Bless you for asking for what lawyers call authority.
1. Passive income definition
Retirement income is not passive because the Internal Revenue Code (Title 26 of the US Code) section 469(c) defines a passive activity as:
any activity— (A)which involves the conduct of any trade or business, and (B)in which the taxpayer does not materially participate.
Later in 469(d) it defines passive losses to be the excess of aggregate losses from passive activities over the income from passive activities and disallows passive losses in 496(a) unless an exception applies.
https://www.law.cornell.edu/uscode/text/26/469
2. Earned income definition
The definition of "earned" vs. "unearned" income is hard to come by because it is defined in multiple places in code and that meaning is usually limited to that particular section. Context matters.
The most general definition I could quickly find is in in I.R.C. 911(d)(2) https://www.law.cornell.edu/uscode/text/26/911#d_2 ... not sure it is helpful to you. What is the exact question. E.g. if you want to know if it is a capital gain, then look to the definition of capital gain. A passive loss/gain, then look to the definition of passive loss.
The term “earned income” means wages, salaries, or professional fees, and other amounts received as compensation for personal services actually rendered, but does not include that part of the compensation derived by the taxpayer for personal services rendered by him to a corporation which represents a distribution of earnings or profits rather than a reasonable allowance as compensation for the personal services actually rendered. I.R.C. 911(d)(2).
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