TEBAC Hodge Program V: Primitive Detector Singularities, Boundary Chow Supply, and Terminal Packet Rank Closure

This master preprint consolidates Module V of the TEBAC Hodge program. It unifies the terminal proof-front submodules V-A through V-W into a single synthesis devoted to primitive detector singularities, boundary Chow supply, Chow--Hilbert source realization, detector-faithfulness, moving-face escape, and finite boundary packet rank closure. The manuscript works with the terminal primitive quotientXᵖ studies nonzero terminal detectors\0 (VXᵖ) ^. \ The central proof-front is the construction of boundary Chow--Hilbert packets whose specialization is visible to \ (\). The resulting target chain is0&-normalized boundary singularity \\&--Hilbert boundary source \\& boundary packet \\& (Sp_[B) 0. aligned\] The preprint develops the formal reduction from admissible normal-function singularities to boundary Chow packet visibility, including kernel descent, detector-compatible boundary evaluation, scalar boundary residues, primitive source noncancellation, moving-face detector escape, and rank-one packet generation. The terminal finite-dimensional condition is expressed as_ a=_ (_), , a0. \ The manuscript is status-explicit. It does not claim that the Hodge Conjecture is already unconditionally proved. Instead, it identifies the remaining non-formal theorem target as the explicit detector-selected boundary packet construction: \_ (_) _ (P_) _ (L, ). \ Conditional on this terminal packet construction, the established rank-closure mechanism yields the expected TEBAC terminal implication ₐ Gₗ, ₏=VXᵖXᵖ=0Xᵖ=Aᵖ (X). \