Manuscript En02-A@1 · En02-A-v1.tex · definition · bb1319d5

Definition: Certified nets

Certified rational nets and a budgeted mesh theorem · lines 1179–1206

For $N \geq s$ , define

R_{fg} (N, s) = {m / M : C_{FG} (s, m) \leq N},

including zero coordinates at unsupported outcomes. Also set

R_{cert} (N, s) = R_{fg} (N, s) \cup {m / M : s M \leq N} .

The second term uses primitive multiplicities and the symmetry certificate of Proposition prop:symmetry. Both nets are finite. They are sufficient anchoring sets, not a classification of all forceable laws.

For either net $R$ , define its covering radius

δ_{R} (N, s) = p \in Δ_{2^{s}} max q \in R (N, s) min d_{TV} (p, q) .

Displayed formulas in this passage

unlabeled · line 1181
$R_{fg} (N, s) = {m / M : C_{FG} (s, m) \leq N},$
unlabeled · line 1188
$R_{cert} (N, s) = R_{fg} (N, s) \cup {m / M : s M \leq N} .$
unlabeled · line 1200
$δ_{R} (N, s) = p \in Δ_{2^{s}} max q \in R (N, s) min d_{TV} (p, q) .$

Nearby in this section

section: Certified rational nets and a budgeted mesh theorem
proposition: Proposition: Binary mesh values
lemma: Lemma: Common probability modulus
theorem: Theorem: C : anchoring and mesh control
remark: Remark: No boundary cocycle estimate without residual control
section: Certified rational nets and a budgeted mesh theorem