The Electromagnetic Cascade: Wave Structure, Spectral Architecture, and the Hydrogen Spectrum from Bilateral Stella Geometry

The Electromagnetic Cascade:

Wave Structure, Spectral Architecture, and the Hydrogen Spectrum

from Bilateral Stella Geometry

Kevin Birke Packler1 & Claude Sonnet 4.62 (Anthropic)

1Aureole Foundation, Wake Forest, NC

2Anthropic AI Systems

Companion to Cosmic Egg Theory v22·September 2026

Abstract

We derive the full wave structure of the electromagnetic field from the bilateral

Stella geometry established in Cosmic Egg Theory v22, closing four formal gaps

left open by that framework and recovering the spectral architecture of classical

and quantum electrodynamics without additional postulates.

Beginning from the bilateral substrate field equation □Φ = 0 and the parity

constraint Φ(−x,t) = Φ(x,t), we prove that the only bilateral-symmetric solu-

tions are standing waves—identifying particles as symmetric-sector resonances of

the bilateral field. Propagating electromagnetic waves are shown to be bilateral-

symmetry-breaking excitations left in the substrate by a moving Stella, with dis-

persion relation ω= ck forced by the ground-state geometry.

Extending the scalar treatment to the bilateral 4-vector field Aµ, we show that

the Lorenz gauge condition ∂µAµ = 0 is a direct consequence of the bilateral

balance condition established in Step 8 of CET. The photon polarization count

Npol = 2 is proved via a Span Theorem on the Stella’s four tetrahedral axis pro-

jections. Circular polarization states are identified with the T1 and T2 tetrahedra;

photon spin ±ℏ follows from the 60◦bilateral rotation of Step 4.

The cascade-frequency correspondence λN = 2πℓP·2N establishes that each

step in the Packler attenuation cascade corresponds to one octave in electromag-

netic frequency. Wien’s displacement law, the Stefan-Boltzmann T4 radiation law,

and the Planck distribution are recovered as direct consequences of the cascademode structure and bilateral occupation statistics.

The Rydberg formula is expressed in cascade coordinates as Nγ(n1,n2) =

RCET−log2(1/n2

1−1/n2

2), where RCET = Ne+ 1 + 2 log2(α−1). Fifteen hydrogen

emission lines spanning five spectral series are confirmed to sub-percent precision.

The virial theorem ⟨T⟩=

1

2 |⟨V⟩|for Coulomb binding is derived directly from the

bilateral balance condition, closing the ”+1” in RCET from pure bilateral geometry

with no classical mechanics import.

Four Zero Free Parameter results are established or upgraded: Wien’s dis-

placement law (zfp Row 22), the Stefan-Boltzmann T4 law (zfp Row 23), the

Rydberg cascade formula (zfp Row 24), the virial theorem for bilateral bound

states (zfp Row 25), and the polarization count upgraded from stated to proved

(zfp Row 20 upgrade). No free parameters are introduced beyond those already

entering v22.