UED Reconstruction Programme — Paper 6: Atomic Configuration and Spectral Resolution

Paper 6 of the UED Reconstruction Programme reconstructs atomic configuration and optical spectroscopy from the persistence architecture established in Paper 5 together with the optical and event architecture developed in Papers 3 and 4. An atomic state is treated operationally as a persistent, distinguishable internal configuration basin rather than as a pre-assigned orbital, wavefunction, or particle trajectory. Each persistent basin is assigned an effective configuration energy EaE_a, and stable states satisfy a stationary condition with positive second variation on non-symmetry directions. When a resolved optical event connects two persistent configurations, the observed spectral line follows the gap relationhνab=∣Eb−Ea∣h\nu_{ab}=|E_b-E_a|.A bound-to-continuum transition is represented by a thresholdΦa=Ec−Ea\Phi_a=E_c-E_a,with excess outgoing kinetic consequence given byKout=hν−ΦaK_{\text{out}}=h\nu-\Phi_awhen the channel is open. The paper separates transition energy from transition strength. A transition-sensitivity functional provides an operational route to selection rules, while finite transition coherence generates a Lorentzian spectral profile with linewidth determined by the coherence time. Environmental changes shift line centers through changes in configuration-energy differences, making spectroscopy a probe of changed configuration geometry. Population kinetics are represented through a configuration-transition network. Absorption, emission, continuum thresholds, line strength, linewidth, and environmental shifts are therefore reconstructed as distinct properties of persistent configuration and coupling. The paper does not derive Planck’s constant, real atomic basin geometry, electric charge, or magnetic response. Its purpose is to establish the minimum mathematical architecture that any later microscopic UED atomic model must reproduce before claiming explanatory closure.