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(1) In filling out the ADS, do I simply enter that new application A is a continuation of application B, or do I need to enter the whole chain? A preliminary amendment to the specification of application A lists the whole chain.
(2) Follow up question, assuming I do need to enter the whole chain in the ADS: If I didn't enter the whole chain in the ADS, but did enter it in the specification via preliminary amendment, what steps do I need to take to correct the omission in the ADS?
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The unstated key element to both questions is that you want to ensure that a proper claim of priority is made to all of the parent applications. 37 C.F.R. 1.78 specifies that to claim priority to a parent application, a child application must contain a reference to the parent application. 37 C.F.R.1.78(A)(2)(iii) indicates that the reference may be contained in an ADS
or in "the first sentence(s) following the title."
That said, you have a situation where information in the ADS is inconsistent with information in another document. Per MPEP 601.05: "Resolution of inconsistent information supplied by both an application data sheet and other documents (e.g., the oath or declaration under 37 CFR 1.63, or 37 CFR 1.67) are addressed in 37 CFR 1.76(d).
If an ADS is inconsistent with the information provided in another document that was submitted at the same time or previous to the ADS submission, the ADS will control. 37 CFR 1.76(d)(1) provides that the latest submitted information will govern notwithstanding whether supplied by an application data sheet, an amendment to the specification, a designation of a correspondence address, or by an oath or declaration under 37 CFR 1.63 or 37 CFR 1.67, except as provided by 37 CFR 1.76(d)(3). This is because the application data sheet is intended as the means by which applicants will provide most information to the Office.
In the small number of instances where another document has more accurate information than a concurrently supplied application data sheet (37 CFR 1.76(d)(2)), a supplemental application data sheet should be submitted to conform the information presented by the supplemental application data sheet with the correct information in the other document(s) (37 CFR 1.76(d)(1))."
To answer your questions directly:
(1) The whole chain should be entered in the ADS.
(2) I would submit a supplemental ADS (assuming the PA and ADS were submitted at the same time), so that the ADS conforms with the information in the PA. If the PA was submitted after the ADS, I would likely take no action, as the latest submitted information about the application will control. Though I might consider submitting a supplemental ADS just to make sure that the PTO does not get confused.