TruePrime tests a flow-editing technique from the Navier–Stokes proof

Interactive profile experiment

Make an edit. See what it costs elsewhere.

Change the inner feature and toggle compensation to see how the selected outer quantities respond. The plot shows changes from the original profile, so the requested edit and its collateral effects are easy to compare.

Loading the checked profile states…

Gold band: inner edit region. Gray bands: permitted compensation regions for the selected component. The vertical scale adjusts with edit strength and component, but stays fixed when compensation is toggled.

How this demo works: 101 precomputed settings from the small-step correction path are displayed here. Every setting was checked with 3,840-node quadrature and compared with Newton’s method. The chart and export use 801 samples. No time-dependent fluid simulation runs in your browser; these are static, dimensionless constructed profiles. There is no demonstrated animation, energy or dollar saving.

Inspect the demo dataset · Read the methods and reproduce the original experiment

From a mathematical result to a useful operation

At TruePrime, we look for software that can save people time and money. Following OpenAI’s September 8 announcement of a Navier–Stokes proof, we investigated whether a finite part of its construction could support a practical tool. The original proof belongs to its authors; our contribution is this application experiment and its reproducible implementation. Read OpenAI’s announcement.

The question that led somewhere was simple: if a simulated flow already exists, can we deliberately edit its interior while preserving selected quantities outside the changed region?

That changes what counts as success. In a prediction task, changing a profile away from the reference is an error. In an editing task, the requested local change is the desired output. The original profile also supplies the quantities we want to preserve, so we can calculate and cache those targets before editing.

What the experiment achieved

We implemented a five-moment correction procedure from the paper and applied it through 1,000 small editing increments. Four checkpoints were checked independently using higher-resolution quadrature. At the largest edit, the maximum change in the inner swirl-profile component E was 9.84%; the companion component U changed by up to 36.9%.

The outer discrepancy combines sampled pressure and three construction-specific quantities, scaling each difference by the larger of 1 and the original magnitude. It is a numerical diagnostic, not a percentage reduction in time, energy or cost.

The same final correction was also obtained with ordinary Newton iteration, in eight iterations for the largest edit. It was much more direct than the 1,000-increment path. We therefore make no speed-advantage claim for that path.

Where this could become useful

A small vortex-profile editor is the most concrete candidate. A creator could load a supported profile, change its interior, choose where compensation is permitted, and inspect the result before export. The hoped-for benefit is less manual work when reusing an effect. That benefit still needs measurement in an actual creator workflow.

The same constrained changes could also help generate challenging test cases for physics AI: different interiors can share selected aggregate observations. Another possibility is compressing saved profiles while retaining declared quantities. Neither application has been validated as a product.

Fluid editing already has a substantial history. Relevant comparisons include divergence-free editing and reuse of existing flows and real-time control with Laplacian eigenfunctions. Our study does not establish that this approach outperforms those methods.

What remains to be tested

• Visual acceptability: whether creators can tolerate the compensating changes.
• Later motion: preserving instantaneous quantities does not guarantee unchanged future fluid evolution.
• Broader inputs: arbitrary smoke, liquid surfaces, obstacles and imported three-dimensional simulations are outside this prototype.
• Practical value: editing time, compute cost and customer savings have not been measured.

This is not the full singular-flow construction or an independent verification of the complete mathematical or Lean proof. Numerical checks use floating-point arithmetic and are not formal certification. No independent expert review has been obtained for this application experiment.

Methods and reproduction

The package contains the editing script, its supporting numerical component, the recorded results, the largest edited profile, reproduction instructions and file hashes. It includes no customer data. The original paper and formalization are linked rather than redistributed.

python3 -m venv .venv
source .venv/bin/activate
python3 -m pip install -r requirements.txt
OPENBLAS_NUM_THREADS=1 python3 creative-agent/edit_test.py

Run these commands from the extracted package directory. See its README for environment and interpretation details.

Credit and contribution

OpenAI’s authors receive credit for the published Navier–Stokes proof and its construction. Earlier fluid-control and numerical-method researchers provide the prior work on which this investigation also depends.

Robert Luecke initiated and directed TruePrime’s search for practical applications. AI agents performed the implementation, numerical experiments, technical review and drafting. A second agent proposed reframing the correction as an intentional editing operation; the primary agent reviewed the code, results and product limitations. TruePrime is publishing that experiment and application framing. This note does not assert priority over all related work, patentability, or invention of fluid editing.

Suggested citation: TruePrime. “TruePrime tests a flow-editing technique from the Navier–Stokes proof.” Research Note 001, version 1.0, September 10, 2026. https://trueprime.ai/research/navier-stokes-flow-editing/