λEnter Calculus CompanionRegistered manuscripts, kept distinct

Manuscript II@2 · II.tex · figure · 50d64def

From coupling data to a finite certificate

Problem and contribution › Three mathematical layers · lines 283–300

II@2#fig:layers

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Fixed action data
d,θ;q(d)=b2+c2−ac−bed,\theta;\qquad q(d)=b^2+c^2-ac-be
tree prescription →
Response functions on X\mathcal X
r(d,θ)=q(d)m+∑ℓ=115120θℓnℓr(d,\theta)=q(d)m+\sum_{\ell=1}^{15120}\theta_\ell n_\ell
evaluation →
Evaluation on SS
S=(β0,β+,β−),rS=q(d)mS+NSθS=(\beta_0,\beta_+,\beta_-),\quad r_S=q(d)m_S+N_S\theta
SEP-finite
rank⁡NS=rank⁡[NS∣mS]=2,mS=NSα\operatorname{rank}N_S=\operatorname{rank}[N_S\mid m_S]=2,\quad m_S=N_S\alpha

Does not establish a global contact identity.

The action, the global response function, and its finite evaluation are distinct objects. The closed result concerns the right-hand object on one specified family.

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