We give an exact arithmetic and representation-theoretic description of a finite Weil filtration generated by three-character Heisenberg fingerprints. For every odd prime q and non-zero total character c=c₁+c₂+c₃, the cumulative Fourier mode set at depth n is the cyclic sumset \ Kₙ=c[- (n+1), n+1+\0, (c₂+c₃) \+\0, c₃\. \] This closed form turns the filtration into a union of at most nine cyclic intervals. It yields an exact spacing criterion for boundary porosity and reduces the full Weil stabiliser to the multiplicative symmetry group of Kₙ. Weyl quantisation then identifies the induced Mackey carrier internally as a direct summand of End (Cq). Its generic principal-series constituents occur in canonical multiplicity-two pairs with commutant M₂ (C). The finite Harper operator selects one axis in every such doublet and produces the universal normalised split 1 q^-1/2. The eliminated-sector residue supplies a second axis precisely when an explicit cyclotomic phase determinant is non-zero. The odd Weyl-symbol sector is itself a pure doublet reservoir for q14, but it is exactly protected by the parity-even algebra generated by the deposited projectors and Harper dynamics. An orbit-divisibility sieve constrains every multiplicative stabiliser, and uniform constructions give exact C₄ and C₆ exceptional families, together with a third, near-saturation C₄ family with four-point complement. An unconditional almost-periodicity lemma shows that every multiplicative stabiliser shifts the mode set with additive defect exactly twice the run count, and a run-correspondence argument with a Diophantine descent proves that the stabiliser is \1\ whenever every run and gap of the mode set is longer than the run count. Completeness of the exceptional orders is thereby reduced to a degenerate boundary regime; exhaustive finite audits find no order beyond six there through q=73 and also expose exact vanishings of selected boundary character sums. Interpretive status. The construction supplies finite two-level spectral splitting, mixing frames, and mass-square kinematics at an operator stratum. It does not derive Dirac masses, an absolute mass scale, Standard-Model generations, hypercharge, or a matter-sector Higgs mechanism.
Jérôme Beau (Tue,) studied this question.