Aphanics at the Pathion Level: Spectrum Stratification and the Universal Clifford Triad

We extend the Aphanes framework from the sedenion algebra 𝕊 to its Cayley–Dickson double, the pathion algebra ℙ = 𝕊 ⊕ 𝕊·ℓ of dimension 32. At sedenion level, prior work establishes that for any aphanic basepoint p the closed-form Berry curvature operator C_{a,b}(p) has a four-dimensional kernel structure giving F(p) ≅ u(1) ⊕ su(2) and a G₂-equivariant rank-4 closure. Lifting these results to pathion exposes structurally new phenomena: the Gram operator G_p = L_p^⊤ L_p has spectrum {0, ‖p‖², 2‖p‖²} at dyadic basepoints and an eight-valued spectrum at generic aphanics. We establish two theorems describing the kill set of a ↦ C_{a,∗}(p); in each, the containment (sufficiency) direction is proved symbolically, while the exact kill-set dimension (necessity) is certified numerically (Appendix A). The Pathion Universal Kill Set Theorem states that at every pathion-aphanic p with dim K_p = 4, this kill set is exactly the three-dimensional space q_p^univ = span_ℝ{p, ℓ₁₆, ℓ₁₆·p}. The Pathion Q-Centralizer Vanishing Theorem at Dyadic Basepoint states that under the additional hypothesis of a three-valued Gram spectrum of canonical Stratum-II type, the kill set extends to a five-dimensional space q_p^(32) ⊃ q_p^univ. Both theorems follow from a structural result which is the heart of this paper: the three operators L_p, L_{ℓ₁₆}, L_{ℓ₁₆·p} form a pairwise anti-commuting Clifford triad on ℙ. We prove this Triad Theorem algebraically, reducing the third pair to a sedenion identity Δ(s₁, s₂) = 0 for orthogonal imaginary s₁, s₂ ∈ Im(𝕊), which in turn reduces by a four-block Cayley–Dickson decomposition to a three-variable octonion identity Ω(A, B; c) = 0. The latter falls to a two-line argument from polarization, Artin's theorem on two-generator subalgebras of the octonions, and the composition norm form. The dim-5 structure q_p^(32) = q_p^univ ⊕ q_p^anti is shown to be ℤ₂-graded: each summand is independently Clifford-internal at every aphanic basepoint, but mixed pairs across the grading do not anti-commute. Hence the dyadic-only extension to q_p^(32) uses a mechanism distinct from the universal Clifford triad. All symbolically proved identities are additionally certified numerically; each certification states its epistemic basis in Appendix A.