_{11}$ , the two scalar derivatives at the interaction and the two at the stress vertex give the following monomial degrees:

Interaction/stress monomials	Derivatives on the two lines	Primitive degree	Degree minus codimension
mass/mass	$0$	$4$	$0$
kinetic/mass or mass/kinetic	$2$	at most $6$	at most $2$
kinetic/kinetic	$4$	at most $8$	at most $4$
temporal kinetic component	$4$	$8$	$4$

A mass row disappears when its mass coefficient vanishes. These are primitive monomial statements, not a claim that tensor summation cannot lower the degree.

For $y = v$ , use $r = y - v$ and retain $x, u, v$ as tangential variables. Its codimension is four even when $x \neq = v$ . Multiplying the primitive by the independent spectator coefficient does not turn this partial diagonal into the total diagonal. Whether the complete product has a uniform transverse microlocal estimate remains a separate obligation.

The parallel-line primitive

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