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 a short boundary character sum over at most four hole pairs is non-zero: a Galois separation theorem eliminates the cyclotomic phase determinant for every generic character, and the vanishing locus of the boundary sum is completely classified into antipodal-pair, cube-triple, and double-pair mechanisms. 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 an unconditional almost-periodicity lemma, a run-correspondence argument, and a Diophantine descent prove 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, where a fourth-moment argument proves that every proper Gaussian box has exact stabiliser C₄, and a free four-point complement orbit has the same exact stabiliser. An exhaustive audit through q=151 finds 75 exceptional sets, all of order four or six and all within three refined mechanisms, with no order eight at q=193, 241, 257. Finally, the porous depths of a uniform block converge to an explicit point process, with count law (3/20, 7/24, 9/40, 5/24, 1/8), mean 28/15, and piecewise affine intensity. 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 (Thu,) studied this question.