Convergence 19: The Undecidability of AGI Alignment: Unverifiability Theorem + Soundness-Completeness-Tractability Trilemma (Trakhtenbrot's Wall)

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Michael Darius Eastwood
Michael Darius Eastwood · Independent AI alignment researcher
Published
Michael Darius Eastwood · Research Notes · 3 July 2026 · Part of the Research evidence spine
Michael Darius Eastwood, independent researcher, London: originator of the embedded-correction alignment thesis (manuscript 8 December 2024, SHA-256 anchored: f0d1f38f).
Register entry 19 of 19. Domain: Mathematics. Institution: Gumbau Mezquita (Universitat Jaume I). External date: 2026-06-26. Measured against: A1 (~18.5 months after A1). Classification: CONVERGENT.
Primary source: arXiv:2606.28639 (SHA-256 8e4483b1287146da6d725e6078ed4bf708be602f4bd2751b9d0e040a45b1c9a7)

What happened

The Undecidability of AGI Alignment: Unverifiability Theorem + Soundness-Completeness-Tractability Trilemma (Trakhtenbrot's Wall).

Why it is in the register

Gumbau Mezquita's undecidability paper proves two formal results: alignment verification is structurally unverifiable, and soundness, completeness and tractability cannot be jointly achieved. His stated conceptual foundation is the Hernández-Espinosa paper. The chain therefore runs from a paper about cognitive diversity to a theorem that vindicates a manuscript written eighteen months earlier by an author neither of them had heard of. That is the register's final row, and the strongest.

The honest caveat

Source: arXiv:2606.28639, with SHA-256 of the PDF published in the evidence vault.

How to check this entry

Open the primary source above. Confirm the date. Confirm the finding. Then compare it against the manuscript passage or artifact named in the register entry, whose SHA-256 hash is published on the evidence page. Nothing in this article asks for trust; the entry either survives that comparison or it comes off the register, publicly, the way the programme's retracted scaling figure did.

From the book Infinite Architects: Intelligence, Recursion, and the Creation of Everything by Michael Darius Eastwood.

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