Manuscript X-J-ST@1 · X-J-ST.tex · section · 8f0d1a36

General outcome-law discrepancy

Section B: selective amplitude visibility › General outcome-law discrepancy · lines 1159–1176

X-J-ST@1#eq:generalTV

Write $β_{y} = tr B_{y}$ and $γ_{y} = tr C_{y}$ . For every fixed instrument,

d_{TV} (P_{z}, P_{0}) = \frac{1}{2} y \sum ∣ β_{y} tanh (z / σ) + γ_{y} (sech (z / σ) - 1) ∣ .

An endpoint equality can occur by cancellation, even when the instrument is not constant on the whole family. Thus positivity will be proved for a named instrument, not inferred for every readout.

Displayed formulas in this passage

X-J-ST@1#eq:generalTV · line 1164
$d_{TV} (P_{z}, P_{0}) = \frac{1}{2} y \sum ∣ β_{y} tanh (z / σ) + γ_{y} (sech (z / σ) - 1) ∣ .$