← NS-X72 / X72-47 · Beltrami Tension-Cancellation Dynamics and Source-Lock

NS-X72 · X72-47 Source-Lock Dynamics 2026-08

X72-47: Beltrami Tension-Cancellation Dynamics and Source-Lock

Building on Round 46's scalarization of visibility into a single scalar carrier, this round derives the carrier's complete dynamics: writing the exact equations for the amplitude source, the tension source, and the total visibility gap (built from three channels — vorticity stretching, gradient stress, and the transport commutator), distinguishing a 'state-level cancellation' from the stronger 'source-level cancellation,' and, near a constant-amplitude Beltrami background, obtaining the linearized visibility normal operator, proving that its tangential kernel corresponds exactly to the symmetric tangent directions. Proves that the Beltrami-invariant branch satisfies cancellation at every level simultaneously, but in general only source-level cancellation determines the true contact order of visibility. Route halts at STOP-C51 (state–source cancellation / Beltrami-normal-coercivity gap): the coercivity of this normal operator on the quotient space is not yet proved, nor has an unconditional source-cancellation mechanism been found, left to the next round to examine the operator's kernel.

This round's status: Source-Lock Dynamics — Taken from the file's own objective/executive-result section, meaning preserved, not a full verbatim translation.

Connections

Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.

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