← NS-X72 / X72-27 · Coherence Dynamics and Angular Phase Locking

NS-X72 · X72-27 Dynamization 2026-08

X72-27: Coherence Dynamics and Angular Phase Locking

Continuing from Round 26's result that 'the signed kernel has zero mean and finite variance, but no universal synchronization bias' (STOP-C30), this round converts the static-sign question into a dynamical one: it derives exact angular evolution equations for the strain eigenframe rotation, vorticity direction, quotient direction, and the pairwise line-of-sight direction, proving that the self-amplification term -S² makes no direct rotational contribution to the eigenframe (it only reshapes the strain, without rotating the frame). It establishes a non-stationary angular cancellation lemma — when the phase velocity |θ'|≥Ω>0, the accumulated signed coupling is suppressed unless the amplitude or phase-velocity modulation is strong enough — and also gives an exact locking condition and a pairwise Biot–Savart phase-decomposition formula. The route halts at STOP-C31 (angular-phase-locking / coherence-persistence gap): unconditional control of either a phase-velocity lower bound or a locking-duration upper bound is still missing, passing the baton to the next round to test whether this phase-locking manifold is itself stable.

This round's status: Dynamization — 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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