Legal Question in Real Estate Law in California

I'm not going to quote all of Corporations Code section 5034 (which can be looked up on line), but I think the explanation is incorrect but the conclusion is correct. Step One in applying 5034 is to determine that the meeting was "duly held," e.g. proper notice was given, etc. Step Two is to determine that at least 57 votes were present at the meeting. "Votes" might be different than "voters' because some voters might have multiple votes (because of owning multiple units, holding proxies, etc.). If both criteria (Step One and Step Two) are met, then the measure can be passed by a simple majority of the votes cast.

In your situation, if holders entitled to cast 57 votes were present and voted, a majority of 29 would prevail. If holders entitled to cast 56 votes were present and voted, and no more, the election would be invalid. If holders of 183 votes were present and voted, 92 votes in favor would be necessary for a measure to be approved. So, the comparison that must be made is the percentage of favorable votes cast in relation to total votes cast, not in relation to the quorum. Meeting the quorum is an additional requirement that allows the vote to be taken in the first place.

Note that the actual language of CC 5034 goes a bit further, and discusses the possibility of voting without actual attendance by written ballot, and the possibility that some HOA voting structures may call for voting by class, unit or grouping of members per their bylaws.

You have a problem if your HOA is governing itself using the Corporations Code, which is to regulate the governing bodies of corporations, instead of complying with any recorded covenants.

You need to clarify your statement that "The recall required 112 yes votes to pass and received 105." What is basis of your belief that 112 yes votes were needed. If in fact the measure needed 112 yes votes, and only received 105, it did NOT pass. By the way, the Corporations Code DOES govern these matters if your HOA is a corporation, which most are.