Fixed-Point Logic Unlocks Boolos' Hardest Puzzle — E8 Intelligence Research

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Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-19
DOI
https://doi.org/10.5281/zenodo.22841047
Primary Topic
Computability, Logic, AI Algorithms
Type
preprint
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preprint

Fixed-Point Logic Unlocks Boolos' Hardest Puzzle — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Computability, Logic, AI Algorithms
preprint

Fixed-Point Logic Unlocks Boolos' Hardest Puzzle — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: The "hardest logic puzzle" (Boolos) reduces to a ternary fixed-point problem — the solution requires constructing a self-referential question that maps truth-teller/liar/randomizer states onto a stable answer set, exploiting category-theoretic fixed points rather than brute-force case analysis. | MATH: The puzzle's core is a 3-state automaton (True, False, Random) with a question operator Q that must satisfy Q(s) ∈ {yes,no} for all s, but Random's output is a free variable — the fixed point is a function f: {T,F,R} → {Y,N} such that f(f(s)) = s for deterministic states, with R as a chaotic attractor. The known solution uses a "double question" embedding: Q1 = "If I asked you Q2, would you say 'ja'?" — this creates a logical fixed point equation: Answer(Q1) = (TruthValue(Q2) XOR (speaker is liar)) — collapsing to a stable binary output independent of the "ja"/"da" language mapping. The ternary structure maps to the cyclic group Z₃, with the randomizer as a non-invertible elemen Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Computability, Logic, AI Algorithms
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Fixed-Point Logic Unlocks Boolos' Hardest Puzzle — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS