P1PROVEN
Deriving the Schrödinger Equation from a Compressible Fluid Theory
The Schrödinger equation for hydrogen is derived from four physical axioms, without assuming any result from quantum mechanics. The derivation proceeds through Nelson stochastic mechanics, with all three required inputs — the diffusion coefficient, the Coulomb potential, and the Born rule — derived independently from IWT's axioms.
What this establishes — Schrödinger emerges from four physical axioms. No quantum postulates required as inputs.
P2PROVEN
A Physical Derivation of the Exponential Gravitational Metric and the Classical Tests of General Relativity
IWT derives the exponential gravitational metric from a Beer-Lambert shadowing argument: matter atoms attenuate the GM flux multiplicatively, producing an exponential EM density profile. All five classical tests of General Relativity are then derived and numerically confirmed, with the exponential (Yilmaz) metric numerically identical to the Schwarzschild metric at every tested order.
What this establishes — GR's five classical tests pass. The exponential metric follows from Beer-Lambert attenuation — a physical mechanism no prior treatment provided.
P3PARTIAL
The Physical Model of the Electron: A Three-Layer Topological Vortex
The electron is described as a three-layer Hopf vortex in the EM medium, with three nested length scales — the classical electron radius rₑ, the Compton wavelength λ_C, and the Bohr radius a₀ — separated by exactly α at each step. Two internal self-consistency conditions are derived exactly. The hydrogen spectrum is rederived from pressure balance. The proton mass ratio mₚ/mₑ = 1836.15 is derived to 0.003%.
What this establishes — The electron's three-scale structure is self-consistent, and the nested ratios encode a single self-similar topology. The proton-to-electron mass ratio follows from this picture.
P4PROVEN
The Feynman Path Integral from GM Pre-Sampling
The Feynman path integral is derived from IWT's three-layer medium structure in four steps: the Kac theorem (exact mathematics) connects the Feynman integral to the Wiener integral under Wick rotation; D = ħ/(2M) is derived from the IWT Weizsäcker equation of state; the GM layer maintains the EM vacuum at non-zero density everywhere; and GM's faster-than-c propagation pre-establishes boundary conditions before any EM event — the physical mechanism for 'sampling all paths.'
What this establishes — The imaginary phase exp(iS/ħ) in the path integral is the Wick rotation of Brownian motion. The GM medium pre-sampling is the physical mechanism Feynman described but could not explain.
P5CONFIRMED
Multi-Electron Structure and Molecular Validation: The Weizsäcker Functional as Kohn-Sham DFT
The multi-electron Schrödinger equation is derived in 3D from the IWT N-electron Weizsäcker functional, without 3N-dimensional configuration space. The central result is the algebraic identity T_W = T_standard for any nodeless orbital — exact, proven in one line — which establishes that the IWT functional is identical to the Kohn-Sham DFT functional. Helium energy is computed to 0.39%, H₂ bond length to 0.05%, and six molecules give bond lengths within 1% and angles within 0.3° of experiment.
What this establishes — IWT is the physical realisation of the Hohenberg-Kohn theorem. Every KS-DFT result is simultaneously an IWT result, derived in 3D without configuration space.
P6PROVEN
Lepton Mass Ratios from Hopf Topology: A Derivation from Two Integers
All three charged lepton mass ratios are derived from two integers alone — N_q = 3 (quark colours) and N_gen = 3 (fermion generations) — through the Koide-Brannen parametrisation with phase angle θ_K = 2/9. The predictions are mμ/mₑ = 206.770 (0.001% error), mτ/mₑ = 3477.47 (0.007% error), and mτ/mμ = 16.818 (0.006% error). No free parameters appear anywhere; α does not enter.
What this establishes — Lepton mass ratios follow from colour and generation structure alone. N_q = 3 is shown to be the unique integer consistent with the observed muon-to-electron mass ratio.
P7IN PROGRESS
The Fine Structure Constant: Diagnosis, Partial Derivation, and the Road Forward
The most complete account of α = 1/137.036 within IWT: four physical perspectives on what α is, a fixed-point equation derived from three simultaneous physical conditions that gives 1/α = 135.615 with the Rankine core (1.04% error) and 1/α = 137.036 exactly with the correct Hopf soliton core constant C_Hopf = 0.21343. The single remaining step is computing C_Hopf from the 3D Hopf profile integral — a well-posed numerical PDE problem.
What this establishes — A fixed-point equation containing α as its unique solution has been derived. The gap is reduced to one computable number: the Hopf soliton core constant C_Hopf.
P8CONFIRMED
The Anomalous Magnetic Moment of the Electron from Hopf Vortex Mechanics
g = 2 exactly is derived from the Q_H = 1 Hopf soliton structure of the electron — no approximation, no dependence on α. The Schwinger correction aₑ = α/2π is derived from the interaction of the electron's Hopf soliton with the EM vacuum through virtual Hopf-pair creation. The four-loop QED series in IWT gives aₑ = 0.0011596522, matching experiment to 11 significant figures.
What this establishes — g = 2 is not an algebraic accident of the Dirac equation — it is a physical consequence of the electron being a toroidal current loop with half-integer Hopf winding number.
P9PARTIAL
Quark Mass Structure: Geometric Nesting, the Koide Obstruction, and the Role of QCD Confinement
The lepton Koide formula does not extend to quarks — and the precise reason is identified. Quarks have no pole masses; their MSbar masses run strongly under QCD renormalisation, distorting the EM topological signal by a factor α_s/α ≈ 54. In place of the failed Koide extension, two clean quark mass predictions from IWT geometric nesting are found: mₓ = m_t·α = 1260 MeV (PDG: 1270 ± 20 MeV, 0.5σ) and m_u from constituent quark scaling (0.3σ from PDG).
What this establishes — The Koide obstruction for quarks is precisely diagnosed. Two quark mass predictions from IWT nesting work cleanly at the level of QCD uncertainties.
P10CONFIRMED
Hydrogen Fine Structure from the IWT Klein–Gordon Envelope
The complete hydrogen fine structure is derived from the IWT Klein–Gordon equation by retaining the second time-derivative term that Paper 1 discarded. This generates the complete Pauli Hamiltonian at order α²: a relativistic kinetic-energy correction, a Darwin term, and spin-orbit coupling. The 2p fine-structure splitting is computed as 0.04528 meV, within 0.15% of the experimental value 0.04537 meV (Lundeen & Pipkin 1981).
What this establishes — Hydrogen fine structure (all three O(α²) corrections) derived from IWT Klein–Gordon envelope with no additional assumptions. Lamb shift is physically identified and computed to 4% in leading-log approximation.