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April 22, 20260 citationsOpen Access

Bell-Inequality-Inspired Semantic Validation in SPVU: From Quantum Correlations to the MetaBell Operator

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DFDinc Fatih

Key Points

  • To establish a semantic Bell inequality for validating multi-agent systems and to introduce the MetaBell operator as a rigorous witness.
  • Developed a formal semantic Bell inequality for multi-agent systems.
  • Introduced the MetaBell operator within the PoISV consensus protocol and connected it to the Tsirelson bound.
  • Defined an Immutable Incident Log compliant with EU regulations and outlined empirical validation using the Semantic Bell Test Corpus.
  • The MetaBell operator behaves as a reliable Bell witness for independent understanding.
  • A new data-driven calibrated threshold for validation was established with Ψ* at approximately 1 - |S̃|/(2√2).
  • A structured framework was proposed for compliance and validation of multi-agent systems.

Abstract

We introduce a formal semantic Bell inequality for multi-agent validation systems and show that the MetaBell operator Ψ, deployed in the PoISV consensus protocol, functions as a rigorous Bell witness for genuine independent understanding. We derive Ψ ≈ 1 − |S̃|/(2√2), connecting Ψ to the Tsirelson bound and replacing the ad-hoc threshold with a data-driven calibrated threshold Ψ*. We further define a Bell-augmented SPVU goal state, an Immutable Incident Log satisfying EU AI Act Art. 12/17/19, a zero-knowledge proof of MetaBell compliance via Nexus zkVM, a Svetlichny-type k≥3 group extension, and the Semantic Bell Test Corpus (SBTC) for empirical validation. DOI: 10.5281/zenodo.19656679

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Dinc Fatih (2026) studied this question.

synapsesocial.com/papers/69e8677e6e0dea528ddeba03https://doi.org/10.5281/zenodo.19656678
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