Financial numerical reasoning demands rigorous adherence to domain-specific logic and precise evidence foundation.However, large language models (LLMs) are prone to forced generation when confronting ambiguous evidence or complex recursive dependencies, often hallucinating values to bridge information gaps.To address this, we propose graph-bounded financial reasoning (GBFR), a neuro-symbolic framework that imposes semantic and structural constraints via a financial metric knowledge graph (FMKG).Unlike sequential generation paradigms, our approach employs a parallel graph-constrained reasoning algorithm that orchestrates specialized operators to simultaneously explore heterogeneous derivation paths of complex financial metrics.Through cross-path verification, the framework aggregates only semantically consistent results, ensuring reasoning is bounded by available context.Crucially, this approach enables safe abstention by distinguishing genuine data absence from retrieval failure, thereby preventing ungrounded fabrication.To evaluate this capability, we further construct counterfactual samples by perturbing entities, times, and metrics to synthesize unanswerable scenarios.Empirical evaluations on standard benchmarks demonstrate that GBFR significantly outperforms state-of-the-art baselines.

Real-world networks containing hyper-relational facts can be represented by Hyper-relational Knowledge Graphs (HKGs), which contain rich semantics compared to hypergraphs. In an HKG, multiple entities with a shared property playing different roles form a hyperedge. To mitigate information loss in HKG representation learning, it is important to integrate entity-level roles and hyperedge-level properties. However, such multi-grained semantics are often inadequately learned, as conventional message passing only operates along one granularity, i.e, hyperedges. We propagate information between entities and hyperedges to aggregate entity-level roles at the hyperedge level for message passing. In this paper, we propose an HKG representation learning method based on Multi-granularity Semantic aware Message Passing (HyperSMP), preserving both semantic and structural information. Specifically, we design a fine-grained aggregation layer in HyperSMP to aggregate different roles of entities in hyperedge embeddings using an entity-level attention mechanism. Based on hyperedge embeddings, we propose a granularity-aligned propagation layer that recursively propagates information from hyperedges to entities and properties, capturing message passing paths in and out of hyperedges, respectively. As a result, multi-grained semantics are learned through unification at the hyperedge level to adapt to the message passing mechanism, and the high-order structure is captured through entity information exchange channeled via hyperedge embeddings. Further, HyperSMP discovers multi-hop associations among entities by stacking the above layers. Experimental results on public datasets show that HyperSMP outperforms state-of-the-art methods by at least 9.66% in F1 score.