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This work investigates a deterministic algorithm that verifies periodicity in complex cubic irrationals.

July 13, 2026Open Access

A deterministic sin2-type algorithm for complex cubic irrationalities with exact periodicity certificates

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This work investigates a deterministic algorithm that verifies periodicity in complex cubic irrationals.
Implemented a deterministic algorithm for signature (1,1) data using negative score expressions.
Conducted campaigns on a fixed sample of complex cubic polynomials, certifying transitions with exact comparisons.
Examined deformed bases and quantified behavior in transition graphs across different fields.
Achieved 194/194 successful closures with exact unit certificates in an exhaustive campaign.
Demonstrated invariance of the terminal cycle across 457 deformed starting bases.
Certified finite transition graphs for four fields, revealing no saturation in the bounded height set.

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Randomized trial demonstrates an algorithm for exact periodicity in complex cubic irrationals, highlighting continuous mathematical exploration.

Ludovic Tagnon (2026) studied this question.

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Randomized trial demonstrates an algorithm for exact periodicity in complex cubic irrationals, highlighting continuous mathematical exploration.