Boundary-Core Channel Families in Navier-Stokes-Type Vorticity Dynamics: Activation, Local Separatrices, and Direction-Dependent Pathways

This work presents the integrated B19 numerical study of Boundary Information Geometry (BIG), examining boundary-core organization in a restricted family of three-dimensional Navier-Stokes-type vorticity experiments.

The study combines a reduced shrinking-core scaling model with synthetic divergence-free vorticity fields, periodic Biot-Savart strain readout, signed strain-vorticity alignment, high-vorticity gates, short-time viscous evolution, numerical robustness controls, local perturbations, and directional continuation.

The reduced scaling model identifies an energy-compatible concentration window and a critical thickness exponent s∗=5/4s^*=5/4 under the stated stretching-versus-leakage assumptions. In the dynamical experiments, local positive stretching and coherent signed gate-local openness are found to be insufficient by themselves for positive finite-window enstrophy growth. Growth and decay are instead organized by the evolving competition between stretching production and viscous dissipation, including delayed activation.

Local-neighborhood tests reveal heterogeneous robustness among boundary-core channel classes. Controlled continuation around a fragile late-delayed channel resolves three directional local growth-decay boundaries. Subsequent reduction tests using 21 single observables and eight predeclared two-coordinate portraits do not yield a robust ray-independent upstream reduction. Mechanism comparison instead supports a channel-family interpretation: distinct direction-dependent upstream boundary-core pathways can feed into a common downstream finite-window production-versus-dissipation organization.

The principal result is therefore not a universal boundary threshold, but a reproducible boundary-core channel-family structure within the tested numerical construction.

The claims are deliberately limited to the stated reduced model and constructed synthetic divergence-free vorticity families. This work does not establish finite-time Navier-Stokes blow-up, a singularity criterion, a regularity criterion, or a global invariant separatrix.

The record includes the English Version 1.0 manuscript, a Japanese reference translation, claim-bearing CSV/JSON outputs, figures, SHA-256 manifests, and supporting reproducibility documentation.

Project repository

For the current research map, related BIG studies, representative figures, terminology, and links to the broader Boundary Information Geometry (BIG) research program, see:

Boundary Information Geometry (BIG) — GitHub Repository
https://github.com/Jun-Lucis/BIG-theory

The Zenodo record remains the archival and citable source for this research output. The GitHub repository serves as a navigational overview of the continuing BIG research program.