N_galactic
N_galactic assigns the integer 142 as the discrete rung on the φ-ladder for the galactic memory timescale ratio. Researchers modeling galactic dynamics from Recognition Science first principles cite this constant when discretizing log_φ(τ★/τ₀) for rotation-curve calculations. The definition is a direct numerical assignment with no computation or proof steps.
claimLet $N$ denote the integer approximation to the base-φ logarithm of the galactic-to-reference timescale ratio, with $N = 142$.
background
The Gravity Parameters module classifies each galactic gravity parameter by its connection to φ: derived, RS-basis, or phenomenological. The φ-ladder supplies discrete rungs via powers of φ for masses and timescales, with the exact ratio defined upstream as log_φ(τ★/τ₀) in the GalacticTimescale module. The module_doc states that a₀ and r₀ are linked by τ★ = √(2π r₀ / a₀), and the integer rung closes the discretization step for downstream bounds.
proof idea
Direct constant definition. No lemmas or tactics are applied; the body is the literal integer 142.
why it matters in Recognition Science
The definition supplies the fixed rung consumed by galactic_status, the N_galactic_approx theorem (140 < N < 145), and A_amplitude_bounds. It instantiates the φ-ladder rung for galactic timescales, linking the T5 J-uniqueness and T7 eight-tick octave to observable parameters while satisfying the module's derived-parameter column.
scope and limits
- Does not derive 142 from the exact logarithmic expression.
- Does not apply outside galactic memory timescales.
- Does not carry uncertainty or error bounds.
- Does not replace the upstream real-valued definition.
formal statement (Lean)
199def N_galactic : ℝ := 142
proof body
Definition body.
200
201/-- The timescale constraint linking a₀ and r₀.
202 Given τ★ and r₀, the acceleration scale is forced. -/