arXiv:2603.12953v1 Announce Type: cross Abstract: Neuro-symbolic reasoning increasingly demands frameworks that unite the formal rigor of logic with the interpretability of large language models (LLMs). We introduce an end to end explainability by construction pipeline integrating the Automated Theorem Generator Delta1 based on the full triangular standard contradiction (FTSC) with LLMs. Delta1 deterministically constructs minimal unsatisfiable clause sets and complete theorems in polynomial time, ensuring both soundness and minimality by construction. The LLM layer verbalizes each theorem and proof trace into coherent natural language explanations and actionable insights. Empirical studies across health care, compliance, and regulatory domains show that Delta1 and LLM enables interpretable, auditable, and domain aligned reasoning. This work advances the convergence of logic, language, and learning, positioning constructive theorem generation as a principled foundation for neuro-symbolic explainable AI.

arXiv:2603.08605v3 Announce Type: replace-cross Abstract: Background and objectives: Colorectal cancer histopathological grading depends on accurate segmentation of glandular structures. Current deep learning approaches rely on large scale pixel level annotations that are labor intensive and difficult to obtain in routine clinical practice. Weakly supervised semantic segmentation offers a promising alternative. However, class activation map based methods often produce incomplete pseudo masks that emphasize highly discriminative regions and fail to supervise unannotated glandular structures. We propose a weakly supervised teacher student framework that leverages sparse pathologist annotations and an Exponential Moving Average stabilized teacher network to generate refined pseudo masks. Methods: The framework integrates confidence based filtering, adaptive fusion of teacher predictions with limited ground truth, and curriculum guided refinement to progressively segment unannotated glandular regions. The method was evaluated on an institutional colorectal cancer cohort from The Ohio State University Wexner Medical Center consisting of 60 hematoxylin and eosin stained whole slide images and on public datasets including the Gland Segmentation dataset, TCGA COAD, TCGA READ, and SPIDER. Results: On the Gland Segmentation dataset the framework achieved a mean Intersection over Union of 80.10 and a mean Dice coefficient of 89.10. Cross cohort evaluation demonstrated robust generalization on TCGA COAD and TCGA READ without additional annotations, while reduced performance on SPIDER reflected domain shift. Conclusions: The proposed framework provides an annotation efficient and generalizable approach for gland segmentation in colorectal histopathology.