Hodge Target Identification Without Full Edge-Flow Reconstruction: Accounting-Constrained Inference for Signed-Net Economic Flows on a Declared Network Complex

We study whether the homology-class (harmonic) component of a partially observed signed-net economic flow can be identified without reconstructing the complete bilateral edge-value vector. The information structure consists of a declared finite oriented 2-complex K, independently observed node balances, and signed-net edge observations on a subset Ω. Node balances identify the gradient component exactly; after removing it, boundary-generated circulation remains an unrestricted nuisance, and P_Hx is the target. We prove a necessary-and-sufficient fixed-topology identification theorem: P_Hx is point identified if and only if the inclusion-induced map H₁(K_U; R)→H₁(K; R) from the unobserved-edge subcomplex is zero, equivalently if and only if every class in H¹(K; R) admits a cocycle representative supported on observed edges. This resolves the gap between full reconstruction and target identification: full residual reconstruction requires the unobserved graph to be acyclic, whereas harmonic identification permits hidden cycles precisely when they become boundaries in K. We define κ_H as the minimum number of observed signed-net coordinates sufficient for the target and obtain exact endpoint characterizations: κ_H=β₁ exactly when a curl-free coordinate cohomology basis exists, while κ_H=μ exactly when B₂=0; adding 2-cells can only weakly reduce κ_H for the newly defined topology-conditional target. A quotient singular-value coefficient γ_H separates algebraic identifiability from ill-conditioned recovery and yields deterministic edge-plus-margin error bounds, accounting-reconciliation bias propagation, and exact Gaussian GLS confidence regions under known covariance. The theorem machinery is checked by complete 4,096-mask annulus enumeration, an exact audit of 113 four-vertex complexes and 111 strict face-addition pairs, and a fully specified archived 1,000-mask stress test with zero decision-route discrepancies and zero identified-target recovery failures. The novelty claimed here is the accounting-conditioned target/nuisance architecture, its exact surviving-homology obstruction, and the resulting Hodge-specific disclosure endpoint structure—not a new Hodge decomposition, generic cohomological obstruction, coding-theoretic support invariant, or network-reconstruction method. These are fixed-topology identification results; no claim is made that real economic networks frequently satisfy the strict target-only regime, which remains subject to separately sourced margins, preregistered topology, and certified large-network validation.