Milestone task: reproduce Theorem Ω.1’s derivation from Week 6 by hand (the geometric-series limit argument), then write a short, precise statement of what “the system reaches \(\tau=2\)” means and doesn’t mean. It means: the n-bonacci ladder’s dominant roots converge to 2 as \(n\to\infty\) (proved), and \(\tau=2\) is a load-bearing structure constant with real downstream consequences in AXLE_v6.lean (proved, given the structure). It does not mean — without further argument this course hasn’t made — that contact curvature, the ladder, and any other named construction all provably converge as one unified phenomenon; that stronger claim was removed in Week 7 precisely because its previous form depended on unverified external axioms.
-- dm³ 103 · Week 08 · Milestone VI — precise statement of "τ=2 reached" -- -- Reproduce Theorem Ω.1's geometric-series limit argument by hand. -- Then state precisely: -- PROVED: lim ρ_n = 2 (ladder); tau_embodiment and consequences -- (given τ=2 as structure data) -- NOT PROVED (removed, Week 7): any unified 3-way convergence -- theorem bundling contact curvature with the ladder limit example : True := trivial