# BeTaL-GBI: Admission-Aware Benchmark Tuning and Full-Stack Verification of Geometric Belief Interfaces

arXiv: https://arxiv.org/abs/2608.21503 · HTML: https://mlsanity.com/paper/2608.21503/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [FHIR-AgentBench: Benchmarking LLM Agents for Realistic Interoperable EHR Question Answering](https://mlsanity.com/paper/2509.19319/) (2025)
- [BenchBench: Benchmarking Automated Benchmark Generation](https://mlsanity.com/paper/2603.20807/) (2026)
- [Automating Benchmark Design](https://mlsanity.com/paper/2510.25039/) (2025)
- [Formal Methods Meet LLMs: Auditing, Monitoring, and Intervention for Compliance of Advanced AI Systems](https://mlsanity.com/paper/2605.16198/) (2026)
- [Logit-Boundary Geometric Belief Interfaces and Sparse Sheaf-Enclave Protocols: A Self-Contained Substrate for Secure Network Electronic Health Record (EHR) Interoperability](https://mlsanity.com/paper/2608.10300/) (2026)

## Abstract (arXiv)

A verification substrate is more credible when exposing errors in its own claims, not just model outputs. GBI-DCSE v3 falsified an architectural claim: the reported Fisher value epsilon ~ 0.066 satisfies the kappa^2 <= 10^4 budget only on the slice [epsilon, 3, 4, 5], while the full box [epsilon, 20]^4 requires epsilon ~ 0.326472. This erratum highlights whether an enterprise verification architecture can isolate interface failure, task competence, policy admissibility, and control integrity while keeping claims auditable. BoundaryBench v0.1 established the baseline: Qwen3-4B-Instruct-2507 completed 768 frozen executions, but 0% cleared the contract (369 failed parsing, 399 failed validation), limiting downstream selectivity metrics. This companion study evaluates three successive improvements. First, BeTaL-GBI v0.2 applies Benchmark Tuning with an LLM-in-the-loop over 2,218,750,380 grid points, separating format admission from conditional performance (rho_adm = N_admitted/N; rho_task = N_verified/N_admitted). Following schema repair, a model-free feedback search achieves a 2.87% mean held-out target gap, outperforming non-feedback baselines (13.61%, 11.46%). Second, GBI v2 swaps static keys for a reference-independent witness state W and policy P. Across 512 synthetic tasks, a 16-gate policy detects all 116 injected severe contradictions and accepts all 99 clean records (broad denominator: 4.27%). Hallucinator and evidence-forger surrogates are blocked with zero silent promotions. Third, GBI-DCSE v3 maps 99 claims to machine-readable evidence: 95 of 96 testable claims pass, with 148 standalone checks executed without failure. The harness exercises signed ledgers, PBFT quorums, and enclave forgery across 62 configurations. Under synthetic conditions, GBI-DCSE is a selective, policy-versioned, self-auditing test and routing substrate.