Before Phase I of 102, a precise recap — precise on purpose, because 101 spent sixteen weeks distinguishing proved from argued from axiomatic, and that discipline carries forward. The operator chain \(G = U \circ F \circ K \circ C\) is well-defined by construction (Theorem A, proved, 0 sorry). The period \(T^*=2\pi\) is asserted as structure data in AXLE_v6.lean, with its geometric derivation (Reeb-flow compactification) argued in prose, not yet formalized. \(\varphi \approx 1.618\) is the \(n=2\) rung of the recurrence ladder, proved subcritical (Theorem \(\varphi\).1) — it never completes a dm³ fold on its own, and no AXLE Lean file exists for it yet (unlike \(\eta\), which does — this course’s first stop).
One correction carried forward from 101, worth restating here since it’s easy to misremember: the inner Gronwall basin boundary is \(r^* = 0.77594059\) (\(\approx 0.776\)), numerically certified to 8 decimal places — not the rough \(\approx 0.80\) figure an earlier draft used. The certified value is solid; the general theorem that the basin really is asymmetric (inner_basin_is_asymmetric) is still an axiom in Chain_updated.lean, pending full ODE formalisation. Both facts matter for Week 3.
-- dm³ 101 recap, carried forward: -- Theorem A: G = U∘F∘K∘C well-defined proved, 0 sorry -- T* = 2π: structure data asserted; Reeb-flow argument prose-only -- φ ≈ 1.618: subcritical (Theorem φ.1) proved (classical); no Lean file -- r* = 0.77594059 certified numerically (8dp) -- inner_basin_is_asymmetric AXIOM, not yet proved example : True := trivial