This analysis demonstrates the eigenvalues' relevance across five domains, indicating a unifying physical principle.
Key Points
The research aims to establish the significance of eigenvalues derived from Hamiltonian mechanics and their applications across various physical domains.
Derived the Jacobsthal characteristic polynomial from Hamiltonian mechanics.
Utilized the symplectic trace map and the Cayley-Hamilton theorem to identify eigenvalues.
Conducted a Monte Carlo null test with 491 candidate values to validate predictions against NASA data.
Identified eigenvalues λ = 2 and λ− = -1 as fundamental constants in five domains.
Confirmed that dimensionless ratios correspond to known astrophysical measurements within tight margins.
Predicted a hard bound of n∗ = 7 for compact resonant chain length.