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This paper introduces a mathematical and engineering architecture for Electronic Health Record (EHR) interoperability, focusing on the concept of a logit boundary that facilitates a secure interface for operational exchanges. The framework, termed the Geometric Belief Interface (GBI), employs finite boundary semantics and a Decentralized Cryptographic Sheaf-Enclave (DCSE) protocol to manage the admissibility of proposed data exchanges, ensuring that only validated information is processed. Empirical evaluations using the GBI BoundaryBench v0.1 revealed that a tested model failed to produce any outputs accepted by the benchmark, highlighting the challenges of establishing reliable admission boundaries in EHR systems.
A tested model failed to meet interoperability standards, revealing the critical gaps in EHR data exchange validation.
Electronic health-record interoperability is a boundary problem: legacy systems, generative models, terminology services, identity systems, and human reviewers may each expose rich internal states, while operational exchange requires a narrow shared interface of typed claims, bounded uncertainty, provenance, and explicit admission or abstention. This paper details a mathematical and engineering architecture for that interface. The organizing idea is the logit boundary: a discovery model may propose pre-threshold scores over a local categorical decision, but a deterministic judgment substrate decides whether the proposal is admissible, requires review, or must be quarantined before any Fast Healthcare Interoperability Resources (FHIR) transaction is constructed. The resulting Geometric Belief Interface (GBI) combines finite boundary semantics, local Dirichlet evidence, cellular-sheaf and mapping-cone diagnostics, advisory geometric audit charts, and a Decentralized Cryptographic Sheaf-Enclave (DCSE) protocol sketch for fail-closed deployment. The framework does not establish clinical truth, global representation alignment, or end-to-end safety; it defines certificate-producing checks at a model-to-system boundary. A companion frozen synthetic benchmark, GBI BoundaryBench v0.1, evaluated Qwen3-4B-Instruct-2507 on 256 held-out tasks across three evidence modes (768 canonical executions). All executions completed, but none produced an output accepted by the benchmark contract: 369 were rejected during safe parsing and 399 during schema validation, yielding zero coverage and deterministic quarantine. This empirical result is deliberately narrow - one 4B open-weight model under one frozen interface - and is reported as evidence about the admission boundary, not as a general claim about LLM capability or clinical safety. A Julia appendix verifies numerical certificates using standard libraries.
