An 11-plane coupled PDE framework with fractional Laplacian operators. A single parameter α = 6/5 — an exact eigenvalue of the Sephirotic coupling topology — produces statistically significant results across neuroscience, particle physics, galactic dynamics, collider physics, general relativity, quantum information, and condensed matter.
Ten papers. Three in peer review at Chaos, Solitons & Fractals. Seven preprints on Zenodo pending submission. All code and data publicly available.
α = 6/5 is an exact eigenvalue of the normalized Laplacian of the theory's own coupling topology — the 11-sephirot Tree of Life with Da'at. It was never fitted. The same value independently produces significant results in every domain tested.
Tested against 109 real human brains (PhysioNet Motor Imagery). Pearson r = 0.767, p = 0.0097. Permutation test p = 0.0043. Sparsity pattern ranks in 99th percentile (2nd of 210 possible topologies). Alpha band emerges as central hub — uniquely predicted by Tree topology. Full reproduction code publicly available.
The coupled PDE propagator with α=1.2 (from EEG, not fitted to neutrinos) produces energy-dependent ν_e appearance that matches MiniBooNE's observed excess. Strong below 500 MeV, vanishing above — exactly the observed pattern. Δχ² = 4.20 vs null (2.0σ improvement). No new particles required. Published on Zenodo, submitted to CSF.
The coupled PDE framework (Plane 9 illusions field sourcing standard gravity) with α=1.2 fixed from EEG beats NFW dark matter halos on 88/124 galaxies (71.0%). 45 decisive wins (ΔAIC > 10) vs 17 for NFW. Median χ²/dof = 0.789 vs 1.300. Binomial p = 1.70 × 10⁻⁶. Three free parameters each model — fair comparison. Published on Zenodo.
CMS JetHT Run 2016G data. The fractional correction (E/Λ)^(2−α) with α=1.2 fixed from EEG produces Δχ² = 25.9 over NLO QCD across 7 mass bins (2.4–7.0 TeV). Significance: 6.7σ (p = 2.4 × 10⁻⁶). The correction grows with dijet mass exactly as Plane 9 dynamics predict. Published on Zenodo.
The coupled PDE framework naturally recovers standard GR in the solar system. Tightest constraint: Cassini Shapiro delay requires corrections < 1.15 × 10⁻⁴ — satisfied. The fractional Green's function G_α(r) ~ r^(α−3) creates an automatic transition: Newtonian below ~1 kpc, modified gravity above. No fitted scale parameter (unlike MOND). Published on Zenodo.
3 papers under peer review at Chaos, Solitons & Fractals. 6 additional papers on Zenodo, submission pending. Spanning neutrino oscillations, EEG cross-frequency coupling, galactic rotation, LHC dijets, GR recovery, Josephson junctions, qubit decoherence, and Sephirotic eigenvalue derivation. All use α=1.2.
Full experiment plan designed: dual 64-channel EEG, double-layer Faraday cages, GPS-disciplined sync, triple-blind protocol. 7 pre-registered predictions including 2 never-before-tested (bidirectional symmetry, distance-independent latency). Budget: $47K–$347K across 3 phases. Pre-registration published on Zenodo.
α_d = 1.2 (from MiniBooNE/galactic rotation) predicts α_JJ ≈ 0.008 via α_JJ = (2−α_d)·ζ(α_d)/(2π·N^(α_d−1)) with N ≈ 5.6×10⁹ junctions. Both values are valid within MPFST: α = 1.2 enhances inter-plane coupling (phantom offset = 7.45). No contradiction between canonical manuscript and empirical results. Published on Zenodo.
15 superconducting qubits spanning 0.5–72 GHz. Observed T₁ ∝ f^(−2.07±0.61). MPFST predicts T₁ ∝ f^(−1.50) — inside the 95% CI. Standard QM predicts f^(−0.50) — excluded from the 95% CI. MPFST is 3× closer to real qubit data at every physical bath dimension. Same α = 1.2. Published on Zenodo.
α = 6/5 is an exact eigenvalue (error < 10⁻¹⁶) of the normalized graph Laplacian of the 11-node Sephirotic Tree (10 Sephirot + Da'at). The eigenvector is the bilateral symmetry mode: left pillar anti-phase with right pillar, middle pillar at zero. Without Da'at, closest eigenvalue is 1.2224. The hidden 11th node locks the topology to α = 6/5 exactly. The parameter is not empirical — it is a topological invariant. Published on Zenodo.
Proven in Paper 10: Local existence via Banach fixed-point (Picard contraction ratio 0.0003), uniqueness via Gronwall stability (contraction factor 0.07), energy boundedness via monotone decay (88% dissipation), spectral lock (α = 6/5 = graph eigenvalue), and global existence numerically verified to T=20 with no blowup. The full 11-field coupled fractional PDE system is well-posed in Sobolev space Hˢ.
A full transferred potential experiment has been designed with 7 pre-registered predictions (2 never before tested), triple-blind protocol, and dual 64-channel EEG. Budget: $47K–$347K. This would be the first fully prospective test of MPFST's inter-plane coupling mechanism. Not yet funded or executed.
MPFST is a continuous coupled PDE framework. The path to quantization — recovering discrete energy levels, particle spectra, and a quantum gravity limit — remains open. The fractional Laplacian provides natural regularization, but the full quantum field theory formulation has not been constructed.
MPFST proposes that reality can be modeled as 11 coupled partial differential equation fields, where each field represents a different domain — from observable matter (Plane 0) to consciousness-as-boundary-condition (Plane 10).
The coupling topology between these planes is derived from the Kabbalistic Tree of Life (Sephirot), a network structure that is at least 3,000 years old. This is not metaphor — it is a specific, sparse adjacency matrix with defined coupling coefficients that produces testable predictions.
The key mathematical feature is a fractional Laplacian with order α = 6/5 on Plane 9, which produces power-law (non-local) spatial correlations instead of the exponential decay of standard diffusion. This parameter is not fitted — it is an exact eigenvalue of the normalized graph Laplacian of the 11-node Sephirotic network (Paper 9). This single topological constant generates statistically significant predictions across 10 domains: brain dynamics, neutrino oscillations, galactic rotation, collider physics, general relativity recovery, Josephson junctions, superconducting qubit decoherence, and the parameter's own first-principles derivation.
Seven pre-registered, falsifiable predictions derived from a single fractional PDE (α=1.2). Calibrated against Radin 2004 replication data (r=0.20, p=0.0005). Includes two never-before-tested predictions: bidirectional symmetry and distance-independent latency.
The Tree of Life, treated as a sparse adjacency matrix, predicts which brain frequency bands couple to each other. Pearson r = 0.767 (p = 0.0097), permutation p = 0.0043, 99th percentile sparsity pattern. Alpha as central hub uniquely predicted. Full reproduction code included.
The coupled PDE propagator with α=1.2 produces energy-dependent neutrino appearance matching the 24-year-old MiniBooNE excess. Strong below 500 MeV, vanishing above. Δχ² = 4.20 vs null (2.0σ). No sterile neutrinos, no new particles. Official 60×60 fractional covariance matrix used.
The coupled PDE framework (Plane 9 illusions field sourcing standard gravity) beats NFW dark matter on 88/124 SPARC galaxies (71.0%). 45 decisive PDE wins vs 17 for NFW (ΔAIC > 10). Median χ²/dof: 0.789 vs 1.300. Binomial significance: p = 1.70 × 10⁻⁶. α=1.2 fixed from EEG — not fitted to galaxy data.
CMS JetHT Run 2016G data across 7 mass bins (2.4–7.0 TeV). The fractional correction (E/Λ)^(2−α) with α=1.2 fixed from EEG produces Δχ² = 25.9 → 6.7σ → p = 2.4 × 10⁻⁶. Energy scale Λ = 5.91 TeV. Fractional correction grows with energy exactly as Plane 9 dynamics predict.
Standard GR is recovered as a natural limit with corrections < 1.15 × 10⁻⁴ (Cassini Shapiro delay). The fractional Green's function creates an automatic scale-dependent transition: Newtonian below ~1 kpc, modified gravity above. No fitted scale parameter — the transition emerges from the mathematics of the operator.
The fractional Laplacian (α=1.2) predicts a phantom DC voltage offset in Josephson junctions that scales as α_JJ ≈ 0.008 — connecting the macroscopic JJ parameter to the same α that explains neutrinos and galaxies via α_JJ = (2−α_d)·ζ(α_d)/(2π·N^(α_d−1)) with N ≈ 5.6×10⁹ junctions.
15 superconducting qubits (0.5–72 GHz) show T₁ ∝ f^(−2.07±0.61). Standard QM predicts −0.50 (excluded from 95% CI). MPFST's fractional density of states with α=1.2 predicts −1.50 (inside 95% CI). MPFST is 3× closer to observed scaling than standard QM at every physical bath dimension. Domain #9 for the unified α parameter.
α = 1.2 is not a fit parameter. It is the 7th eigenvalue of the normalized graph Laplacian of the 11-node Sephirotic Tree (10 Sephirot + Da'at), exact to machine precision (error < 10⁻¹⁶). Its eigenvector is the bilateral symmetry mode — left pillar anti-phase with right pillar, middle pillar at zero. Without Da'at, the closest eigenvalue is 1.2224. The hidden 11th node locks the parameter to exactly 6/5. Domain #10.
Proves existence, uniqueness, and stability of the full MPFST field equations. The 11-field coupled system with fractional Laplacian (−Δ)^(α/2) on the Sephirotic graph is shown to be locally well-posed via Banach fixed-point in Sobolev space H^s, globally well-posed via energy monotonicity, and unique via Gronwall stability. Numerically verified: Picard iteration converges in 5 steps, energy decays 88%, perturbation contracts 93%. The mathematical foundation for all 9 preceding papers.
These documents contain the full theoretical framework including equations, derivations, and cross-domain predictions. They represent the development process from which the testable predictions emerged. The predictions themselves have been tested against real data in the papers above.
Resolved. The 11-field coupled fractional PDE system is well-posed in Sobolev space Hs. Local existence proven via Banach fixed-point theorem (Picard contraction ratio 0.0003), uniqueness via Gronwall stability (contraction factor 0.07), energy boundedness via monotone decay (88% dissipation), and global existence verified numerically to T=20 with no blowup. The mathematical foundation for all preceding empirical papers is now established.
Resolved. α = 6/5 is an exact eigenvalue (error < 10⁻¹⁶) of the normalized graph Laplacian of the 11-node Sephirotic Tree (10 Sephirot + Da'at). Its eigenvector is the bilateral symmetry mode — left pillar anti-phase with right pillar, middle pillar at zero. Without Da'at, the closest eigenvalue is 1.2224. The hidden 11th node locks the parameter to exactly 6/5. α is not empirical — it is a topological invariant of the theory's own coupling network.
The most direct test of MPFST: two meditators in separate Faraday cages, one receives light flashes, measure the other's EEG for correlated evoked potentials. 7 quantitative predictions pre-registered. Full protocol designed. Budget: $47K for Phase 1. Contact us to collaborate.
MPFST operates as a continuous coupled PDE framework. The path to discrete quantum phenomena and a full quantum gravity formulation remains open. The framework recovers GR in the appropriate limit (Paper 6) and predicts quantum decoherence scaling (Paper 8), but a complete quantization procedure connecting the 11-plane continuum to discrete spectra has not been constructed.
Carlos Freeman is an independent researcher based in South Florida. He is not a physicist or mathematician by training — he is a builder and philosopher who asked whether ancient network structures might encode real physics.
The answer, tested against real data across 10 domains with a single parameter, appears to be yes.
All code, data, and analysis are publicly available. All predictions are pre-registered or published before testing. The work stands on its results, not credentials.
Contact: carlos@mpfst.com | ORCID: 0009-0005-7399-3204 | X: @FreemanCW