Large Language Models (LLMs) often generate specious hallucinations, creating an urgent need for post-hoc factuality verification against reliable evidence. Existing verification methods incur substantial computational overhead due to joint evidence–claim encoding. While bi-encoders offer a highly efficient alternative, they struggle with asymmetric entailment and are severely vulnerable to contextual noise. To address these challenges, we propose Gated Residual Discrepancy (GRD), a highly efficient bi-encoder framework for factuality verification. To explicitly capture asymmetric entailment, GRD pioneers a difference-dominant paradigm, extracting dual-view vector differences. To mitigate the vulnerability to contextual noise, GRD employs an adaptive gating mechanism that dynamically filters contextual noise, preventing large semantic backgrounds from masking critical errors, thereby enabling highly sensitive verification over broad evidence contexts. Experiments across various benchmarks show GRD achieves 79.99% average Macro-F1, trailing the strongest cross-encoder baseline by only 1.15 points while delivering a 23.55× speedup with only a fraction of the computational FLOPs.

As Large Language Models (LLMs) increasingly generate reasoning-driven outputs that weave isolated events into intricate logical topologies, factuality depends not only on isolated atomic facts but critically on the faithful relations connecting them. However, current verification paradigms prioritize individual facts and remain fundamentally blind to relational distortions. This oversight creates a dangerous false sense of security, where verifiers inadvertently endorse relationally corrupted claims simply because their constituent events are factual. Furthermore, the community lacks a systematic benchmark to evaluate this crucial relational layer. To address these critical vulnerabilities, we introduce BeyondAtoms, a novel benchmark for relational fact verification. Our evaluations reveal that generic verification pipelines often fail by misclassifying relational manipulations as supported. While explicitly guided reasoning models can resolve these structural errors, they incur prohibitive computational costs. To counter this pervasive relation blindness, we propose CARVE, a completely training-free verification framework. By decoupling structural dependencies through deterministic extraction and bi-directional relational alignment, CARVE achieves a favorable accuracy–efficiency trade-off: it remains highly competitive on relational and general fact verification while avoiding the heavy inference cost of reasoning-based LLMs.