Model G Put to the Test, and Where the Flow Comes From: the Temporal Dynamics Framework in Model G and in a real fluid

Two papers and every run behind them, testing the readings of the Temporal Dynamics Framework (TDF) in Model G (Pulver & LaViolette 2013), each round written down and sealed with a SHA-256 fingerprint before it ran. Every run is reported and every miss stays on the record.

Model G Put to the Test (rounds one to nineteen): the Model G particle on its own, on the published equations and settings. The particle, the singularity in the core, the half line and its end, nesting, emission, growth and stopping, motion, and the fountain in two, three and four dimensions.

Where the Flow Comes From (rounds twenty to thirty-four): a proof structure for a Navier–Stokes flow driven by a self-sustaining particle, mapped in 2D and 3D. The particle sits inside a real fluid, the incompressible Navier–Stokes equations, with nothing driving the fluid but the particle's own push. The rungs:

• The source. The particle switches the flow on at a sharp threshold. A perfectly round particle breaks its own symmetry and starts the stirring, in 3D too.
• Why it moves. The core's flip sets what comes out: fast flips hold the electrons in, slow flips let them out, and the core stays whole while they leave. In 2D a halo of about 50 settles round the core at every seed.
• The order in it. The flip's steady beat pulls the quiet point between two unequal partners onto the half line, closer than no flip and closer than random flips with the same timing.
• Heat. More heat into the atom drives more electrons out and thins the core.
• The checks. Twice the grid points and half the time step, a finer 3D grid, five fresh seeds, an energy budget that closes to about 2%, and a symmetry check.
• The link to the Riemann work. The half-line rung meets the helix reading of the Riemann critical line; carrying it across is the open bridge rung.
• 3D. The source, the flip and the whole core carry over into the 3D equations.
• The junction. A P side and an N side in the fluid: equal and opposite partners balance at two-thirds of the way across in the fluid and near the half without it, a gentle flow passes three times more one way than the other, and heat and low friction bring the balance back towards one half. All eight sealed bars of that round missed and stay on the record.

The open step is named: the Clay Mathematics Institute's question is about the 3D Navier–Stokes equations on their own, and the 3D smoothness bound is the step above these rungs.

Ledger across rounds one to thirty-four: 62 sealed predictions hold, 48 miss or the data go the other way, and 3 equal-partner results are counted apart as symmetry checks.

Contents:

• the two papers (PDF, Markdown, LaTeX) with their figures
• every round's pre-registration and SEAL.txt
• the code: Python for rounds one to twenty, Julia from round twenty-one, including the 3D model
• every run and the scored results
• the ledger of every reading
• a page for reviewers

Christopher Sciacchitano (Subquantum Kinetics) proposed putting the TDF into Model G; that idea is where this work began.