Manuscript X-H-ST@1 · X-H-ST.tex · section · 943aa27e

Reports and sound threshold certificates

Stage C: finite evaluations of the classical residuals › Reports and sound threshold certificates · lines 1411–1437

A dictionary entry contains:

a task identifier, quantity type, formal order, and coefficient-extraction rule;
the support and input-description contract;
a supplied real value $a_{j}$ together with a rational enclosure
$I_{j} = [L_{j}, U_{j}], L_{j} \leq a_{j} \leq U_{j};$
a declared rational threshold $τ_{j} > 0$ .

For the proved zero tasks one can use $I_{j} = [0, 0]$ .

Define the status

status (I, τ) = ⎩ ⎨ ⎧ PASS, FAIL, UNDETERMINED, I \subset [- τ, τ], I \cap [- τ, τ] = \emptyset, otherwise .

Displayed formulas in this passage

unlabeled · line 1420
$I_{j} = [L_{j}, U_{j}], L_{j} \leq a_{j} \leq U_{j};$
unlabeled · line 1429
$status (I, τ) = ⎩ ⎨ ⎧ PASS, FAIL, UNDETERMINED, I \subset [- τ, τ], I \cap [- τ, τ] = \emptyset, otherwise .$