Research in cross-lingual modeling for historical and extremely low-resource languages is hindered by the absence of standardized evaluation benchmarks. To address this, we present ManCC—the first task-anchored benchmark for Manchu–Classical Chinese translation. ManCC consists of a high-quality parallel corpus of 16,627 sentence pairs, derived from the Qing-dynasty historical text Manwen Laodang-Taizong, and a reproducible evaluation protocol that combines automatic metrics (BLEU and chrF) with a three-dimensional human assessment (fidelity, fluency, linguistic normativity). Through systematic evaluation across three model families (non-pretrained, multilingual pretrained, and large language models), we find that linguistic differences significantly influence performance, broader language coverage in multilingual pretraining facilitates low-resource transfer, and automatic metrics often fail to capture essential errors in historical translation—underscoring the necessity of human evaluation. ManCC not only provides foundational resources for Manchu–Classical Chinese translation but also establishes a diagnosable, reproducible platform for cross-lingual modeling of historical low-resource languages.

Geometry Problem Solving (GPS) is a fundamental task in mathematical reasoning, with applications in intelligent education and automated theorem proving. Existing neuro-symbolic solvers often rely on two restrictive assumptions: textual conditions are expressed as atomic geometric statements, and target derivation can be reduced to eager elimination of intermediate variables. These assumptions break down in realistic problems, where coupled geometric descriptions lead to combinatorial growth in parsing patterns, and nonlinear constraints make explicit elimination inefficient or even intractable. We propose RIGOR, a neuro-symbolic GPS framework based on Atomic Semantic Normalization and Declarative Constraint Reasoning. RIGOR uses a Geometric Semantic Normalizer trained on our newly constructed GSN-15K dataset to normalize geometric texts into atomic statements for reliable formalization. It then adopts a Declarative Symbolic Engine that globally accumulates derived geometric constraints and determines target values through constraint entailment, while also reconstructing proof-grounded reasoning traces. Experiments on multiple standard GPS benchmarks show that RIGOR outperforms state-of-the-art methods while producing interpretable derivations. Our project is available at https://github.com/dongyuhang22/RIGOR.