Chemical Bonding as M3(C) Spectral Resonance: Logical Necessity of Redefinition Following Particle Ontology Elimination in Cognitional Mechanics

Chemical bonding has been defined, since the early twentieth century, in terms of electron sharing and Coulombic interaction between charged particles. This definition presupposes particle ontology at every level. Cognitional Mechanics (CM) establishes that particles are not ontological primitives but Tier-3 projections of Tier-2 spectral structure generated by the unique minimal non-commutative algebra M₃(ℂ). Once particle ontology is eliminated — as demonstrated in the companion paper "Particles Are Unnecessary" (DOI: 10.5281/zenodo.18810386) — the standard definition of chemical bonding becomes logically unavailable. A definition built on Tier-3 artifacts cannot serve as a foundational account of Tier-2 structure without circularity. This paper provides the necessary reconstruction. Chemical bonding is redefined as a spectral resonance condition between two M₃(ℂ) operational domains, governed by the chemical projection constant n_A = 36 derived from Axiom A2 alone. The spectral coupling constant ξ ≡ μα — the unique Tier-1 composite in which particle-ontological prerequisites cancel — connects the mass-hierarchy and electromagnetic projections of M₃(ℂ) to the chemical energy scale without invoking particle concepts. Bond energy ratios between molecular species are parameter-free, falsifiable Tier-1 predictions derived from the A3 cyclotomic invariants Φ₃ = 13 and Φ₆ = 7. Absolute energy scales remain Tier-3 quantities requiring empirical calibration; this is a structural consequence of the Tier architecture, not a limitation. The periodic table admits a spectral reordering, developed in the companion paper on chemical periodicity, in which the anomalies of the particle-indexed arrangement are dissolved as projection artifacts.