Atomic Structure
Derive how electron knots change atomic orbitals, exchange discrete energy, obey selection rules, and produce the observed spectral lines within the Graviton Mesh.
The Problem
HGUT interprets orbitals as physical dynamical corridors or allowed configurations in the organized Mesh. The open problem is to show exactly how an electron leaves one allowed state and arrives in another, what occurs during the transition in underlying time, how energy and angular momentum are transferred, and why the observed transition spectrum is discrete.
Scientific Importance
Orbital transitions connect the electron, the atom, light emission and absorption, spectroscopy, and the quantum measurement process. They are a direct arena in which HGUT's mechanical picture must reproduce precise data.
Progress Ledger
A corridor-based interpretation of orbitals has been proposed.
The electron is treated as a stable topological structure rather than a probability cloud.
Transitions have been discussed as movement between allowed lanes rather than residence in forbidden half-states.
No complete field-level transition trajectory, rate law, or selection-rule derivation has yet been established.
Pass-or-Fail Structure
Every gate must be addressed before this problem can be considered closed. Partial success does not establish the complete identification.
Derive an orbital as a stable atom-Mesh-electron configuration.
Specify the continuous underlying dynamics connecting two discrete stationary outcomes.
Derive absorption and emission of the exact transition energy.
Recover allowed and forbidden transitions from topology and symmetry.
Derive spontaneous and stimulated rates, lifetimes, and line widths.
Recover observed atomic spectra and fine structure within stated accuracy.
Definition of Success
This problem closes only when the following conditions are satisfied together.
Stable orbital configurations are derived from the atom-Mesh equations.
A complete transition trajectory is obtained without forbidden stationary occupancy.
Energy and angular momentum remain conserved throughout the process.
Discrete spectral energies and selection rules are recovered.
Spontaneous and stimulated rates agree with observation.
Emission and absorption connect consistently to the completed light sector.
Prerequisites
Open Collaboration
Connected Research
Matter and Particle Closure
Determine whether a stable, charged, finite-energy Q=1 Hopf-type Harrison Knot reproduces the complete physical identity of the electron.
Quantum Foundations
Derive why identical electron knots cannot occupy the same complete quantum state and recover the many-electron exclusion structure from topology, exchange, and orbital corridors.
Light and Transport
Derive light completely as a transported HGUT process, including propagation, polarization, energy and momentum flow, interference, emission, absorption, and quantized exchange.
The Question Remains Open
Successful arguments, failed attempts, independent simulations, corrections, and falsifying evidence all move the research program forward.
