Manuscript Oai069-A@1 · Oai069-A.tex · section · a4913aab

Two probes with complete coverage inside that class

Phase 3: an independent free-scalar consistency audit › Two probes with complete coverage inside that class · lines 1514–1535

If two matched probes have discrepancies $∣Δ p_{1} ∣ \leq e_{1}$ , $∣Δ p_{2} ∣ \leq e_{2}$ , then

∣Δ a ∣ \leq 2 e_{1}, ∣Δ b ∣ \leq \frac{2 e _{1} + e _{2}}{6} .

Consequently every further declared matrix-element test $F$ inside the class obeys

∣Δ T (F) ∣ \leq 2 e_{1} ∣ T^{can} (F) ∣ + \frac{2 e _{1} + e _{2}}{6} ∣ C (F) ∣.

A bound on those fixed matrix elements is still required for a numerical tolerance.

This reproduces the finite-class coverage discipline discussed in Oai282-B Cheung282B, without treating its supplied theorem as a proof premise.

Displayed formulas in this passage

unlabeled · line 1518
$∣Δ a ∣ \leq 2 e_{1}, ∣Δ b ∣ \leq \frac{2 e _{1} + e _{2}}{6} .$
unlabeled · line 1524
$∣Δ T (F) ∣ \leq 2 e_{1} ∣ T^{can} (F) ∣ + \frac{2 e _{1} + e _{2}}{6} ∣ C (F) ∣.$