Volume V’s own audit chapter lists eight constants with real Lean proof snippets (rfl, decide, norm_num) — a concrete, checkable inventory rather than a narrative claim. This course has now independently derived or verified most of them across 101–103: \(T^*=2\pi\), \(\mu_{{\max}}=-2\), \(\tau=2\), \(\varepsilon_0=1/3\), \(g^6=33\), and \(\tau\cdot\varepsilon_0=2/3\) among them, each with a specific proof tactic named in the source rather than asserted generically.
CollatzDescent.lean sorry (102 Week 11), Bridge 0 (this course, Week 10), the \(\varphi\) Lean-formalization gap (101), and the \(G^6\) conjecture (last week). “Complete” names a specific, real mathematical arrival — the fixed point is reached — not an absence of open problems in the wider research programme.
-- dm³ 103 · Week 14 · The 8 Verified Constants (Vol V audit) -- Proved, real tactics per source (chV-constants.html): -- T* = 2π (structure data) -- μ_max = -2 (rfl/norm_num, per fold double-root) -- τ = 2 (ladder limit, Theorem Ω.1) -- ε₀ = 1/3 (Gronwall, gronwall_outer) -- g⁶ = 33 (τ⁵+1, decide/norm_num) -- τ·ε₀ = 2/3 (norm_num) example : (2:ℝ) * (1/3) = 2/3 := by norm_num -- "Complete Completeness" = the fixed point τ=2 is reached (G⁵), -- NOT "no open problems remain" — several real ones do (catalogued -- across this course). example : True := trivial