Beyond Bohr Atomic Structure: Laws and Reformulation via Ziwave Dynamics

The Bohr model describes atomic structure via discrete orbits K, L, M, N withoutdefining an underlying sample space. We identify this as a foundational flaw: a dynamicswithout a stage. We introduce Stage = Sample Space = Ω with partition Ω = (Ω \\ΩC ) ∪ ΩC , and reformulate the electron via mapping and certified domain: ZDM: Z(t) =MZ [I] + ∆(t) and ZBPT: ΩC = ∆−1(0).In this framework, Ziwave zt evolves on Ω \\ ΩC and certifies as Avatar m = MZ [I] onΩC . Four laws — orbital, transition, duality/bonding, and periodic — are shown incom-plete without Ω using a Law / Error / Correction / Proof pattern. The periodic tableis reinterpreted as a hierarchy of certification capacities Ω(n)C , not empirical occupancy2, 8, 18, 32, and Nn = 2n2 is derived as |Ω(n)C | = 2n2.