Formula Catalog

Every specific formula shown on this site, one level more atomic than the Catalog’s theory-level classification: each equation gets its own page stating plainly whether it’s Proven (real derivation and independent confirmation exist) or Unproven (PBT’s own claim, with no independent derivation or confirmation beyond the paper it appears in) — and, where this site’s own audits found a formula doesn’t even reproduce its own paper’s claimed numbers, that finding is stated directly on the formula’s page rather than left for a reader to rediscover.

This now covers all 13 papers. Most later papers repeat formulas already introduced in Papers 1, 2, 5, and 6 rather than adding new ones — those pages link back here.

Proven

Real, established physics — used by PBT correctly, whether reused unmodified or recontextualized.

Isotropic Radiation Pressure — $P=\varepsilon/3$
Newtonian Tidal Acceleration — $\Delta a = 2GMR/d^3$
Newtonian Circular Orbital Velocity — $v=\sqrt{GM_{enc}(r)/r}$
Weak-Field Light Bending — $\theta\approx4GM/(c^2b)$
Magnetic Dipole Field — $B=(\mu_0/4\pi)[3(\mathbf{m}\cdot\mathbf{r})\mathbf{r}/r^5-\mathbf{m}/r^3]$
Lorentz Force Law — $F=q(\mathbf{v}\times\mathbf{B})$
Spin Precession Equation — $dS/dt=-(g\mu_B/\hbar)S\times B$
QED Anomalous Magnetic Moment — $g=2(1+\alpha/2\pi)$
Fermi’s Weak Decay Rate Formula — $\Gamma_{weak}=G_F^2m^5/192\pi^3$ — real formula, misapplied in this series (13 orders of magnitude off for the neutron)
Friedmann Equation — $H^2=(8\pi G/3)\rho+\Lambda c^2/3$
CHSH Inequality and the Tsirelson Bound — CHSH $\le2\sqrt2\approx2.828$
One-Loop Beta Function (λφ⁴ Theory) — $\beta(\lambda)=3\lambda^2/16\pi^2$
Semi-Empirical Mass Formula — $B/A=a_V-a_SA^{-1/3}-a_CZ(Z-1)/A^{4/3}-a_A(N-Z)^2/A^2$
Bohr-Wheeler Fissionability Parameter — $(Z^2/A)_{crit}=2a_S/a_C$

Unproven

PBT’s own claims. Not automatically wrong — but no independent derivation or experimental confirmation exists yet, and in several of these cases, this site’s own audits found the formula doesn’t reproduce its own paper’s claimed numbers, or isn’t even dimensionally consistent, when checked directly.

Hierarchical Energy Density Scaling — $\varepsilon(l)=\varepsilon_0(l_0/l)^\gamma$
Effective Gravitational Coupling — $G_{eff}(l)\approx\varepsilon(l)\sigma(l)^2/(4\pi m(l)^2)$ — found to be a normalization of the theory’s own free parameters, not an independent prediction
Rotation-Curve Effective Gravity — $G_{eff}(r)=G[1+k(r/r_0)^\gamma]$ — found to be off by ~32x (Paper 1) and ~2x (Paper 4) from its own claimed output
Black-Hole-Collapse Stabilization ODE — found not to stabilize at its claimed scale at all
Asymmetry-Term Ladder Toy Model — one real, exact partial result (the quadratic form) inside an otherwise unproven derivation
Vorticity Spin Quantization — $\omega=\nabla\times v$, spin as literal fluid vorticity
Aether Spin/Entanglement Coupling Lagrangians — real Dirac Lagrangian plus PBT’s own unconfirmed coupling terms
Aether Flux Evolution Equation — $\nabla_\alpha u^\mu\approx\delta_{flux}/flux_0$
Λ_QCD as a Pressure/Density Ratio — found to be dimensionally inconsistent as written
Proton Decay Suppression Estimate — found to be on the wrong side of the real Super-Kamiokande bound
Higher-Spin Fronsdal-Aether Coupling — builds on a real but itself-unconfirmed framework (Vasiliev-Fronsdal higher-spin theory)
Grand-Unification Coupling Convergence — real RG technique, unconfirmed GUT-scale unification claim

See the Catalog for how whole theories are classified, and Established Physics for the real theories several of the Proven formulas above are drawn from.