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

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.