Geometric depletion of enstrophy production in the extreme vorticity tail: a Reynolds-number study toward the Navier-Stokes regularity question

v5 = paper v0.6 (2026-07-01), a correction-and-extension revision following an independent adversarial verification pass (every reference checked against its primary record; every derived claim re-derived; analysis code audited) and one new measurement. Corrections: the cross-Reynolds “statistically resolved at top-1%” claim is withdrawn (normal-vs-t interval slip; proper two-sample test now reported); the asserted “conservative” resolution-bias direction is falsified by a new paired coarse-graining experiment (§6.1) that measures the bias directly (−0.018±0.005 on the top-1% ratio) and finds it absorbs most of the observed cross-Reynolds difference; §7 now credits prior art (Lushnikov–Silantyev–Siegel 2021) whose periodic-domain threshold our scan reproduces, and downgrades the a=0.96 classification to inconclusive; two citation errors are fixed ([Yeung32768] author list, [CHH21] DOI). The central result — extreme-tail geometric depletion resolved below unity at both Reynolds numbers — is unchanged and strengthened by the measured systematic. A full change log precedes the references.

A human-led, agentic-AI research study of the geometric depletion of enstrophy production, D = <ω·Sω> / <|ω|²|S|>, in the extreme vorticity tail of three-dimensional turbulence, conducted entirely on consumer hardware (a single RTX 5090/5070 workstation) using a validated pseudospectral DNS and direct analysis of the Johns Hopkins Turbulence Database via a free SciServer container.

Results (honest status). At Rλ≈433 the extreme vorticity tail is more geometrically depleted than the bulk (regularizing), a result robust to an independent resample. At higher Reynolds number the extreme-tail ratio is not resolvable at ~5×10⁵ points: a data-provenance audit shows the isotropic8192 dataset mixes two Reynolds numbers (snapshots 0-4 at Rλ≈1200-1300, snapshot 5 at Rλ≈610) that must not be pooled, and a convergence audit shows order-unity scatter in the top-0.1% between statistically-identical snapshots. We make no claim of a Reynolds-number trend in the extreme tail. A one-dimensional Okamoto-Sakajo-Wunsch model corroborates the depletion mechanism in a decidable setting.

Methodology and transparency. The work was produced by an agentic large-language-model system (literature mapping via a Topic-Keyed Hash Routing memory, code authoring, computation, and drafting) under continuous human direction and validation; a human author is solely accountable for all claims. During the study the AI system twice produced confident but incorrect extreme-tail conclusions that a human-prompted audit retracted before they could stand — we report this as the central methodological result: an AI research apparatus built around an accountable human validation layer catches its own overreach. All code, data, and this disclosure are provided so the work is checkable.

This record is a preprint; results are reproducible from the public JHTDB datasets and the archived code.