Dear Editors, Please find attached my manuscript entitled: “Logically Constrained Latent Geometry: Entailment-Modulated Metric Preconditioning and Sherman-Morrison Matrix-Free Retraction” for consideration as a Regular Paper in Neurosymbolic Artificial Intelligence. This work introduces a geometric framework for enforcing hard logical consistency within neural latent spaces through an Entailment-Modulated Metric Tensor (EMMT), formulated as a low-rank Riemannian preconditioner. The paper derives an exact Sherman-Morrison matrix-free retraction operator, establishes a discrete-time confinement theorem for logically valid trajectories, and presents a scalable PyTorch implementation (please see attached also for review) suitable for modern neuro-symbolic systems. The manuscript aims to contribute a mathematically grounded alternative to conventional soft-penalty neuro-symbolic methods by embedding symbolic constraints directly into latent geometry rather than treating them as auxiliary losses. I believe the work aligns closely with the journal’s focus on neural-symbolic integration, differentiable reasoning, and the unification of symbolic and continuous learning systems. This manuscript is original, has not been published elsewhere, and is not currently under consideration by another journal. Thank you very much for your time and consideration. I would be honored to have the work reviewed by the Neurosymbolic Artificial Intelligence community. Kind regards, Sebastian Sklair Delgado AI Specialist | CEO & Founder of VYBSTAK Seb@vybstak.com