DECIDED / VERIFIED / DEFINED settled by the author, recomputed by a script, or defined in a paper mixed part settled, part open OPEN the author's call
Exponents and thresholds
| Symbol | Definition | Status | Notes |
|---|---|---|---|
| μ_max | Transverse Floquet exponent of Γ. Vol II Lemma 3.1 gives only its sign (μ_max < 0, "Floquet theory, [1] Thm 3.3"), for each system separately; it gives no value and no uniformity in z. Toy value −2 is the z → ∞ limit of the explicit linearization λ(z) = −2 + 2e^(−z), which is monotone decreasing in z (0 at z = 0, negative only for z > 0), so the limit exists there by the formula. on 1 page of this book | OPEN | Open: for a general dm³ system, what μ_max is as a limit (lim, limsup or sup over z) and why it exists. Lemma 3.1 does not supply that; Book 4 ch10 calls its proof "numerical". Pages that state μ or μ_max as a z → ∞ / regularized limit, and so rely on this row (keyword match, 7): book1/vol2-dashboard.html, vol2-contact.html, vol2-toymodel.html, book4/ch03.html, book4/ch06b.html, book4/ch10.html, book7/ch-grothendieck.html. Not edited. |
Operator chain
| Symbol | Definition | Status | Notes |
|---|---|---|---|
| dm³ | The contact 3-manifold (X, α) with α = dz − ρ²dθ (more generally α = dz − λ, dλ = ω) carrying a hyperbolic limit cycle Γ, with the operator chain G = U∘F∘K∘C acting on it; the same structure expressed across many domains and scales. It is the minimal case, generalized to contact (2n+1)-manifolds in the GCM framework (base M arbitrary, M̂ = M × ℝ; Theorem C on ℝ^(2n+1)). The toy ODE is one vector field on the 3-manifold. | DECIDED (author, 2026-09-30) | Vol I Fig. 3: "Dimension 3 is the minimum in which this structure is non-trivial (§16)." The GCM page's "dm³ system" (M, g, Γ, V, ξ) is the generalized setting; for n = 1 the base M is the 2-dimensional (r, θ) plane. |
| dm³ / dm3 (naming) | Write dm³ in prose and on grant and site pages; dm3 is the ASCII alias in code, filenames and Lean identifiers. Define it once here; other pages point to this row instead of restating it. | DECIDED (author, 2026-09-30) | A convention. If any paper uses "dm³ system" for a specific object beyond the name (the GCM quintuple does), that object's definition is the row above. |
Terms used but not defined (candidates)
"reduced system", "contact class of α", "multi-scale coherence" (GCM page); "Coherence Bridge" (Vol I figure). Define or remove.
Rows that do not occur anywhere in this book are left out: ε₀, B(Γ), r*, r_s, τ, τ normalization, τ₁₂, κ*, κ chain, W(Γ), C, K, F, U, U family.
Generated 2026-10-01 from docs/definitions.md (sha1 8f178c3635) by tools/chapter_zero.py. Re-check the verified numbers with python3 tools/chapter_zero_verify.py. The Book 4 Student Edition and the Book 5 "How to Begin" chapter are orientation pages; this chapter is the reference.