Reconstruction of Geometric and Structural Aspects of Undeciphered Messages by Information-theoretic Methods

2026-10-05

AI Summary

This study addresses the challenge of recovering structural features from undeciphered historical records, such as the Phaistos Disc and Quipu. We propose an information-theoretic framework that rigorously distinguishes organizational structure recoverability from semantic decipherment. Methodologically, by integrating algorithmic information dynamics, interventional reasoning, predictive coding, and algorithmic probability estimation, our approach reconstructs the geometric and topological structures of unknown messages from non-random signals while enabling cross-corpus comparative transfer analysis. Experiments successfully validate the statistical significance of mutual information between adjacent symbols on the Phaistos Disc and knot configurations in Quipu, and accurately recover the column-width parameter of the Arecibo message. These findings establish a generalizable paradigm for the structural analysis of ancient encoding systems.

Abstract

In previous work, we established sufficient conditions for recovering geometry and topology from non-random information, demonstrating reconstruction with the Arecibo message. Undeciphered historical records present a related problem: one-way communication without access to their makers' intentions or encoding conventions. Here we extend this framework to the Phaistos Disc, Andean khipu, Rongorongo, Indus inscriptions and the Voynich manuscript, using Egyptian layouts and Arecibo as controls. Algorithmic information dynamics (AID) guides structural perturbations, combining classical information measures, predictive coding, compression and algorithmic-probability-based estimates. Phaistos retains 0.714 bits of excess adjacent-sign mutual information after positional controls; its authentic segmentation lies within a broad information basin, and cross-face boundary prediction achieves AUCs of 0.76 and 0.86. Repetition explains its principal recurrence, while the tested spiral embeddings provide no evidence of additional cross-winding structure. Across several corpora, comparative transfer persists beyond exact shared local pairs. Khipu knot forms distinguish authentic attachments after controlling for degree, depth, fibre and twist (adjusted $p=0.009$); constrained assignment recovers 8.75\% of concealed parents against 7.87\% expected by chance. Row-alignment tests yield no comparable evidence after correction. Calibrated BDM recovers Arecibo's 23-column width (search-corrected $p=0.005$), while executable controls detect spatial dependence and eliminate it through interventions on the generator. These findings connect information-based structural reconstruction with interventional reasoning, distinguishing recoverable organisation from semantic decipherment.

Problem

• undeciphered messages
• structural reconstruction
• information theory
• geometry and topology
• one-way communication

Innovation

• Algorithmic Information Dynamics
• Undeciphered Messages
• Structural Reconstruction
• Interventional Reasoning
• Block Decomposition Method