思合 Scixiv — 把知识整理成逻辑链的推导工具

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测试推演 mvpjmoe7:任意两点之间可以连一条线段
Lemma 65 ([Cleared finite differential closure]). Consider one fixed finite collection of primitive functions, their argument graphs, and a finite differential and algebraic construction from them. Assume that, after one fixed exact graph …
Lemma 58 ([Crossings of a boundary arc]). A periodic orbit meets each regular boundary arc on which (V,T) has a fixed nonzero sign at most once. A connected nonsingular boundary arc on which this determinant vanishes identically is …
Lemma 64 ([Graph and finite-jet lifting]). Suppose an analytic transfer Φ(u) , on an open set of its original independent arguments u , has an exact analytic decomposition into finitely many transfers, with auxiliary arguments and …
Lemma 57 ([Termination of the resonant redo]). Around these finitely many resonances, apply the rational weighting U=u/τ^α and repeat the preceding rational subdivision once. The old resonance widths and old generator smallness can be …
Theorem 11.1 ([Projection count]). Let F(p,x)=0 be admissible open data as in Definition 63 ([Admissible open data]), with p∈^a , x∈^n , and m≤n . Suppose that F_x has row rank m throughout the zero set under consideration and that the …
Lemma 56 ([Uniform box data]). After the preceding finite subdivision, each nonzero comparable-scale field has, on a fixed larger state disk D and a smaller real interval I D , a positive globally subanalytic scale L(p,x) and constants K,m …
Lemma 62 ([Boundary corners of the chosen domains]). The independent-argument domains in this section can be chosen so that the following holds for every sequence in any one of them, including a sequence on which imposed strict margins …
Lemma 55 ([Compatible change of Euler center]). Suppose that the old clock is D_0=(x-a_0(p))∂_x . After simultaneous preparation and finite subdivision, all the required data can be represented in an Euler clock D=(x-a(p))∂_x=τ∂_τ=hD_0, …
Lemma 61 ([Structural extensions and the physical chain rule]). The terminal kernels can be chosen on independent-argument neighborhoods so that every layer-vanishing identity required by its primitive theorem holds throughout that …
Proposition 54 ([Quantitative primitive input bounds]). For the primitive constructions in Sections, , and, the family requirement in Assumption 19 ([Differentiated primitive data]) follows from the estimates on common argument boxes …
Lemma 60 ([Identity on the nearby tied endpoint graph]). Every transfer constructed above computes the actual scalar mismatch for all nearby proposed endpoints on its argument graph. The terminal state coordinate has nonzero transverse …

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