| Description: |
The Kansūron modification of Euler’s identity — the K-wave identity —reinterprets natural numbers as rotating vectors whose overlaps generate deterministicstructures on the time axis. When applied to atomic structure, these overlaps reproducethe observed electron shell sequence as natural resonance plateaus. The result is nota final proof, but an initial conceptual derivation that situates shell filling within auniversal harmonic law. This work is presented as a first recorded attempt to connectKansūron number-theoretic framework with atomic physics, establishing historicaltraceability for future refinements. . v1.0.1 adds DOI and typography fixes ; v1.0.3 — camera-ready: Corrected abstract; restored full body; expanded Discussion; revised Historical Note and Conclusion; normalized \Kansuron{} macro; minor typography fixes. ; @misc{hedges2025_atomic_harmonics_v103, author = {Dean Hedges}, title = {Atomic Harmonics and the Shell Rule (2, 8, 18, 32 …): Exploratory Derivations from Kansūron Overlap Equations}, year = {2025}, version = {1.0.3}, publisher = {Zenodo}, doi = {10.5281/zenodo.17096054}, url = {https://doi.org/10.5281/zenodo.17096054}, note = {With technical contributions from ChatGPT (OpenAI)}} |