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April 5, 2026Open Access

Five Domains, One Eigenvalue and Two Stubborn Lambdas

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Authors

DCDavid Coates

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Overview

Mathematical models reveal consistent eigenvalues in planetary and dynamic systems, suggesting fundamental laws.

Key Points

  • This study derives the Jacobsthal characteristic polynomial and its implications in planetary systems and dynamics.
  • Analysis of the Jacobsthal polynomial derived from Hamiltonian mechanics.
  • Application of the symplectic trace map and Cayley-Hamilton theorem for matrices.
  • Comparison of planet period ratios across five distinct domains including TRAPPIST-1 and the solar system.
  • Statistical validation using Monte Carlo methods and tools like FSRE and CANLE.
  • Identified eigenvalues λ = 2 and λ− = -1 related to physical quantities.
  • Confirmed the pattern of dimensionless period ratios in five separate domains.
  • Validated predictions against NASA data with p < 3.1 × 10−4, indicating statistical significance.

Cite This Study

David Coates (2026) studied this question.

synapsesocial.com/papers/69d1fe18a79560c99a0a4940https://doi.org/10.5281/zenodo.19393451
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