The Standard Model accounts for fermion masses through Yukawa couplings, but thenumerical values and hierarchical pattern of these couplings remain external inputs. Thisarticle develops a geometric octonionic framework in which fermion-mass hierarchies areencoded in the spectrum of a projected non-associative vacuum operator. The constructionstarts from three octonion-valued fields, whose associator is promoted to a dynamicalvacuum quantity. A master action is formulated, its non-associative vacuum equationsare reduced in a canonical sector, and an algebraically motivated symmetry-breakingterm is introduced through a preferred associative quaternionic subalgebra and a Fanooriented vacuum direction. The resulting structure defines a self-adjoint associator numberoperator and a geometric spectral mass operator. Four closure statements are formulated:vacuum-scale closure, associator spectral closure, projector normalization closure, andRG reconstruction closure. The main result is not a claim of experimentally proven exactfermion masses, but a mathematically explicit framework in which exact masses wouldfollow once four closure blocks are solved without additional phenomenological input: theabsolute octonionic vacuum scale, the exact associator Hessian spectrum, the projectornormalization of the fermion sectors, and the renormalization-group matching to measuredmass conventions. In the minimal Fano-plane vacuum, the linearized associator matrix isevaluated explicitly and yields the non-zero spectral levels 4,8,12, i.e. the normalizedgeneration skeleton N1 : N2 : N3 = 1 : 2 : 3. A charged-lepton benchmark then shows howthe same spectral template can reproduce the measured e,µ,τ hierarchy once the sectorinvariants are fixed. The paper therefore provides a controlled route from octonionicnon-associativity to fermion mass hierarchies and identifies the remaining mathematicalrequirements for a parameter-free mass prediction. In its final form the closure programis strengthened by an explicit full-Hessian decomposition, a projector-uniqueness theoremmodulo the vacuum stabilizer, a finite charged-lepton trace test, and a component-levelcontraction formula for the lepton Hessian moments that makes the no-fit criterionoperational before comparison with observed masses.