Collaborate

Every paper makes a specific, falsifiable prediction using α = 6/5. If you have access to experimental data in any domain — condensed matter, particle physics, astrophysics, biophysics, plasma physics — you can test whether the fractional Laplacian with this exact exponent outperforms the standard theory.

Especially valuable: domains NOT yet tested. Turbulence, seismology, financial time series, quantum chemistry, nuclear structure, superconducting circuits, or any system governed by a Laplacian operator.

The test is straightforward: run your analysis with α = 2 (standard) and α = 6/5 (MPFST). Compare fit quality. Report whatever you find.

The strongest possible test is one designed to BREAK the theory. If you can find a domain where α = 6/5 is definitively excluded by high-quality data, that's a significant result.

Constructive challenges focus on: Is α truly 6/5, or is there a better fit nearby? Paper 24 derives the topology from three axioms — can the uniqueness proof be strengthened? Are the statistical tests robust to different analysis choices?

Destructive challenges: Find a domain where MPFST makes a clear prediction that fails. That would be more valuable than 10 papers showing it works.

The papers cover 30 domains so far. But any physical system with a Laplacian is a candidate. Some promising untested domains:

• Turbulence intermittency in fluid dynamics
• Anomalous heat transport in nanoscale systems
• Quantum chemistry — molecular orbital calculations
• Seismology — wave propagation in heterogeneous media
• Financial physics — option pricing with fractional diffusion
• Network science — anomalous spreading on real-world graphs
• Acoustic metamaterials — fractional wave equations

Several computational questions remain open:

• Larger-scale universe simulations — what structures emerge from the coupled PDE on cosmological grids?
• Machine learning: can a neural network rediscover α = 6/5 from multi-domain data?
• Optimizing the eigenvalue: does 6/5 sit at a special point in the space of possible graph topologies?
• Connecting to quantum gravity: does the fractional Laplacian produce the right spectral dimension running?

The best way to engage is through the work itself. Read a paper, run the code, and report what you find — whether it confirms or contradicts the predictions.

Public discussion on @FreemanCW on X is welcome. Paper-specific questions can be posted on the Zenodo record pages.