Hydrogen is not one problem. It is a firing squad.

Hydrogen is where quantum orthodoxy expects the classical program to die. Fine. Then hydrogen is where we stop arguing by reputation and force both stories onto the same phase-space map.

First: publish the wound

Standard stochastic electrodynamics is not a finished answer. Long numerical and analytical work by Theo Nieuwenhuizen found that the ordinary Coulomb hydrogen atom in standard SED self-ionizes; his 2020 study reports that several noise-renormalization attempts do not cure it. That red cell stays public.

Then demand the spectrum

A first executable crack: phase closure, not energy quantization

A continuous phase field on a closed Coulomb orbit cannot return with an arbitrary phase mismatch. Single-valued closure permits integer winding numbers. If one further assumes a single action scale S relating field phase to momentum and frequency—p=S k and E=S ω—ordinary Coulomb orbital balance yields rₙ∝n² and Eₙ∝−1/n². No discrete energy levels are inserted as a separate rule.

The executable test uses only the observed unresolved NIST Hα line to calibrate S, then freezes it. It predicts n=4…10 with 0.0493 cm⁻¹ holdout RMSE and maximum residual 1.63σ; the fitted action scale is S=0.999903 ħ. That is genuine gross-structure prediction after one calibration.

The candidate does not yet derive p=S k or E=S ω from deeper field dynamics; it supplies no attractor that stabilizes the winding modes against radiation; and it has not paid for fine structure, Stark/Zeeman splitting, selection rules, strengths or lifetimes. Its public status is therefore GROSS_STRUCTURE_PHASE_CLOSURE_ONLY.

Open the executable phase-closure receipt.

Now the action scale has a mechanism candidate

Timothy Boyer's 2026 classical-electrodynamics preprint closes one of the largest holes in that toy. For a relativistic charged particle in a circular Coulomb orbit driven by Lorentz-invariant classical zero-point radiation, he explicitly calculates radiation power gained and lost and obtains the balance condition Jφ = Jrad = ħ. The scale is therefore no longer fitted to Hα in this mechanism: it enters through the empirically normalized classical zero-point field and emerges as the balanced ground-orbit action.

Our source audit catches the next step: the excited-state section introduces Jₙ=nJ₁ before arguing that repeated radiation sweeps supply the required resonant power. We therefore classify it GROUND_ACTION_BALANCE_DERIVED_EXCITED_SELECTION_PARTIAL. There is not yet a demonstrated stochastic attractor calculation showing arbitrary initial actions collapse onto only the integer sequence, and average power balance does not erase the published SED self-ionization problem.

There is also an immediate numerical warning. Applying the preprint's simple circular integer-action energy formula directly to the preserved unresolved Balmer ledger misses it by about 6.08 cm⁻¹ RMS with electron mass. So the mechanism earns the ground action scale; it does not inherit the full spectrum by declaration. Open the audit receipt.

One stable direction is not a stable atom

We can now sharpen the 2026 result. Substituting Boyer's circular-orbit frequency into his mode-by-mode gain and loss powers gives Pgain/Ploss=Jrad/J. Because dU/dJ=ω>0, the mean action drift points upward for J<ħ and downward for J>ħ. In normalized form, after absorbing only a positive prefactor into a nonphysical time coordinate, dj/ds=1/j−1. Every tested circular initial action on both sides converges to j=1. Open the circular-drift receipt.

The hostile control survives intact. In the published standard-SED eccentric limit, the mean energy change per orbit becomes proportional to [0.588084−L/ħ]; sufficiently eccentric near-ionizing trajectories below that angular momentum are driven outward. The critical perihelion is about 0.1729 a₀. Open the RED control.

Boyer's preprint does not yet give the missing bridge: no diffusion tensor for (Jr,Jφ), no stochastic radial-action/eccentricity law, and no long-time capture/escape process. We therefore publish INSUFFICIENT_DYNAMICS_FOR_STOCHASTIC_STABILITY rather than inventing a simulation. Off-integer excited-state capture is likewise undefined by the published equations: OFF_INTEGER_SELECTION_UNDEFINED_EXCITED_PARTIAL. Stochastic audit · excited-state audit.

A magnetic coefficient that is not uniquely spin

Boyer's follow-up magnetic-field preprint proposes two resonant circular branches, clockwise and counter-clockwise. With |Lz|=ħ, the classical orbital calculation gives branch shifts ±μB B, hence total separation 2μB B—the familiar leading electron two-state magnetic separation. That coefficient therefore does not, by itself, uniquely diagnose intrinsic spin ontology.

But the coefficient is the easy part. The preprint has not yet produced a quantitative stochastic evolution from a generic ensemble into exactly two stable populations with the observed weights, beam profiles, hyperfine structure and anomalous corrections. Coefficient status: ZEEMAN_COEFFICIENT_MATCH_SELECTION_MECHANISM_PARTIAL; population status: TWO_BRANCH_COEFFICIENT_ONLY_POPULATION_DYNAMICS_UNDEFINED. Coefficient audit · population audit.

The historical cracks are useful—but not enough

Sommerfeld’s old quantum theory famously obtained the hydrogen fine-structure formula using relativistic elliptical orbits, a historical warning that a successful formula does not uniquely certify the later ontology. But old quantum theory imposed quantization conditions, so it does not satisfy this project’s fully classical ontology contract. It is evidence against simplistic historiography, not a completed reconstruction.

The Stark effect is even more instructive. Hooker, Greene and Clark found that a classical hydrogen-orbit treatment can reproduce the linear Stark energy shift accurately given appropriate initial conditions, while the quadratic Stark effect fails except toward the correspondence limit. That gives us a precise green/red boundary instead of a slogan.

Semiclassical success must stay labeled semiclassical

A 1999 semiclassical random-electrodynamics calculation uses a classical zero-point electromagnetic field but quantum atomic states. It recovers the Einstein A coefficient and the nonrelativistic QED Lamb shift. Valuable? Yes. A fully classical atom? No. The scoreboard credits the electromagnetic mechanism without laundering the matter model.

Atomic audit, v0.3

Primary controls

Nieuwenhuizen (2020): standard SED hydrogen self-ionization
Hooker, Greene & Clark (1997): classical Stark effect
Semiclassical random electrodynamics (1999): spontaneous emission and Lamb shift
NIST: Sommerfeld and the fine-structure constant

Do not ask whether a classical atom can be imagined. Ask whether one set of objective dynamics can survive this entire table.