A companion chapter in the same book project (\(ch4\)-neural, part of the CEFR-leveled writing-pedagogy series referenced in Week 9) uses neural oscillation binding as a worked example of the K (curvature) operator specifically, not \(\varphi\) directly. The frequency-band structure is concrete and checkable: \(\delta\) (0.5–4 Hz, deep C-phase compression) \(\to\) \(\theta\) (4–8 Hz, C→K transition, rising synchrony) \(\to\) \(\alpha\) (8–12 Hz, K idle threshold) \(\to\) \(\gamma\) (30–100 Hz, K fires — the binding event). The chapter’s central example: a 40 Hz gamma oscillation coupling to hippocampal theta, binding spatially distributed cortical populations into a single coherent percept within roughly 25 milliseconds — framed as a Hopf bifurcation, \(\dot z = (\lambda+i\omega)z - |z|^2 z\), crossing a critical coupling strength \(\lambda^*\) from a damped oscillation into a sustained limit cycle.
The companion \(ch6\)-resonance chapter extends the same frame to cardiac resonance and heart-rate variability, where \(\varphi\)-adjacent ratios have been reported in some HRV spectral analyses in the physiology literature — a genuinely contested empirical claim in that literature, independent of dm³, and one you should not treat as settled just because a source chapter cites it. The right posture, consistent with this whole course: read the neuroscience/physiology claims on their own evidentiary terms, and separately evaluate whether the dm³ operator labels add explanatory content or just relabel an existing model.
AXLE_v6.lean — theorem names and Lean identifiers above point at the actual source files.-- dm³ 101 · Week 14 · Applications — no new Lean this week -- -- This week is deliberately non-formal: neural/cardiac applications -- are illustrative analogies drawn from companion chapters, not -- claims with Lean-checked status. Treat them under F1–F4 -- (Week 3 falsifiability conditions) rather than as proved. example : True := trivial