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 quotient\[V_X^p\]and studies nonzero terminal detectors\[0≠ λ∈ (V_X^p)^ .\] The central proof-front is the construction of boundary Chow--Hilbert packets whose specialization is visible to \(λ\). The resulting target chain is\[{aligned}0≠λ&-normalized boundary singularity \&--Hilbert boundary source \& boundary packet \&λ(Sp_τ[B])≠0 .{aligned}\] 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\[T_τ a=δ_τ(ν_λ),λ,τa≠0.\] 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:\[δ_τ(ν_λ)_τ( P_τ)_τ( Lλ,τ).\] Conditional on this terminal packet construction, the established rank-closure mechanism yields the expected TEBAC terminal implication\[spanQ GX,p=V_X^p_X^p=0_X^p=A^p(X).\]