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Initial state is set by the value and/or the D(efault) appearance.
Details on how to render annotations and their appearances are in ISO 32000-1:2008.
Figured it out... need to set the initial visibility based on the Annotation flags, bit position 2 ("Hidden"), defined in ISO 32000-1:2008 Table 165 (page 385). The field definition and widget annotation definition are merged into a single dictionary... that was what threw me off:
Table 165 – Annotation flagsBit position
If set, do not display or print the annotation or allow it to interact with the user, regardless of its annotation type or whether an annotation handler is available.
NOTE 1 In cases where screen space is limited, the ability to hide and show annotations selectively can be used in combination with appearance streams (see 12.5.5, "Appearance Streams") to display auxiliary pop-up information similar in function to online help systems.