Spectral Reordering of the Periodic Table: M3(C) Automorphism Classes as the Algebraic Foundation of Chemical Periodicity

The periodic table of elements, established empirically by Mendeleev in 1869, has been explained post-hoc by quantum mechanical electron configuration rules. Its primary ordering axis — atomic number Z, a count of protons — presupposes particle ontology at every level. Several structural anomalies persist within this framework: hydrogen's dual chemical character, helium's ambiguous placement, and the discontinuous displacement of lanthanides and actinides from the main table body. These anomalies have no Tier-1 justification within the current framework. This paper derives the periodic table from the automorphism structure of the unique minimal non-commutative algebra M₃(ℂ) of Cognitional Mechanics (CM), with zero free parameters. Elements are classified by their spectral resonance class — the equivalence class of M₃(ℂ) Cartan configurations under the automorphism action — rather than by atomic number Z. Four primary Cartan sets S1–S4 are derived from Axioms A1–A3, and their composite resonances generate the full element sequence. The period lengths 2·8·8·18·18·32·32 emerge from the A3 cyclotomic invariants Φ₃ = 13 and Φ₆ = 7 via the slot formula N_ℓ = 2 + 4(ℓ−1), where the increment 4 = n+1 follows from the A1 dimension n = 3. Zero free parameters are introduced. The nuclear stability maximum of iron-56 and the chemical basis of carbon-based life are established as algebraic necessities of the M₃(ℂ) automorphism structure. The three anomalies of the current periodic table are dissolved as Tier-3 projection artifacts. This paper presupposes the chemical projection framework established in the companion paper (DOI: 10.5281/zenodo.19122094). Files