IndisputableMonolith.Masses.NumericalPredictions
The module assembles numerical bounds on successive powers of phi together with derived mass ratios for particle generations. A physicist checking Recognition Science mass predictions against measured quark and lepton values would cite these intervals. Each bound follows from direct application of algebraic identities to the interval results imported from PhiBounds and AlphaBounds.
claim$phi^6 in (17,18)$ for the generation mass ratio $m_b/m_s$ or $m_tau/m_mu$ (with corrections), obtained from the Fibonacci identity $phi^6 = 8 phi + 5$.
background
Recognition Science places particle masses on a phi-ladder whose rungs are integer powers of the golden ratio, scaled by a yardstick set by the fundamental time quantum. The module imports the definition tau_0 = 1 tick from Constants, interval bounds on alpha inverse from AlphaBounds, and rigorous bounds on phi = (1 + sqrt(5))/2 from PhiBounds. The latter module establishes its intervals via the quadratic comparison 2.236^2 < 5 < 2.237^2.
proof idea
This is a module of bound statements rather than a single proof. Each declaration applies the imported PhiBounds lemmas together with the Fibonacci identity phi^6 = 8 phi + 5 and interval arithmetic to produce the stated numerical ranges.
why it matters in Recognition Science
The module supplies the concrete numerical intervals required to compare the Recognition Science phi-ladder mass formula with experimental generation ratios. It therefore supports quantitative checks of the T5 J-uniqueness and T6 phi fixed-point steps in the forcing chain. No downstream declarations are listed as using it yet.
scope and limits
- Does not derive the underlying mass formula or the phi-ladder structure.
- Does not include experimental data or measurement uncertainties.
- Does not cover all particle species or higher phi powers beyond the listed siblings.
- Does not address the full forcing chain from T0 to T8.
depends on (3)
declarations in this module (17)
-
theorem
phi_pow_6_bounds -
lemma
phi_pow_7_eq -
theorem
phi_pow_7_gt_28 -
theorem
phi_pow_7_lt_30 -
theorem
phi_pow_7_bounds -
theorem
phi_pow_7_gt_29 -
lemma
phi_pow_11_eq -
theorem
phi_pow_11_bounds -
theorem
kappa_bounds -
theorem
hbar_range -
theorem
muon_electron_ratio_bounds -
theorem
tau_muon_ratio_bounds -
theorem
charm_up_ratio_bounds -
theorem
bottom_strange_ratio_bounds -
theorem
top_charm_ratio_bounds -
theorem
neutrino_squared_mass_ratio -
structure
NumericalPredictionsCert