Multi-Plane Field Syntergic Theory

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.

Shows that quantum discreteness and gravity both emerge from one operator — the fractional Laplacian (−Δ)^(3/5) on the 11-node Sephirotic topology — with zero free parameters. The discrete eigenvalue spectrum produces quantized energy levels without imposing canonical quantization. The fractional Green's function G(r) ~ r^(α−3) produces emergent gravity that recovers GR at α→2. Phase-locking transitions at critical coupling thresholds replace the measurement postulate. QFT and GR are recovered simultaneously as the α→2 local limit. Domain #12.

Tests MPFST predictions against 55 published measurements from 15 tokamak devices across 5 independent observables: power spectral density (β = 1.2), Hurst exponent (H = 0.6), ELM waiting-time statistics (Weibull k = 1.2), pedestal pressure gradient scaling (−5/6), and anomalous transport exponent (γ = 1.2). Combined χ² = 7.75 with 55 degrees of freedom (p ≈ 1.000). Standard models (Kolmogorov, Bohm, SOC) are excluded. Zero free parameters — α = 6/5 is the same topological invariant from all previous domains. Domain #13.

Analyzes 486 GWOSC gravitational wave events. 109 pass quality filters — 73 favor MPFST power-law decay over GR exponential (67.0%, p = 9.16×10⁻⁵). Win rate increases with SNR: 63% (low) → 71% (mid) → 89% (high). Fixed α = 6/5 outperforms free-α fits. Combined with galactic rotation curves (Paper 4) and GR recovery (Paper 6) via Fisher's method: 5.8σ across 233 measurements spanning three gravitational regimes. Zero free parameters. Domain #14.

The spectral gap of the Sephirotic graph Laplacian (Δλ = 0.328, largest in the spectrum) dynamically reduces 11 internal planes to 2 effective modes under the fractional Laplacian (−Δ)^(3/5). Mode 0 (λ = 0, topologically protected) couples universally → gravity. Mode 1 (λ = 0.318, bilateral symmetry) splits the tree into signed sectors → gauge field. 9 heavy modes acquire topological mass (τ = 0.72–1.24) and drop below 1% of energy at t = 2.25. Nonlinear stability confirmed through g = 1.0 (light modes retain 96% energy). No geometric compactification. Zero free parameters. Domain #15.

Six computational tests on the stochastic MPFST PDE. Spectral gap survives noise (2 light modes retain >90% energy at σ=0.5). Noise-driven meltdown at σ_c=0.55. Kramers escape with R²=0.997 confirming Arrhenius barrier crossing. Stochastic resonance amplifies gauge mode 2.3× at optimal noise. Zero-noise recovery |ψ_stoch − ψ_det| < 10⁻⁴. Zero free parameters. Domain #16.

The fractional Laplacian (−Δ)^(3/5) modifies the gravitational equation of state to w = −(2α−1)/(3α−1) = −11/15 ≈ −0.733. Tested against 1,590 Pantheon+ Type Ia supernovae: MPFST χ² = 684.92 vs ΛCDM χ² = 684.60 (Δχ² = 0.32, statistically indistinguishable). DES Y5 (2024) measures w = −0.70 ± 0.09 — MPFST is 0.37σ away. DESI (2024) measures w₀ = −0.55 ± 0.21 — MPFST within 0.87σ. The cosmological constant Λ is not needed: accelerated expansion is fractional gravity at cosmological scales. Same α = 6/5. Zero free parameters. Domain #17.

The fractional memory function M(ω) ~ ω^(2−α) = ω^(4/5) predicts optical self-energy exponent β = 0.800 for cuprate high-Tc superconductors. Tested against 16 published measurements across 6 independent studies (BSCCO, YBCO, Tl-2201, Hg-1201, LSCO): MPFST χ² = 5.6 vs Marginal Fermi Liquid χ² = 51.0 — MPFST is 4.8× better. Weighted mean observed β = 0.765 ± 0.024. The 30-year anomalous mid-infrared power law is a direct consequence of fractional transport. Same α = 6/5. Zero free parameters. Domain #18.

The spectral dimension d_s = 2α/2 on a 2D horizon with α = 6/5 predicts logarithmic entropy correction c_log = −(d_s/2 − 1) = −2/3. This matches Asymptotic Safety gravity exactly, while Loop Quantum Gravity (−3/2) and string theory (−1/2) predict different values. Same derivation as Paper 8 qubit decoherence. BH evaporation time scales as M^(2+α) instead of M³ — testable for primordial black holes. Zero free parameters. Domain #19.

Flagship letter submitted to Physical Review Letters (es2026mar07_508). Synthesizes all 18 papers into a single unified result: α = 6/5, an exact eigenvalue of the 11-node Sephirotic graph Laplacian, generates zero-parameter predictions across 18 independent physical domains. Combined significance via Fisher's method: 5.8σ. No free parameters. No fitting. One topology — eighteen domains.

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.