Neuro-Symbolic Financial Reasoning via Deterministic Fact Ledgers and Adversarial Low-Latency Hallucination Detector

arXiv:2603.04663v1 Announce Type: new Abstract: Standard Retrieval-Augmented Generation (RAG) architectures fail in high-stakes financial domains due to two fundamental limitations: the inherent arithmetic incompetence of Large Language Models (LLMs) and the distributional semantic conflation of dense vector retrieval (e.g., mapping ``Net Income'' to ``Net Sales'' due to contextual proximity). In deterministic domains, a 99% accuracy rate yields 0% operational trust. To achieve zero-hallucination financial reasoning, we introduce the Verifiable Numerical Reasoning Agent (VeNRA). VeNRA shifts the RAG paradigm from retrieving probabilistic text to retrieving deterministic variables via a strictly typed Universal Fact Ledger (UFL), mathematically bounded by a novel Double-Lock Grounding algorithm. Recognizing that upstream parsing anomalies inevitably occur, we introduce the VeNRA Sentinel: a 3-billion parameter SLM trained to forensically audit Python execution traces with only one token test budget. To train this model, we avoid traditional generative hallucination datasets in favor of Adversarial Simulation, programmatically sabotaging golden financial records to simulate production-level ``Ecological Errors'' (e.g., Logic Code Lies and Numeric Neighbor Traps). Finally, to optimize the Sentinel under strict latency budgets, we utilize a single-pass classification paradigm with optional post thinking for debug. We identify the phenomenon of Loss Dilution in Reverse-Chain-of-Thought training and present a novel, OOM-safe Micro-Chunking loss algorithm to stabilize gradients under extreme differential penalization.