In the U.S. House, successful discharge petitions are rare, as the signatures of an absolute majority of House members are required.[2]
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An early form of the discharge petition was introduced into U.S. House rules in 1910 as part of a series of measures intended to check the power of the disliked Speaker Joseph Gurney Cannon (R–Illinois). The modern version, however, was adopted in 1931 by the 71st House. In 1935, the rules were changed so the number of signatures required to force a vote went from one-third of the chamber (145 votes) to an absolute majority (218 votes).[3][4]
The House doesn’t have filibuster rules like the Senate; nothing in the House requires two-thirds.
Discharge petitions do.
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https://en.wikipedia.org/wiki/Discharge_petition
To quote your quotes:
An absolute majority is one half, not two-thirds.
Must have gotten wrong information then, my apologies.