For Scientists
Every result is reproducible. Every paper includes complete source code.
Quick Start
Step 1: Pick any paper below. Each Zenodo record contains the PDF and a Python script (typically under 500 lines).
Step 2: Install dependencies — usually just numpy, scipy, and matplotlib. No GPU required for most papers.
Step 3: Run the script. It downloads or generates the data, runs the analysis, and outputs the key statistics. Compare to the paper's Table 1.
pip install numpy scipy
python3 sephirotic_eigenvalue.py
# Output: λ₆ = 1.200000000000000 (error < 10⁻¹⁶)
The Verifiable Claim
MPFST asserts that replacing the standard Laplacian (α = 2) with a fractional Laplacian (α = 6/5) — using no other adjustable parameters — produces predictions that match published experimental data better than the standard theory in 30 independent domains.
This is a concrete, falsifiable claim. To test it:
- Pick any domain below
- Obtain the published data (all sources are cited, most are freely available)
- Run the MPFST prediction with α = 6/5 (code provided)
- Run the standard prediction with α = 2 (same code, change one parameter)
- Compare χ², BIC, or whatever statistical test is appropriate
If α = 2 consistently outperforms α = 6/5, the framework fails. If α = 6/5 consistently wins, the framework has made a successful prediction with zero degrees of freedom.
Paper-by-Paper Reproduction Guide
Click any paper to see its prediction, data source, and reproduction steps
Technical Details
The Operator
The fractional Laplacian (-Δ)α/2 with α = 6/5 is defined via Fourier transform: F[(-Δ)α/2f](k) = |k|α F[f](k). On finite graphs, it is Lα/2 where L is the normalized graph Laplacian. Well-studied in probability (Lévy flights), PDEs (anomalous diffusion), and harmonic analysis.
The Graph
11 nodes (Keter, Chokmah, Binah, Da'at, Chesed, Gevurah, Tiferet, Netzach, Hod, Yesod, Malkuth) with 24 edges. Da'at connects only to Chokmah and Binah (degree 2). Tiferet has highest degree (8). The normalized Laplacian's eigenvalues are: 0, 0.291, 0.749, 0.908, 0.926, 1.183, 1.200, 1.278, 1.403, 1.520, 1.542.
Why α = 6/5?
Paper 9 proves that λ₆ = 6/5 exactly for the 11-node graph with Da'at. Without Da'at (10-node), the closest eigenvalue is 1.2224. Da'at's specific connectivity (degree 2, connecting only to Chokmah and Binah) locks the topology to the exact rational value. This is a topological invariant — it doesn't depend on edge weights, coupling constants, or any continuous parameter.
Limitations
The framework has not been peer-reviewed. Some domain tests (LENR, GW echoes) have marginal significance. Paper 24 derives the Sephirotic topology from three axioms (existence, isotropy, self-reference) via constructive geometry, though the uniqueness proof relies on discrete classification rather than a variational principle. The author is an independent researcher without institutional affiliation. All limitations are discussed in the individual papers.