IndisputableMonolith.Masses.NumericalPredictions
Module supplies interval bounds and equalities for powers of φ, centered on φ^6 ∈ (17,18) as a proxy for generation mass ratios such as m_b/m_s. Researchers deriving particle spectra from the phi-ladder would cite these results. Content consists of definitions and bounds assembled from Fibonacci identities together with imported interval modules for φ and α^{-1}.
claim$φ^6 ∈ (17,18)$ with the identity $φ^6 = 8φ + 5$, serving as a numerical stand-in for generation mass ratios $m_b/m_s$ or $m_τ/m_μ$ after corrections.
background
The module sits inside the Masses domain of Recognition Science and imports the base time quantum τ₀ = 1 tick from Constants, interval bounds on α^{-1} from AlphaBounds, and algebraic bounds on φ = (1 + √5)/2 from PhiBounds. The latter module obtains its φ bounds from the quadratic inequalities 2.236² < 5 < 2.237². Local notation follows the phi-ladder convention in which mass ratios are expressed as yardstick × φ^(rung - 8 + gap(Z)).
proof idea
This is a definition module, no proofs. It aggregates equalities and interval statements for successive powers of φ by direct appeal to Fibonacci relations and the imported numeric bounds.
why it matters in Recognition Science
Supplies the concrete numerical layer that converts the abstract self-similar fixed point φ (T6) into testable mass ratios. The supplied doc-comment identifies the direct link to generation mass ratios m_b/m_s. No downstream declarations are recorded in the current graph.
scope and limits
- Does not derive the underlying mass formula.
- Does not supply bounds for φ powers outside the listed siblings.
- Does not fold in experimental mass values.
- Does not connect to the full T0-T8 forcing chain.
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