When you have cognitive dissonances with the Phillips curve it is NOT your fault but rather a sure sign of mental health. The Phillips curve is misspecified since Samuelson/Solow. To make matters short the elementary version of the correct structural Phillips curve is shown on Wikimedia.#1 The structural Phillips curve consists alone of measurable variables and is therefore identical with what you call the observed Phillips curve.
For the derivation see Sections 5 to 7 of the working paper ‘Keynes’s Employment Function and the Gratuitous Phillips Curve Disaster’.#2
|Structural Phillips curve|
Related 'Rethinking the Phillips curve'